#help-49 | Mathematics | Page 143

cosmic cobalt Jan 20, 2025, 3:23 PM

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i am so confused :<

silver bluff Jan 20, 2025, 3:23 PM

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wait

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i can say i am applying a force of 4N

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this makes no sense cuz i did not say along what direction

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this force can be along x or y or z or any other direction

cosmic cobalt Jan 20, 2025, 3:24 PM

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ok now am more confused

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😭

silver bluff Jan 20, 2025, 3:24 PM

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do you know the difference between a scalar and a vector?

cosmic cobalt Jan 20, 2025, 3:25 PM

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yes

silver bluff Jan 20, 2025, 3:25 PM

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CgWaVWtRMiHUFb222CE3n9gBG8S2PKW7oAFket2eAo4mQL-7hng4XQeKc3uKh0axFUdBca0Utdu4bMB0aQiXWrwcB1sLcDz97N_QPutQbhH558CPH5B9QHKto_GY8O6KCbY18GXiZJ5tmZoGuw.png

cosmic cobalt Jan 20, 2025, 3:25 PM

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vector has a direction

silver bluff Jan 20, 2025, 3:25 PM

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exactly

cosmic cobalt Jan 20, 2025, 3:25 PM

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am asking why i did a vector addition

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like when should i think of this

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and what is Fa?

silver bluff Jan 20, 2025, 3:26 PM

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youre dealing with forces and acceleration
both of them a vectors
so to add or subtract them you need to use vector addition because they may have different directions

cosmic cobalt Jan 20, 2025, 3:27 PM

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right now ar we doing Fy net or Fx net = ma?

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cuz am confused

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and i dont know what is Fa

silver bluff Jan 20, 2025, 3:27 PM

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cosmic cobalt and what is Fa?

the vehicle is accelerating towards the right
so the rope applies force towards the right on the ball

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this horizontal force is Fa

cosmic cobalt Jan 20, 2025, 3:27 PM

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oh i never thought of this

silver bluff Jan 20, 2025, 3:28 PM

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cosmic cobalt right now ar we doing Fy net or Fx net = ma?

do you know what a free body diagram is?

cosmic cobalt Jan 20, 2025, 3:28 PM

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yes

silver bluff Jan 20, 2025, 3:29 PM

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okay

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so make one for the ball

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the force by the rope will be along the rope
the weight (mg) would be vertically downwards

cosmic cobalt Jan 20, 2025, 3:30 PM

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ok so F tension - Fg

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thats what i did

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40

silver bluff Jan 20, 2025, 3:30 PM

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wait

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what we need to figure is

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what net force is acting along x

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towards right

cosmic cobalt Jan 20, 2025, 3:33 PM

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so we are finding fx net?

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not fy net?

silver bluff Jan 20, 2025, 3:33 PM

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since the rope is at a constant angle from the floor
the vertical component of the force due to the rope will be equal to mg

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this is to cancel the net force along y

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otherwise the ball would start moving up/downwards

cosmic cobalt Jan 20, 2025, 3:35 PM

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cosmic cobalt so we are finding fx net?

is this correct

last slate Jan 20, 2025, 3:45 PM

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I'm pre university math and I'm getting spammed with hard Maths or some physics

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I can't even help it

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Sed

silver bluff Jan 20, 2025, 3:45 PM

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cosmic cobalt is this correct

yes

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see the gravitational force = 40

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it is equal to the vertical component of the force by the rope

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and the horizontal component of the force by the rope is equal to the net horizontal force on the ball

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do you see a right angled triangle forming with its hypotenuse as 50 and one side as 40?

midnight plankBOT Jan 20, 2025, 3:52 PM

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@cosmic cobalt Has your question been resolved?

midnight plankBOT Jan 20, 2025, 4:07 PM

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lofty cairn Jan 20, 2025, 4:26 PM

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In the context of integration how does one do this?

midnight plankBOT Jan 20, 2025, 4:26 PM

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lofty cairn In the context of integration how does one do this?

lofty cairn Jan 20, 2025, 4:29 PM

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Because integration of velocity function yields displacement, how does one obtain distance?

silver bluff Jan 20, 2025, 4:30 PM

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for distance you would need the equation of the path followed by the body

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say the path function is y=f(x)

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then the distance on the path covered between 2 points can be given by

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*correct me if im wrong

midnight plankBOT Jan 20, 2025, 4:44 PM

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@lofty cairn Has your question been resolved?

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cerulean temple Jan 20, 2025, 5:02 PM

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what criterium should i use to determine absolute convergence of this series?

midnight plankBOT Jan 20, 2025, 5:02 PM

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cerulean temple what criterium should i use to determine absolute convergence of this series?

cerulean temple Jan 20, 2025, 5:02 PM

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n-th root of this yields 1 so i can not use that

west iron Jan 20, 2025, 5:12 PM

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what would the end behavior of $(\f{n-2}n)^n$ look like?

grand pondBOT Jan 20, 2025, 5:12 PM

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Dreyuk

cerulean temple Jan 20, 2025, 5:14 PM

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west iron what would the end behavior of $(\f{n-2}n)^n$ look like?

like 1/e^2?

west iron Jan 20, 2025, 5:15 PM

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yeah

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then how to turn that into what you have here (using exponent laws)

cerulean temple Jan 20, 2025, 5:16 PM

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west iron then how to turn that into what you have here (using exponent laws)

hm i dont think i follow

west iron Jan 20, 2025, 5:18 PM

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west iron what would the end behavior of $(\f{n-2}n)^n$ look like?

How to turn this into the thing you're summing

cerulean temple Jan 20, 2025, 5:22 PM

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$\sum_{n=1}^\infty\left(\frac{n-2}{n}\right)^{n^\frac{3}{2}}=\sum_{n=1}^\infty\left(\frac{n-2}{n}\right)^{n}\cdot\left(\frac{n-2}{n}\right)^{\sqrt{n}}$

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and the first series is divergent since its limit for n to infy is not zero and thus the sum of any series with divergent series is divergent?

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@west iron

west iron Jan 20, 2025, 5:24 PM

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no there's no exponent law like that

cerulean temple Jan 20, 2025, 5:24 PM

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ah yes im stupid ffs

grand pondBOT Jan 20, 2025, 5:26 PM

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Slowaq

cerulean temple Jan 20, 2025, 5:29 PM

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once again im stuck

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what should i do?

cerulean temple Jan 20, 2025, 5:31 PM

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west iron what would the end behavior of $(\f{n-2}n)^n$ look like?

limit comparison with this yields 0 so it doesnt tell me anything

west iron Jan 20, 2025, 5:31 PM

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Still no

cerulean temple Jan 20, 2025, 5:32 PM

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wdym

west iron Jan 20, 2025, 5:32 PM

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That would be $\left(\frac{n-2}n\right)^{n+\sqrt n}$

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what you have on the right there

grand pondBOT Jan 20, 2025, 5:32 PM

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Dreyuk

cerulean temple Jan 20, 2025, 5:34 PM

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but isnt $\left(\frac{n-2}n\right)^{n^\frac{3}{2}}=\left(\frac{n-2}n\right)^{\sqrt{n}n}=\left(\left(\frac{n-2}n\right)^{n}\right)^{\sqrt{n}}

grand pondBOT Jan 20, 2025, 5:35 PM

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Slowaq

west iron Jan 20, 2025, 5:38 PM

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No

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Both the first and third equalities are wrong here

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n^(3/2) is not the same thing as 3/2 * n

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and 1/2 * n is not the same thing as sqrt(n)

cerulean temple Jan 20, 2025, 5:45 PM

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$\left(\frac{n-2}n\right)^{n^\frac{3}{2}}=\left(\frac{n-2}n\right)^{\sqrt{n}n}=\left(\left(\frac{n-2}n\right)^{n}\right)^{\sqrt{n}}$

grand pondBOT Jan 20, 2025, 5:46 PM

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Slowaq

west iron Jan 20, 2025, 5:46 PM

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Yes!

cerulean temple Jan 20, 2025, 5:47 PM

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finally xd kms

west iron Jan 20, 2025, 5:47 PM

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Formally we can't just replace ((n-2)/n)^n with 1/e^2 just because it tends there

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But if we go out far enough in the sum, we know, say, that ((n-2)/n)^n < 1/2

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And so if we can show the sum of (1/2)^√n converges we should be good

cerulean temple Jan 20, 2025, 5:51 PM

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yes that should converge since its geometric series

hard umbra Jan 20, 2025, 5:52 PM

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its not

cerulean temple Jan 20, 2025, 5:54 PM

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,w sum_{n =1}^inf (1/2)^sqrt(n)

grand pondBOT Jan 20, 2025, 5:54 PM

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cerulean temple Jan 20, 2025, 5:54 PM

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what am i not comprehending?

hard umbra Jan 20, 2025, 5:54 PM

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its not a geometric series

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obviously it converges but you need to justify why

cerulean temple Jan 20, 2025, 6:00 PM

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well its non zero non increasing sequence so this should do it

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,w int_1^\infty 1/2^sqrt(n) dn

grand pondBOT Jan 20, 2025, 6:00 PM

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cerulean temple Jan 20, 2025, 6:01 PM

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but something is wrogn because it should diverge acording to my teacher

hard umbra Jan 20, 2025, 6:02 PM

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cerulean temple ,w int_1^\infty 1/2^sqrt(n) dn

i mean do you know how to evaluate that integral?

hard umbra Jan 20, 2025, 6:04 PM

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cerulean temple but something is wrogn because it should diverge acording to my teacher

the series you posted originally does converge

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so either your teacher is wrong, you're reading the wrong solutions, or there's a transcription error

midnight plankBOT Jan 20, 2025, 6:16 PM

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@cerulean temple Has your question been resolved?

cerulean temple Jan 20, 2025, 6:33 PM

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hard umbra i mean do you know how to evaluate that integral?

yes i can do it but thanks for making sure i can

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hm so then he must ahve made a mistake because he says that this limit does not converge absolutely

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,w sum_{n=1}^inf |((n-2)/n)^(n^(2/3))|

grand pondBOT Jan 20, 2025, 6:39 PM

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cerulean temple Jan 20, 2025, 6:40 PM

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,w lim n to inf |((n-2)/n)^(n^(2/3))|/|((n-2)/n)^n|

grand pondBOT Jan 20, 2025, 6:40 PM

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west iron Jan 20, 2025, 6:51 PM

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cerulean temple ,w sum_{n=1}^inf |((n-2)/n)^(n^(2/3))|

Well yes if you replace the 3/2 with 2/3 then it diverges

cerulean temple Jan 20, 2025, 6:53 PM

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,w sum_{n=1}^inf |((n-2)/n)^(n^(3/2))|

grand pondBOT Jan 20, 2025, 6:53 PM

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cerulean temple Jan 20, 2025, 6:54 PM

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west iron Well yes if you replace the 3/2 with 2/3 then it diverges

ah yes sorry my bad then the teacher got it wrong

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there is simmilar problem right after the original

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and if i employ the same steps as in the previous

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ill have to stow that $\sum_{n=1}^\infty \left(\frac{1}{2}\right)^{n^{\frac{2}{3}}}$

grand pondBOT Jan 20, 2025, 7:11 PM

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Slowaq

cerulean temple Jan 20, 2025, 7:11 PM

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but im struggling to do that

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nvm i got it

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thanks for help

midnight plankBOT Jan 20, 2025, 7:52 PM

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@cerulean temple Has your question been resolved?

heady plume Jan 20, 2025, 8:15 PM

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T_T

cerulean temple Jan 20, 2025, 8:30 PM

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.close

midnight plankBOT Jan 20, 2025, 8:31 PM

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Channel closed

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midnight plankBOT Jan 20, 2025, 9:31 PM

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gleaming skiff Jan 20, 2025, 9:49 PM

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Am I stupid or is a and b the same

midnight plankBOT Jan 20, 2025, 9:49 PM

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gleaming skiff Am I stupid or is a and b the same

small jasper Jan 20, 2025, 9:49 PM

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gleaming skiff Am I stupid or is a and b the same

They are

lavish venture Jan 20, 2025, 9:49 PM

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this is a property of dot products

small jasper Jan 20, 2025, 9:49 PM

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(aka dot products are commutative)

lavish venture Jan 20, 2025, 9:49 PM

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you can prove this quite easily using the axioms for real numbers

gleaming skiff Jan 20, 2025, 9:50 PM

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Ok lmao I'm still struggling a little with dot products so I want sure

grim vector Jan 20, 2025, 9:50 PM

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ab = ba so all good

gleaming skiff Jan 20, 2025, 9:50 PM

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TYSM everyone!

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. Close

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.Close

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...

grim vector Jan 20, 2025, 9:50 PM

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close

small jasper Jan 20, 2025, 9:50 PM

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.close

midnight plankBOT Jan 20, 2025, 9:50 PM

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Channel closed

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dark locust Jan 20, 2025, 10:57 PM

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do u guys have any limit word problem bc our teacher wants us to construct our own after researching. ive researched now but then i found out we have to still construct ad add like formulas from chem, etc.... business math.. etc

midnight plankBOT Jan 20, 2025, 10:57 PM

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dark locust do u guys have any limit word problem bc our teacher wants us to construct our o...

dark locust Jan 20, 2025, 10:57 PM

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😭

surreal moon Jan 20, 2025, 11:01 PM

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dark locust do u guys have any limit word problem bc our teacher wants us to construct our o...

Well known problems
https://en.m.wikipedia.org/wiki/Zeno's_paradoxes

Zeno's paradoxes

Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia. Zeno devised these paradoxes to support his teacher Parmenides's philosophy of monism, which posits that despit...

dark locust Jan 20, 2025, 11:02 PM

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surreal moon Well known problems https://en.m.wikipedia.org/wiki/Zeno%27s_paradoxes

thank you, ill try researching abt thiss

midnight plankBOT Jan 20, 2025, 11:17 PM

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@dark locust Has your question been resolved?

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mint ravine Jan 20, 2025, 11:37 PM

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i need help on this physics question

midnight plankBOT Jan 20, 2025, 11:37 PM

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mint ravine i need help on this physics question

mint ravine Jan 20, 2025, 11:39 PM

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nvm

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.close

midnight plankBOT Jan 20, 2025, 11:39 PM

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midnight plankBOT Jan 20, 2025, 11:54 PM

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last slate Jan 21, 2025, 12:12 AM

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how can i use anumber line to show "x^2<—3x—2"

midnight plankBOT Jan 21, 2025, 12:12 AM

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last slate how can i use anumber line to show "x^2<—3x—2"

last slate Jan 21, 2025, 12:13 AM

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idk what that means

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ts is the simplest thing ever but idek how to do it

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\

olive matrix Jan 21, 2025, 12:17 AM

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i think they want you to graph each side?

last slate Jan 21, 2025, 12:18 AM

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huh?

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im lwk gonna fail this final

olive matrix Jan 21, 2025, 12:18 AM

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i'm not sure what it wants tbh

last slate Jan 21, 2025, 12:18 AM

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ok

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well thats alr

visual tiger Jan 21, 2025, 12:18 AM

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no idea either

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I would just factor

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after bringing everything to one side

last slate Jan 21, 2025, 12:19 AM

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i did that in class and the teacher yelled at me💀

visual tiger Jan 21, 2025, 12:19 AM

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???

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and how did the teacher do it then?

last slate Jan 21, 2025, 12:19 AM

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funny stuff

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idk

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he said some math stuff that i dont understad thats why im here lol

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but thats ok

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thanks for your help

visual tiger Jan 21, 2025, 12:19 AM

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did he "draw a number line"?

last slate Jan 21, 2025, 12:19 AM

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he didnt show me or nothing

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he js said "do this and that"

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and boom

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magic

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idrk

visual tiger Jan 21, 2025, 12:20 AM

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and what's the this and that in question?

last slate Jan 21, 2025, 12:20 AM

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im not sure

visual tiger Jan 21, 2025, 12:20 AM

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sounds very unhinged to do as a teacher

last slate Jan 21, 2025, 12:20 AM

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yeahj

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but thats alr hes a good teacher anyways

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im outta here i gotta finish studying

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.close

midnight plankBOT Jan 21, 2025, 12:20 AM

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Channel closed

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last slate Jan 21, 2025, 12:28 AM

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.reopen

midnight plankBOT Jan 21, 2025, 12:28 AM

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✅

last slate Jan 21, 2025, 12:29 AM

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was not amistakebut i have another questioon

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if i have 10x^2-5x

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does that js factor to x(x-something)?

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these other questions from people make ts look easy now

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cool

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.close

midnight plankBOT Jan 21, 2025, 12:35 AM

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Channel closed

Closed by @surreal surge

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last slate Jan 21, 2025, 12:42 AM

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why is it not going back to unclaimed

midnight plankBOT Jan 21, 2025, 12:50 AM

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Available help channel!

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sterile wharf Jan 21, 2025, 12:54 AM

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hello can somebody help me please with the pythagorean theorem basics im a 9th grader and i dont understand it much 😓

midnight plankBOT Jan 21, 2025, 12:54 AM

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sterile wharf hello can somebody help me please with the pythagorean theorem basics im a 9th g...

short ginkgo Jan 21, 2025, 12:55 AM

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like r u tryna figur out the hypotenuse?

sterile wharf Jan 21, 2025, 12:55 AM

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i rlly dont know HAHAHAHHAHAH

short ginkgo Jan 21, 2025, 12:55 AM

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💀

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ok

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so

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dyk what a b and c are

sterile wharf Jan 21, 2025, 12:56 AM

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the legs?

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idk dude 😭😭

short ginkgo Jan 21, 2025, 12:57 AM

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ignoer the bttm pt of this img

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oh shoot this img sucks 1 sec

sterile wharf Jan 21, 2025, 12:57 AM

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okok

short ginkgo Jan 21, 2025, 12:57 AM

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so here is a right triangle

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dyk how to find the area

sterile wharf Jan 21, 2025, 12:58 AM

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no i dont

short ginkgo Jan 21, 2025, 12:58 AM

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ok dw

sterile wharf Jan 21, 2025, 12:59 AM

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this is what i know

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goes like this

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short ginkgo Jan 21, 2025, 1:00 AM

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wait what was the og question

sterile wharf Jan 21, 2025, 1:00 AM

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idk my friend sent it to me

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i tried asking her but she dunno either

short ginkgo Jan 21, 2025, 1:01 AM

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ngl i dont rlly get whats happinging in this question

sterile wharf Jan 21, 2025, 1:02 AM

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oh

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so its like

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12² becomes 144 and 20² becomes 400

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it was copied down

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then 144 plus 400 is 256

short ginkgo Jan 21, 2025, 1:03 AM

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o and ur tryna figure out b?

sterile wharf Jan 21, 2025, 1:03 AM

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then it became 16 how it became 16

sterile wharf Jan 21, 2025, 1:03 AM

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short ginkgo o and ur tryna figure out b?

trynna figure out a

short ginkgo Jan 21, 2025, 1:03 AM

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ok

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so the pythagoream theorem is just an equation

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the height of the triangle squared x the base squared = the hypotenuse (the longest pt) squared

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so the btm pt of this

sterile wharf Jan 21, 2025, 1:05 AM

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b is the hypotenuse?

short ginkgo Jan 21, 2025, 1:05 AM

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im guessing c=20 and b=12?

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c is the hypotenuse

sterile wharf Jan 21, 2025, 1:05 AM

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ow 😭

short ginkgo Jan 21, 2025, 1:05 AM

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it fine

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dyk the right angle

sterile wharf Jan 21, 2025, 1:06 AM

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the square inside the triangle?

short ginkgo Jan 21, 2025, 1:06 AM

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yes

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dyk where it is

sterile wharf Jan 21, 2025, 1:06 AM

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the middle of a and b?

short ginkgo Jan 21, 2025, 1:06 AM

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correct

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so since it isn't touching c

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c is the hypotenuse

sterile wharf Jan 21, 2025, 1:07 AM

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i see

short ginkgo Jan 21, 2025, 1:07 AM

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if you think abt it a triangle is just a square cut diagonally

sterile wharf Jan 21, 2025, 1:07 AM

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fr

short ginkgo Jan 21, 2025, 1:07 AM

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so thats all c is trying to find fr

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i mean the pythagorem theorem sry

short ginkgo Jan 21, 2025, 1:08 AM

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short ginkgo im guessing c=20 and b=12?

ok wait so is this tru?

sterile wharf Jan 21, 2025, 1:08 AM

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wdym true?

short ginkgo Jan 21, 2025, 1:09 AM

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is c=20 and b=12?

sterile wharf Jan 21, 2025, 1:09 AM

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dont we have to find the hypotenuse?

short ginkgo Jan 21, 2025, 1:09 AM

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well c is the hypotenuse

sterile wharf Jan 21, 2025, 1:09 AM

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soo a=20??

short ginkgo Jan 21, 2025, 1:09 AM

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not rlly lol

sterile wharf Jan 21, 2025, 1:10 AM

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dang 😔

short ginkgo Jan 21, 2025, 1:10 AM

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the pythagorem theorem finds the hypotenuse

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but you can work backwards

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since a^2+b^2=c^2

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is just an equation

sterile wharf Jan 21, 2025, 1:10 AM

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yeah the formula thing

short ginkgo Jan 21, 2025, 1:10 AM

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if u have c and b

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you only need to find a

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so you can plug in the values and solve

sterile wharf Jan 21, 2025, 1:11 AM

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i see

short ginkgo Jan 21, 2025, 1:11 AM

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fire

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so

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if yk c=20 and b=12

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all u need to find is a

sterile wharf Jan 21, 2025, 1:11 AM

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the written in the paper says 12² and 20²

short ginkgo Jan 21, 2025, 1:12 AM

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yes

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ok

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thats probably bc theyre alr using the pythagorem theorem

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but then got mixed up

sterile wharf Jan 21, 2025, 1:12 AM

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ow

short ginkgo Jan 21, 2025, 1:13 AM

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here

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lets just say c=20 and b=12

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can u plug this in and solve

sterile wharf Jan 21, 2025, 1:13 AM

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okok

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done

short ginkgo Jan 21, 2025, 1:14 AM

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🔥

sterile wharf Jan 21, 2025, 1:14 AM

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short ginkgo Jan 21, 2025, 1:14 AM

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ok now plug c and b in to a^2+b^2=c^2

sterile wharf Jan 21, 2025, 1:15 AM

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with the squared?

short ginkgo Jan 21, 2025, 1:15 AM

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yep

sterile wharf Jan 21, 2025, 1:15 AM

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short ginkgo Jan 21, 2025, 1:15 AM

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nice

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can u simplify this?

sterile wharf Jan 21, 2025, 1:16 AM

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how

short ginkgo Jan 21, 2025, 1:16 AM

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ok first

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dyk what 12^2 is

sterile wharf Jan 21, 2025, 1:16 AM

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yea its 12 x 12

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144

short ginkgo Jan 21, 2025, 1:16 AM

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good

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and do that for 20^2 as well

sterile wharf Jan 21, 2025, 1:17 AM

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okayy

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what do i do with a²?

short ginkgo Jan 21, 2025, 1:17 AM

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good question

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can u write out what u have rn

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now that you simplified it a bit

sterile wharf Jan 21, 2025, 1:18 AM

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short ginkgo Jan 21, 2025, 1:18 AM

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okok

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nice

sterile wharf Jan 21, 2025, 1:18 AM

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very epic

short ginkgo Jan 21, 2025, 1:19 AM

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dyk how to make it so that a^2 is the only thing on the left side of the equation

sterile wharf Jan 21, 2025, 1:19 AM

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idk

short ginkgo Jan 21, 2025, 1:19 AM

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um

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ok

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so

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you can move 144 to the other side of an equation

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by subtracting 144 on both sides

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this equals it out

sterile wharf Jan 21, 2025, 1:20 AM

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sooo

short ginkgo Jan 21, 2025, 1:20 AM

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bc its an equation

sterile wharf Jan 21, 2025, 1:21 AM

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144 subtract a² and 400?

short ginkgo Jan 21, 2025, 1:21 AM

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almost

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look at the equal sign

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to the left of it is the left side of the equation

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and to the right of it is the right side

sterile wharf Jan 21, 2025, 1:22 AM

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ook

short ginkgo Jan 21, 2025, 1:22 AM

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so a^2+144-144=400-144

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can u simplify that for me

sterile wharf Jan 21, 2025, 1:23 AM

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is it a = 256?

short ginkgo Jan 21, 2025, 1:23 AM

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almost again

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a^2=256

sterile wharf Jan 21, 2025, 1:24 AM

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o i forgot the ²

short ginkgo Jan 21, 2025, 1:24 AM

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yes

sterile wharf Jan 21, 2025, 1:24 AM

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HAHAHAHHAH

short ginkgo Jan 21, 2025, 1:24 AM

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what is the opposite of that

sterile wharf Jan 21, 2025, 1:24 AM

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wdym

short ginkgo Jan 21, 2025, 1:24 AM

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what is the opposite of the square of smthng

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like the opposite of addition is subtraction

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and the opposite of multiplication is division

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ok i have to go but basically the opposite of the square is the square root

sterile wharf Jan 21, 2025, 1:25 AM

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oh dang

short ginkgo Jan 21, 2025, 1:26 AM

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so to make a^2 you square root it

sterile wharf Jan 21, 2025, 1:26 AM

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i see

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so a?

short ginkgo Jan 21, 2025, 1:26 AM

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but do it onn both sides and you have your answer

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so 256 but its square rt

sterile wharf Jan 21, 2025, 1:26 AM

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alr alr thank you so much tyler

short ginkgo Jan 21, 2025, 1:26 AM

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yw bye bye

sterile wharf Jan 21, 2025, 1:26 AM

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ill try it

midnight plankBOT Jan 21, 2025, 1:41 AM

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@sterile wharf Has your question been resolved?

sterile wharf Jan 21, 2025, 1:42 AM

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yessir

midnight plankBOT Jan 21, 2025, 1:43 AM

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sterile wharf yessir

If you are done with this channel, please mark your problem as solved by typing .close

#

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midnight plankBOT Jan 21, 2025, 2:18 AM

#

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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gleaming skiff Jan 21, 2025, 3:05 AM

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I am not rly sure what to do here but I do have some equations that may be important

midnight plankBOT Jan 21, 2025, 3:05 AM

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gleaming skiff I am not rly sure what to do here but I do have some equations that may be impor...

gleaming skiff Jan 21, 2025, 3:06 AM

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so then this?

rose trout Jan 21, 2025, 3:11 AM

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From the equations you have you should see that

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$\frac{u\cdot v}{|u|} = comp_u(v)$

grand pondBOT Jan 21, 2025, 3:12 AM

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Azyrashacorki

gleaming skiff Jan 21, 2025, 3:12 AM

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oh

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ty let me try that

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i got it, ty

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.close

midnight plankBOT Jan 21, 2025, 3:16 AM

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midnight plankBOT Jan 21, 2025, 3:31 AM

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oblique prawn Jan 21, 2025, 3:42 AM

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midnight plankBOT Jan 21, 2025, 3:42 AM

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oblique prawn

oblique prawn Jan 21, 2025, 3:43 AM

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grand pondBOT Jan 21, 2025, 3:43 AM

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oblique prawn Jan 21, 2025, 3:43 AM

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I’m not sure where I went wrong here

dawn dagger Jan 21, 2025, 3:48 AM

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oblique prawn I’m not sure where I went wrong here

Did you choose v' = e^(-x²)?

oblique prawn Jan 21, 2025, 3:48 AM

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yes

dawn dagger Jan 21, 2025, 3:48 AM

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And how are you doing v?

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e^(-x²) has no antiderivative in terms of elementary functions

oblique prawn Jan 21, 2025, 3:50 AM

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oh

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i did not know that

heady plume Jan 21, 2025, 3:51 AM

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Yes. $\int e^{-x^2} \dd x \neq -e^{-x^2}$

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to realize that, you can differentiate the right side and you'll see

grand pondBOT Jan 21, 2025, 3:51 AM

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Arya

dawn dagger Jan 21, 2025, 3:52 AM

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oblique prawn i did not know that

So based on that you kinda know that you have to choose v = e^(-x²) instead to say the least

midnight plankBOT Jan 21, 2025, 4:05 AM

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@oblique prawn Has your question been resolved?

kindred dagger Jan 21, 2025, 4:10 AM

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Is $e^{-x^2}$ even integrable by hand?

grand pondBOT Jan 21, 2025, 4:10 AM

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King Leo

heady plume Jan 21, 2025, 4:13 AM

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it ain't

dawn dagger Jan 21, 2025, 4:18 AM

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kindred dagger Is $e^{-x^2}$ even integrable by hand?

Consider the taylor expansion sotrue

midnight plankBOT Jan 21, 2025, 4:20 AM

#

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#

Available help channel!

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

upbeat plinth Jan 21, 2025, 5:02 AM

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midnight plankBOT Jan 21, 2025, 5:02 AM

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upbeat plinth One message removed from a suspended account.

upbeat plinth Jan 21, 2025, 5:02 AM

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sharp coral Jan 21, 2025, 5:02 AM

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it says to use euler's method

upbeat plinth Jan 21, 2025, 5:02 AM

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sharp coral Jan 21, 2025, 5:03 AM

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no

upbeat plinth Jan 21, 2025, 5:03 AM

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sharp coral Jan 21, 2025, 5:03 AM

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do you know the steps to euler's method?

upbeat plinth Jan 21, 2025, 5:03 AM

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sharp coral Jan 21, 2025, 5:04 AM

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yes

upbeat plinth Jan 21, 2025, 5:04 AM

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sharp coral Jan 21, 2025, 5:04 AM

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if it doesn't depend on x (actually t) then you just don't plug in x

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it's still "plugged in" even if there isn't any instance of that variable

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e.g. if you have f(x) = 3, then f(5) = 3, that's considered "plugged in" even if there was no x to replace

upbeat plinth Jan 21, 2025, 5:08 AM

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upbeat plinth Jan 21, 2025, 5:10 AM

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sharp coral if it doesn't depend on x (actually t) then you just don't plug in x

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grand pondBOT Jan 21, 2025, 5:10 AM

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upbeat plinth Jan 21, 2025, 5:10 AM

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fading ore Jan 21, 2025, 5:14 AM

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grand pond

what do you get when directly plugging 0 into the rational expression?

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@upbeat plinth

upbeat plinth Jan 21, 2025, 5:14 AM

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lavish venture Jan 21, 2025, 5:15 AM

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lhopitals

upbeat plinth Jan 21, 2025, 5:15 AM

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lavish venture lhopitals

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upbeat plinth Jan 21, 2025, 5:16 AM

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fading ore what do you get when directly plugging 0 into the rational expression?

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lavish venture Jan 21, 2025, 5:16 AM

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0/0

upbeat plinth Jan 21, 2025, 5:16 AM

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lavish venture 0/0

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fading ore Jan 21, 2025, 5:16 AM

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upbeat plinth One message removed from a suspended account.

hmm

upbeat plinth Jan 21, 2025, 5:16 AM

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lavish venture Jan 21, 2025, 5:16 AM

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upbeat plinth One message removed from a suspended account.

condition for lhopitals rule has been met

fading ore Jan 21, 2025, 5:16 AM

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^

upbeat plinth Jan 21, 2025, 5:16 AM

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fading ore Jan 21, 2025, 5:16 AM

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where do we get 0/0?

lavish venture Jan 21, 2025, 5:16 AM

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because upon substitution you had 0/0

fading ore Jan 21, 2025, 5:16 AM

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$\lim_{x \to 0} \frac{f(x) + 1}{\sin{x}} = \frac{f(0) + 1}{\sin{0}} = \frac00$

grand pondBOT Jan 21, 2025, 5:16 AM

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hiidostuff

fading ore Jan 21, 2025, 5:17 AM

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technically not properly written

upbeat plinth Jan 21, 2025, 5:17 AM

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fading ore Jan 21, 2025, 5:17 AM

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but i mean i hope this is clearer

upbeat plinth Jan 21, 2025, 5:17 AM

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fading ore Jan 21, 2025, 5:17 AM

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so from this we can then differentiate the top and bottom

fading ore Jan 21, 2025, 5:17 AM

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upbeat plinth One message removed from a suspended account.

thats ok

upbeat plinth Jan 21, 2025, 5:18 AM

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grand pondBOT Jan 21, 2025, 5:18 AM

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Kenzo

lavish venture Jan 21, 2025, 5:18 AM

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🙂‍↔️

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waht

upbeat plinth Jan 21, 2025, 5:19 AM

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lavish venture Jan 21, 2025, 5:19 AM

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grand pond **Kenzo**

what is this?

upbeat plinth Jan 21, 2025, 5:19 AM

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lavish venture Jan 21, 2025, 5:20 AM

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where did the limit go? what is the derivative of sin(x)? where are your parentheses for f’?

upbeat plinth Jan 21, 2025, 5:20 AM

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lavish venture Jan 21, 2025, 5:20 AM

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what

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\lim_

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\lim_{x \to 0}

upbeat plinth Jan 21, 2025, 5:20 AM

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lavish venture Jan 21, 2025, 5:21 AM

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you didn’t listen

upbeat plinth Jan 21, 2025, 5:21 AM

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lavish venture Jan 21, 2025, 5:21 AM

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also

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use \

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for cos

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\cos x

grand pondBOT Jan 21, 2025, 5:21 AM

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Kenzo

upbeat plinth Jan 21, 2025, 5:21 AM

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lavish venture Jan 21, 2025, 5:21 AM

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now substitute

upbeat plinth Jan 21, 2025, 5:21 AM

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lavish venture Jan 21, 2025, 5:22 AM

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where are you getting -1

upbeat plinth Jan 21, 2025, 5:22 AM

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lavish venture Jan 21, 2025, 5:22 AM

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it’s f’(0) not f(0)

upbeat plinth Jan 21, 2025, 5:23 AM

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lavish venture Jan 21, 2025, 5:23 AM

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you’re given the derivative

lavish venture Jan 21, 2025, 5:23 AM

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upbeat plinth One message removed from a suspended account.

no

upbeat plinth Jan 21, 2025, 5:23 AM

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lavish venture Jan 21, 2025, 5:23 AM

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that is the derivative

upbeat plinth Jan 21, 2025, 5:23 AM

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lavish venture Jan 21, 2025, 5:23 AM

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let x = 0

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what is y?

upbeat plinth Jan 21, 2025, 5:24 AM

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lavish venture Jan 21, 2025, 5:24 AM

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sure but what’s y

upbeat plinth Jan 21, 2025, 5:24 AM

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lavish venture Jan 21, 2025, 5:24 AM

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you do

upbeat plinth Jan 21, 2025, 5:24 AM

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lavish venture Jan 21, 2025, 5:24 AM

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(x,y)

upbeat plinth Jan 21, 2025, 5:24 AM

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lavish venture Jan 21, 2025, 5:25 AM

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(-1)^2 =-1?

upbeat plinth Jan 21, 2025, 5:25 AM

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lavish venture Jan 21, 2025, 5:25 AM

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upbeat plinth Jan 21, 2025, 5:25 AM

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lavish venture Jan 21, 2025, 5:26 AM

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what is this chart

upbeat plinth Jan 21, 2025, 5:26 AM

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lavish venture Jan 21, 2025, 5:28 AM

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yea i mean i just don’t think that’s a good way to teach it

upbeat plinth Jan 21, 2025, 5:28 AM

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lavish venture Jan 21, 2025, 5:29 AM

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you have h = 0.5

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y(0) = 8

upbeat plinth Jan 21, 2025, 5:29 AM

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lavish venture Jan 21, 2025, 5:29 AM

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y’ = y/8(6-y)

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so you don’t need me to check that?

upbeat plinth Jan 21, 2025, 5:30 AM

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lavish venture Jan 21, 2025, 5:30 AM

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so y(0.5) = 8 + 0.5(-2) = 7

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y(1) = 7 + 0.5(-7/8) = 7 - 7/16 = 105/16

upbeat plinth Jan 21, 2025, 5:31 AM

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lavish venture Jan 21, 2025, 5:31 AM

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i think this algorithmic way is way better

upbeat plinth Jan 21, 2025, 5:32 AM

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grand pondBOT Jan 21, 2025, 5:33 AM

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fading ore Jan 21, 2025, 5:33 AM

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lavish venture

every time i see this image as a youtube thumbnail, the video title is always some super deep philosophical topic

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is that what the video is actually about

lavish venture Jan 21, 2025, 5:33 AM

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$y_n = y_{n-1} + h\frac{dy}{dx}\biggr\rvert_{(x_{n-1},y_{n-1})}$

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oof

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bad latex

grand pondBOT Jan 21, 2025, 5:34 AM

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knief

lavish venture Jan 21, 2025, 5:34 AM

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fading ore is that what the video is actually about

nah it’s probably like discussing who is the goat of basketball or some shit

upbeat plinth Jan 21, 2025, 5:34 AM

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lavish venture Jan 21, 2025, 5:34 AM

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lebron vs jordan debate

upbeat plinth Jan 21, 2025, 5:34 AM

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fading ore Jan 21, 2025, 5:34 AM

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lavish venture nah it’s probably like discussing who is the goat of basketball or some shit

what a silly conversation (MJ hands down)

lavish venture Jan 21, 2025, 5:35 AM

#

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lol i remember this meme from 8th grade

fading ore Jan 21, 2025, 5:35 AM

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lavish venture

lmao

lavish venture Jan 21, 2025, 5:35 AM

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RAT

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💀💀

upbeat plinth Jan 21, 2025, 5:35 AM

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lavish venture Jan 21, 2025, 5:35 AM

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upbeat plinth One message removed from a suspended account.

whattt

lavish venture Jan 21, 2025, 5:36 AM

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grand pond **knief**

this is eulers method

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the bar means evaluated at

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think of it was f’(x) for some x_n-1

upbeat plinth Jan 21, 2025, 5:36 AM

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lavish venture Jan 21, 2025, 5:36 AM

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but since dy/dx also might have y in it

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i don’t just write f’(x)

upbeat plinth Jan 21, 2025, 5:36 AM

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lavish venture Jan 21, 2025, 5:37 AM

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upbeat plinth One message removed from a suspended account.

well you have to solve the DE

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it’s separable

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as are all DEs in BC

upbeat plinth Jan 21, 2025, 5:38 AM

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lavish venture Jan 21, 2025, 5:38 AM

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@fading ore

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https://youtu.be/NgsdTMMUK-I?si=FdlefQyOIfaTbHet

YouTube

Junior Studios

Is Fortnite Actually Overrated?

Is Fortnite Actually Overrated refers to the title of a YouTube video from the channel Junior Studios. In the video, three boys discuss the merits of the video game Fortnite and whether or not it is worthy of its popularity. A screenshot from the video later inspired an image macro series in which people edit the name of the video.
On January 6t...

▶ Play video

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lmao this was my second guess

fading ore Jan 21, 2025, 5:38 AM

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nice

upbeat plinth Jan 21, 2025, 5:39 AM

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lavish venture Jan 21, 2025, 5:39 AM

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thought it might’ve been older than that thoigh

fading ore Jan 21, 2025, 5:39 AM

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and the pokemon black and white music off the bat

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S tier video already

upbeat plinth Jan 21, 2025, 5:39 AM

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lavish venture Jan 21, 2025, 5:39 AM

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why is the dy there

grand pondBOT Jan 21, 2025, 5:39 AM

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Kenzo

fading ore Jan 21, 2025, 5:39 AM

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upbeat plinth One message removed from a suspended account.

the differentials are not written properly

lavish venture Jan 21, 2025, 5:39 AM

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bruh

fading ore Jan 21, 2025, 5:39 AM

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but also you dont need to particularly find the function

upbeat plinth Jan 21, 2025, 5:39 AM

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fading ore Jan 21, 2025, 5:40 AM

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oh nvm for part c you do

lavish venture Jan 21, 2025, 5:40 AM

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yea it says particular solution

fading ore Jan 21, 2025, 5:40 AM

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upbeat plinth One message removed from a suspended account.

ok so $\frac{\dd y}{\dd x} = y^2(2x + 2)$

grand pondBOT Jan 21, 2025, 5:40 AM

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hiidostuff

lavish venture Jan 21, 2025, 5:40 AM

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your font is strange

fading ore Jan 21, 2025, 5:40 AM

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mine is?

lavish venture Jan 21, 2025, 5:40 AM

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yes

upbeat plinth Jan 21, 2025, 5:40 AM

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One message removed from a suspended account.

lavish venture Jan 21, 2025, 5:41 AM

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the ok so

fading ore Jan 21, 2025, 5:41 AM

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oh

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idk why

lavish venture Jan 21, 2025, 5:41 AM

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like i know why the d’s are

fading ore Jan 21, 2025, 5:41 AM

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oh its bc the words arent in the $$ bounds

fading ore Jan 21, 2025, 5:41 AM

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upbeat plinth One message removed from a suspended account.

do you see how this is separable?

lavish venture Jan 21, 2025, 5:41 AM

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ok so $\frac{\dd y}{\dd x} = y^2(2x+2)$

grand pondBOT Jan 21, 2025, 5:41 AM

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knief

lavish venture Jan 21, 2025, 5:41 AM

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oh no maybe it’s not

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idk

fading ore Jan 21, 2025, 5:41 AM

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we can rewrite as

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$\frac{1}{y^2} \dd y = 2x + 2 , \dd x$

grand pondBOT Jan 21, 2025, 5:42 AM

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hiidostuff

upbeat plinth Jan 21, 2025, 5:42 AM

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One message removed from a suspended account.

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One message removed from a suspended account.

lavish venture Jan 21, 2025, 5:42 AM

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ok so $\frac{dy}{dx} = y^2(2x+2)$

upbeat plinth Jan 21, 2025, 5:42 AM

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One message removed from a suspended account.

grand pondBOT Jan 21, 2025, 5:42 AM

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knief

lavish venture Jan 21, 2025, 5:42 AM

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yea it’s just the dd i guess

upbeat plinth Jan 21, 2025, 5:42 AM

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One message removed from a suspended account.

grand pondBOT Jan 21, 2025, 5:42 AM

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Kenzo

fading ore Jan 21, 2025, 5:42 AM

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ooh

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nope

lavish venture Jan 21, 2025, 5:42 AM

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upbeat plinth One message removed from a suspended account.

brother

fading ore Jan 21, 2025, 5:43 AM

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how about we write it like this

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$y^{-2} , \dd y = (2x + 2) , \dd x$

lavish venture Jan 21, 2025, 5:43 AM

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also please use \ln

grand pondBOT Jan 21, 2025, 5:43 AM

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hiidostuff

fading ore Jan 21, 2025, 5:43 AM

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maybe writing it like this is clearer

upbeat plinth Jan 21, 2025, 5:43 AM

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One message removed from a suspended account.

fading ore Jan 21, 2025, 5:43 AM

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upbeat plinth One message removed from a suspended account.

well we can use power rule on the left hand side

upbeat plinth Jan 21, 2025, 5:43 AM

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One message removed from a suspended account.

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One message removed from a suspended account.

fading ore Jan 21, 2025, 5:44 AM

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and the right hand side as well i guess

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we ultimately get

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$-\frac{1}{y} = x^2 + 2x + C$

grand pondBOT Jan 21, 2025, 5:44 AM

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hiidostuff

upbeat plinth Jan 21, 2025, 5:44 AM

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One message removed from a suspended account.

fading ore Jan 21, 2025, 5:44 AM

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i did

lavish venture Jan 21, 2025, 5:44 AM

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he did

upbeat plinth Jan 21, 2025, 5:45 AM

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One message removed from a suspended account.

fading ore Jan 21, 2025, 5:45 AM

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finding the explicit representation for y here is pretty easy

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reciprocate both sides and negate

upbeat plinth Jan 21, 2025, 5:45 AM

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One message removed from a suspended account.

fading ore Jan 21, 2025, 5:46 AM

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upbeat plinth One message removed from a suspended account.

if $\frac{1}{a} = b$ then $a = \frac{1}{b}$

lavish venture Jan 21, 2025, 5:46 AM

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1/{} —> {}

grand pondBOT Jan 21, 2025, 5:46 AM

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hiidostuff

fading ore Jan 21, 2025, 5:46 AM

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just doing that

upbeat plinth Jan 21, 2025, 5:46 AM

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One message removed from a suspended account.

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One message removed from a suspended account.

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One message removed from a suspended account.

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One message removed from a suspended account.

lavish venture Jan 21, 2025, 5:47 AM

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whet

fading ore Jan 21, 2025, 5:47 AM

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upbeat plinth One message removed from a suspended account.

remember to reciprocate

upbeat plinth Jan 21, 2025, 5:48 AM

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One message removed from a suspended account.

lavish venture Jan 21, 2025, 5:48 AM

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also it might be nice to solve for c right here

fading ore Jan 21, 2025, 5:48 AM

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(true)

grand pondBOT Jan 21, 2025, 5:48 AM

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Kenzo
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

fading ore Jan 21, 2025, 5:48 AM

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grand pond **Kenzo** Compile Error! Click the <:errors:504266556054962196> reaction for mor...

yes!

lavish venture Jan 21, 2025, 5:48 AM

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before solving for y you can solve for c

fading ore Jan 21, 2025, 5:48 AM

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alright now use the exact value you have to find c

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we know y(0) = -1

upbeat plinth Jan 21, 2025, 5:48 AM

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One message removed from a suspended account.

lavish venture Jan 21, 2025, 5:49 AM

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upbeat plinth One message removed from a suspended account.

you put } after $

upbeat plinth Jan 21, 2025, 5:49 AM

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One message removed from a suspended account.

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One message removed from a suspended account.

fading ore Jan 21, 2025, 5:49 AM

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upbeat plinth One message removed from a suspended account.

so let x = 0 and y = -1

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and you can find c

upbeat plinth Jan 21, 2025, 5:49 AM

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One message removed from a suspended account.

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One message removed from a suspended account.

lavish venture Jan 21, 2025, 5:51 AM

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how

lavish venture Jan 21, 2025, 5:51 AM

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grand pond **hiidostuff**

i would’ve plugged in here btw

fading ore Jan 21, 2025, 5:52 AM

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upbeat plinth One message removed from a suspended account.

close but lets write it out

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we know that

upbeat plinth Jan 21, 2025, 5:52 AM

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One message removed from a suspended account.

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One message removed from a suspended account.

fading ore Jan 21, 2025, 5:52 AM

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yeah there we go

upbeat plinth Jan 21, 2025, 5:52 AM

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One message removed from a suspended account.

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One message removed from a suspended account.

midnight plankBOT Jan 21, 2025, 5:52 AM

#

Channel closed

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last slate Jan 21, 2025, 6:21 AM

#

midnight plankBOT Jan 21, 2025, 6:21 AM

#

last slate

last slate Jan 21, 2025, 6:21 AM

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Hello

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What do they mean by "objects" here?

hard umbra Jan 21, 2025, 6:23 AM

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just elements of the set V

last slate Jan 21, 2025, 6:23 AM

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They also mentioned in later in the book,"Any kind of object can be a vector and the operations of addition and sacalar multiplication need not have any relation to those of R^n".

hard umbra Jan 21, 2025, 6:23 AM

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it's just a generic word for something

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you'd call them vectors to be more specific

last slate Jan 21, 2025, 6:24 AM

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oh

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thanks

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.close

midnight plankBOT Jan 21, 2025, 6:24 AM

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Channel closed

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terse roost Jan 21, 2025, 6:29 AM

#

.reopen

#

.reopen

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last slate Jan 21, 2025, 6:44 AM

#

midnight plankBOT Jan 21, 2025, 6:44 AM

#

last slate

last slate Jan 21, 2025, 6:45 AM

#

#

What happened here ?

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i wasnt able to undertand a single part

sharp coral Jan 21, 2025, 6:47 AM

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so we have some vector (a vector is what we call an object which belongs to a vector space) which we are calling 0

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so V = {0}

hard cypress Jan 21, 2025, 6:48 AM

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How many days are in a week

sharp coral Jan 21, 2025, 6:49 AM

#

for a vector space we need 3 things:

a set of vectors (in this case 0 is the only vector)
a definition of addition, which takes in two vectors from V and returns a vector from V (in this case we define addition to be an operation which returns 0 if given the inputs 0 and 0, which is really the only way we could have defined it)
a definition of scalar multiplication, which takes in a vector from V and a scalar, and returns a vector from V (in this case, we define it so that any scalar multiplied by 0 returns 0, which is again really the only definition it could have given V has only a single vector in it)

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we call the vector 0 because it's clear that it is the "additive identity" aka "zero vector" mentioned in the vector space axioms

last slate Jan 21, 2025, 6:52 AM

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oh we will be defining the addition and scalar multiplication ourselfs before check for the axioms

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one more thing

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we could have defined addition in a different way if the Vector space had more objects instead of just one i.e 0 ?

sharp coral Jan 21, 2025, 6:54 AM

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yes, there are generally different ways of defining addition

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for a finite number of vectors, we can define an operation like addition by what outputs it gives for any given input (like a multiplication table). in this case the only possible input was 0, and the only possible output was 0

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the more interesting thing is that those equations are actually true for the additive identity/"zero vector" of any vector space. which would imply that every vector space actually contains as a subset this zero vector space

last slate Jan 21, 2025, 6:59 AM

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the comparison with multiplication table made it more clear lol

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thank you

#

.close

midnight plankBOT Jan 21, 2025, 6:59 AM

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midnight plankBOT Jan 21, 2025, 7:36 AM

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midnight plankBOT Jan 21, 2025, 7:52 AM

#

karmic slate Jan 21, 2025, 7:52 AM

#

aside from IVT also

zealous schooner Jan 21, 2025, 7:53 AM

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What you're describing is quite literally just IVT

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Also it's not a question

karmic slate Jan 21, 2025, 7:54 AM

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zealous schooner Also it's not a question

oh we're tasked to research and make a problemm

karmic slate Jan 21, 2025, 7:54 AM

#

zealous schooner What you're describing is quite literally just IVT

ive solved for thatt 😭

zealous schooner Jan 21, 2025, 7:54 AM

#

!xy

midnight plankBOT Jan 21, 2025, 7:54 AM

#

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

midnight plankBOT Jan 21, 2025, 8:10 AM

#

@karmic slate Has your question been resolved?

midnight plankBOT Jan 21, 2025, 8:25 AM

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Channel closed

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chrome drum Jan 21, 2025, 8:56 AM

#

midnight plankBOT Jan 21, 2025, 8:56 AM

#

chrome drum

chrome drum Jan 21, 2025, 8:56 AM

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someone help with this plz

midnight plankBOT Jan 21, 2025, 9:11 AM

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@chrome drum Has your question been resolved?

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chrome drum Jan 21, 2025, 9:50 AM

#

if a function is gf(x), then the domain of gf will be equal to the domain of f right

midnight plankBOT Jan 21, 2025, 9:50 AM

#

chrome drum if a function is gf(x), then the domain of gf will be equal to the domain of f r...

chrome drum Jan 21, 2025, 9:50 AM

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just answer this'

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its my question

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dont put that !orignal shit

heady plume Jan 21, 2025, 9:51 AM

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domain of gf is the domain of f for which f values agree with the domain of g

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for example f(2) = 3, f(3) = 4, g(3) = 5
=> g(f(2)) = 5, but g(f(3)) is not defined, so gf is not well defined

chrome drum Jan 21, 2025, 10:03 AM

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heady plume domain of gf is the domain of f for which f values agree with the domain of g

so this is true right

heady plume Jan 21, 2025, 10:04 AM

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this yes, what I wrote is right

chrome drum Jan 21, 2025, 10:13 AM

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heady plume <:this:489575168314966026> yes, what I wrote is right

thanks

#

.close

midnight plankBOT Jan 21, 2025, 10:13 AM

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midnight plankBOT Jan 21, 2025, 11:45 AM

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orchid grove Jan 21, 2025, 12:51 PM

#

midnight plankBOT Jan 21, 2025, 12:51 PM

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orchid grove

orchid grove Jan 21, 2025, 12:51 PM

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By using options C option is correct

#

#

But I want to learn the process

dusty portal Jan 21, 2025, 12:52 PM

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orchid grove

is this for jee or sumn

orchid grove Jan 21, 2025, 12:52 PM

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Yeah JEE

dusty portal Jan 21, 2025, 12:52 PM

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lol

orchid grove Jan 21, 2025, 12:52 PM

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lol?

dusty portal Jan 21, 2025, 12:53 PM

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well do you know the definition of magnitude

orchid grove Jan 21, 2025, 12:53 PM

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I know the definition hence i have solved it?

orchid grove Jan 21, 2025, 12:53 PM

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orchid grove

..

dusty portal Jan 21, 2025, 12:53 PM

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ok

orchid grove Jan 21, 2025, 12:53 PM

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Okay☺️

dusty portal Jan 21, 2025, 12:53 PM

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well i mean im tryna teach the method

orchid grove Jan 21, 2025, 12:53 PM

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Yeah sure sure

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I thought you are joking

dusty portal Jan 21, 2025, 12:53 PM

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no

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ok well lets start with the one on the right

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$\qty|\frac{z-4}{z-8}|=1$

grand pondBOT Jan 21, 2025, 12:54 PM

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;(

orchid grove Jan 21, 2025, 12:54 PM

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So it is saying that the points which are middle of 4,8

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What?

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Lmao

dusty portal Jan 21, 2025, 12:55 PM

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we can divide both of them to get $\qty|1+\frac{4}{z-8}|=1$

rotund reef Jan 21, 2025, 12:55 PM

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why?

grand pondBOT Jan 21, 2025, 12:55 PM

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;(

dusty portal Jan 21, 2025, 12:55 PM

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orchid grove So it is saying that the points which are middle of 4,8

elaborate

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ill brb i need to eat

orchid grove Jan 21, 2025, 12:55 PM

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|z-4|=|z-8|

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Is just a line

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Striaght line

orchid grove Jan 21, 2025, 12:56 PM

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dusty portal we can divide both of them to get $\qty|1+\frac{4}{z-8}|=1$

Okay fine next?

rotund reef Jan 21, 2025, 12:59 PM

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can you wait a bit?

midnight plankBOT Jan 21, 2025, 1:11 PM

#

@orchid grove Has your question been resolved?

orchid grove Jan 21, 2025, 1:15 PM

#

rotund reef can you wait a bit?

Can you leave a bit lol?

rotund reef Jan 21, 2025, 1:16 PM

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It gets big

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how much time do you have?

dusty portal Jan 21, 2025, 1:23 PM

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orchid grove So it is saying that the points which are middle of 4,8

k i understand this now

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sry im waiting for something to cook

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sobbingTEArs

orchid grove Jan 21, 2025, 1:23 PM

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rotund reef how much time do you have?

No time

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Sure

midnight plankBOT Jan 21, 2025, 1:53 PM

#

@orchid grove Has your question been resolved?

midnight plankBOT Jan 21, 2025, 2:53 PM

#

@orchid grove Has your question been resolved?

midnight plankBOT Jan 21, 2025, 3:53 PM

#

Channel closed

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midnight plankBOT Jan 21, 2025, 5:14 PM

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orchid grove Jan 21, 2025, 5:16 PM

#

midnight plankBOT Jan 21, 2025, 5:16 PM

#

orchid grove

#

@orchid grove Has your question been resolved?

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Channel closed

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gray jackal Jan 21, 2025, 6:43 PM

#

midnight plankBOT Jan 21, 2025, 6:43 PM

#

gray jackal

gray jackal Jan 21, 2025, 6:43 PM

#

I got 1 as the answer 😭

slender walrus Jan 21, 2025, 6:43 PM

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good

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are any of those options equivalent to 1?

gray jackal Jan 21, 2025, 6:44 PM

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Bruh my dumbass 😭😭

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A

quiet parcel Jan 21, 2025, 6:47 PM

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😂😂😂

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you made my day man

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its ok it happens 😂

gray jackal Jan 21, 2025, 6:47 PM

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🤣🤣🤣

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Dude I was checking if the book had a mistake

fallow scarab Jan 21, 2025, 6:50 PM

#

,w csc^2(x) - cot^2(x) == 1

grand pondBOT Jan 21, 2025, 6:51 PM

#

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gray jackal Jan 21, 2025, 6:51 PM

#

#

My work is right so far?

lavish venture Jan 21, 2025, 7:01 PM

#

gray jackal

this is like the opposite of the problem we did yesterday

#

yesterday it was $\tan^2 \theta (\cot^2 \theta + \cos^2 \theta)$

grand pondBOT Jan 21, 2025, 7:02 PM

#

knief

lavish venture Jan 21, 2025, 7:02 PM

#

remember that tan = 1/cot

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and cot = cos/sin

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the sin will cancel as will the tan and cot

gray jackal Jan 21, 2025, 7:04 PM

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Honestly I’m having trouble with the canceling for whatever reason

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Let me retry

#

How do I combine what’s in the parenthesis

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Sin^2 + sin^2cos^2 over cos^2

lavish venture Jan 21, 2025, 7:11 PM

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gray jackal How do I combine what’s in the parenthesis

don’t

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just distribute

gray jackal Jan 21, 2025, 7:12 PM

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Wouldn’t it be easier then multiplying by cos^2/sin^2

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WAIT

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let me draw it out

#

#

Pls tell me this is right

lavish venture Jan 21, 2025, 7:17 PM

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it is correct but you didn’t need the additional cos^2’s on the sin^2

gray jackal Jan 21, 2025, 7:17 PM

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Which

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Oh

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Yea but it’s like I’m distributing makes it easier for me to sew

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Anyways I appreciate your help brother

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Ima close

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.close

midnight plankBOT Jan 21, 2025, 7:22 PM

#

Channel closed

Closed by @gray jackal

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midnight plankBOT Jan 21, 2025, 7:37 PM

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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

mint ravine Jan 21, 2025, 7:58 PM

#

Can someone please help me on this question

midnight plankBOT Jan 21, 2025, 7:58 PM

#

mint ravine Can someone please help me on this question

dusty portal Jan 21, 2025, 7:58 PM

#

mint ravine Can someone please help me on this question

!status

midnight plankBOT Jan 21, 2025, 7:58 PM

#

mint ravine Can someone please help me on this question

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

dusty portal Jan 21, 2025, 7:58 PM

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also, draw it!

mint ravine Jan 21, 2025, 7:58 PM

#

yeah i did

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let me send the picture rq

mint ravine Jan 21, 2025, 7:59 PM

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midnight plank ``` What step are you on? 1. I don't know where to begin. 2. I have begun but go...

3

fringe wing Jan 21, 2025, 8:04 PM

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So, area of a triangle is 1/2 base times height. how do you find the height and the base from the information provided? you would use some trig function.

mint ravine Jan 21, 2025, 8:07 PM

#

fringe wing So, area of a triangle is 1/2 base times height. how do you find the height and ...

well you can reflect the triangle to make it a square

#

and then use the diagonal (root 3) and apply it to the formula 1/2*d^2, where d is the diagonal

#

in which i got 1.5

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and divided by 2 to get 0.75 as the area of the triangle

#

but it was wrong

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so idk what to do now

#

<@&286206848099549185>

mint ravine Jan 21, 2025, 8:10 PM

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dusty portal also, draw it!

in this case, square root of 3 is the hypotenuse, right?

gaunt plume Jan 21, 2025, 8:11 PM

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Your problem there is that it becomes a rectangle, not a square

fringe wing Jan 21, 2025, 8:11 PM

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the reason that does not work is because it makes a rectangle not a square

mint ravine Jan 21, 2025, 8:11 PM

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wdym

fringe wing Jan 21, 2025, 8:12 PM

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the diagonal of a square would have the angle 45 not 75

mint ravine Jan 21, 2025, 8:12 PM

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oh yeah

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i forgot to consider that

gaunt plume Jan 21, 2025, 8:12 PM

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fringe wing Jan 21, 2025, 8:13 PM

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it would have worked if it was 45

mint ravine Jan 21, 2025, 8:14 PM

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how do we calculate the length of the rectangle?

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isn't there a relationship between the side lengths of a triangle

gaunt plume Jan 21, 2025, 8:14 PM

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Have you been introduced to trigonometry yet? (sin, cos, etc)

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I'm guessing not

mint ravine Jan 21, 2025, 8:15 PM

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would this help?

fringe wing Jan 21, 2025, 8:15 PM

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you need to use trigonometry to solve this problem.

mint ravine Jan 21, 2025, 8:15 PM

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gaunt plume Have you been introduced to trigonometry yet? (sin, cos, etc)

i've only learned tan

mint ravine Jan 21, 2025, 8:15 PM

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fringe wing you need to use trigonometry to solve this problem.

what topic

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in trig

fringe wing Jan 21, 2025, 8:15 PM

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that diagram does help.

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you would derive that using trig, but that is enough for you to solve your problem.

mint ravine Jan 21, 2025, 8:16 PM

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ok

fringe wing Jan 21, 2025, 8:16 PM

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i dont want to confuse you if you don't know trig already

mint ravine Jan 21, 2025, 8:16 PM

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got it. thanks

gaunt plume Jan 21, 2025, 8:17 PM

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That diagram doesn't help, it's for a triangle with angle 60 not 75

mint ravine Jan 21, 2025, 8:20 PM

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gaunt plume That diagram doesn't help, it's for a triangle with angle 60 not 75

is the answer 9/4 right?

gaunt plume Jan 21, 2025, 8:22 PM

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No sorry

mint ravine Jan 21, 2025, 8:22 PM

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idk what to do then lol

gaunt plume Jan 21, 2025, 8:22 PM

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I'm sure there is a way of doing it without trig but I'm not sure

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Are yoou allowed a calculator? I'm assuming not

mint ravine Jan 21, 2025, 8:23 PM

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this is just homework, so yes i can

gaunt plume Jan 21, 2025, 8:23 PM

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Ah okay

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In that case you can do it with tan

mint ravine Jan 21, 2025, 8:24 PM

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how?

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what is the triangle tangent to

fringe wing Jan 21, 2025, 8:25 PM

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tangent of 75 degrees is the ratio of the height of this right triangle divided by the length at the bottom

mint ravine Jan 21, 2025, 8:26 PM

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fringe wing tangent of 75 degrees is the ratio of the height of this right triangle divided ...

but we dont know what the height/length is

fringe wing Jan 21, 2025, 8:28 PM

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that ratio is the same for any triangle with a 90 degree angle and a 75 degree angle.

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it is given by tangent of 75 degrees

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so, your calculator knows

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are you sure you havent covered sin? i think you need to use sin to find the height

mint ravine Jan 21, 2025, 8:30 PM

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i can use sin on my calculator

fervent ember Jan 21, 2025, 8:30 PM

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fringe wing are you sure you havent covered sin? i think you need to use sin to find the hei...

no. via tan you get a ratio and via pythagoras you get a second equation.

mint ravine Jan 21, 2025, 8:31 PM

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i js don't know what it is

fringe wing Jan 21, 2025, 8:32 PM

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fervent ember no. via tan you get a ratio and via pythagoras you get a second equation.

yeah that would work too

mint ravine Jan 21, 2025, 8:36 PM

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fringe wing yeah that would work too

is the answer 3/4 divided by 2

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so 3/8?

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i think i may have forgotten to divide by 2 somewhere

fringe wing Jan 21, 2025, 8:40 PM

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i got 3/8

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correct

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good job ramennoodleman21

mint ravine Jan 21, 2025, 8:40 PM

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thanks

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.close

midnight plankBOT Jan 21, 2025, 8:40 PM

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Channel closed

Closed by @mint ravine

Use .reopen if this was a mistake.

midnight plankBOT Jan 21, 2025, 8:55 PM

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mint ravine Jan 21, 2025, 9:18 PM

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please help someone

midnight plankBOT Jan 21, 2025, 9:18 PM

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mint ravine please help someone

fallow scarab Jan 21, 2025, 9:19 PM

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mint ravine Jan 21, 2025, 9:22 PM

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fallow scarab

I drew an image

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showing what it says in the problem

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I also know that the perimeters are 4y=3x, y being the side length of the square and x being the side length of the triangle

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the area of the triangle is (x*h)/2=2 root 3

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i don't know what to do from there

fallow scarab Jan 21, 2025, 9:24 PM

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shouldn't use x for two different things

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do you know how to find the height in an equilateral triangle?

mint ravine Jan 21, 2025, 9:24 PM

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oops i mixed it up

mint ravine Jan 21, 2025, 9:26 PM

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fallow scarab do you know how to find the height in an equilateral triangle?

no. is there a relationship or something

fallow scarab Jan 21, 2025, 9:26 PM

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if you bisect the equilateral triangle from a vertex, that length is the height and you'll form a right triangle

mint ravine Jan 21, 2025, 9:30 PM

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fallow scarab if you bisect the equilateral triangle from a vertex, that length is the height ...

like this?

fallow scarab Jan 21, 2025, 9:30 PM

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yea sure

mint ravine Jan 21, 2025, 9:30 PM

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oh wait let me do it straight up so it can be easier

mint ravine Jan 21, 2025, 9:34 PM

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fallow scarab if you bisect the equilateral triangle from a vertex, that length is the height ...

so ((x/2)*h)/2=square root of 3

fallow scarab Jan 21, 2025, 9:34 PM

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i have no idea what you did

mint ravine Jan 21, 2025, 9:34 PM

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okay let me send a picture

mint ravine Jan 21, 2025, 9:37 PM

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fallow scarab i have no idea what you did

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is that good

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root 3 represent the area of the right triangles

fallow scarab Jan 21, 2025, 9:42 PM

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you label as many angles as you can using right triangle and equilateral properties

mint ravine Jan 21, 2025, 9:42 PM

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fallow scarab you label as many angles as you can using right triangle and equilateral propert...

well i know that both the right triangles are 30-60-90 triangles

mint ravine Jan 21, 2025, 9:45 PM

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fallow scarab you label as many angles as you can using right triangle and equilateral propert...

the length of the diagonal of the square equals the hypotenuse of the right triangle, right?

fallow scarab Jan 21, 2025, 9:46 PM

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do you have a picture of the square with diagonal and/right triangle

mint ravine Jan 21, 2025, 9:47 PM

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fallow scarab do you have a picture of the square with diagonal and/right triangle

no, it was just a thought

fallow scarab Jan 21, 2025, 9:47 PM

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draw it

mint ravine Jan 21, 2025, 9:50 PM

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fallow scarab draw it

like this?

fallow scarab Jan 21, 2025, 9:50 PM

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yes

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that diagonal you drew is the diagonal of the square and is also the hypotenuse of a right triangle

fallow scarab Jan 21, 2025, 9:50 PM

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mint ravine the length of the diagonal of the square equals the hypotenuse of the right tria...

ie. this is correct.

mint ravine Jan 21, 2025, 9:51 PM

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ah i see

mint ravine Jan 21, 2025, 9:52 PM

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fallow scarab ie. this is correct.

so the diagonal of the square is equal to 2 root 2?

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oh wait

fallow scarab Jan 21, 2025, 9:55 PM

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i'd need to see your steps

fallow scarab Jan 21, 2025, 9:56 PM

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mint ravine

starting with finding h in terms of x using trig or properties of 30-60-90 triangles, then using the area equation to solve for x

mint ravine Jan 21, 2025, 9:57 PM

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i meant the to say that the answer was 4, but that was wrong too

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here were my steps

mint ravine Jan 21, 2025, 9:58 PM

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fallow scarab starting with finding h in terms of x using trig or properties of 30-60-90 trian...

(x*x root 3)/2=2 root 3

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x= square root of 4

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hypotenuse = 2x or 2 root 4, which is equal to 4

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but i got the answer wrong

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i don't see why

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these were the relationships i was using

fallow scarab Jan 21, 2025, 9:59 PM

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you have x/2, not x

mint ravine Jan 21, 2025, 10:00 PM

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oh stupid mistake

mint ravine Jan 21, 2025, 10:05 PM

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fallow scarab you have x/2, not x

bruh this time i got 8 and its still wrong

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i don't understand what im doing wrong

fallow scarab Jan 21, 2025, 10:05 PM

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me neither

mint ravine Jan 21, 2025, 10:10 PM

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nvm i go the answer

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.close

midnight plankBOT Jan 21, 2025, 10:10 PM

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Channel closed

Closed by @mint ravine

Use .reopen if this was a mistake.

heady plume Jan 21, 2025, 10:11 PM

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mint ravine please help someone

Area of triangle = 4√3x² = 2√3 
=> Square side's square = 9x² = 9/2
=> Diagonal = ?```

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Good job finding the answer 👍

midnight plankBOT Jan 21, 2025, 10:25 PM

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midnight plankBOT Jan 21, 2025, 10:49 PM

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prime hornet Jan 21, 2025, 10:50 PM

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hmmcat

dusty portal Jan 21, 2025, 10:51 PM

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que

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qué occurré?

midnight plankBOT Jan 22, 2025, 12:58 AM

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river scarab Jan 22, 2025, 12:58 AM

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midnight plankBOT Jan 22, 2025, 12:58 AM

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river scarab

river scarab Jan 22, 2025, 12:58 AM

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can someone help me with this question please

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the question says odds of winning

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so why isnt it 0.4?

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nvm

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.close

midnight plankBOT Jan 22, 2025, 12:59 AM

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Channel closed

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midnight plankBOT Jan 22, 2025, 1:14 AM

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