#help-23

1 messages · Page 197 of 1

steep yacht
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What if we select random primes will it hold?

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For example, 27 = (17 + 5 + 3) - (terms - 1)

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It's weird how it's (p + q) - 1 = Prime. Telescopes outwards

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There has to be a some sort of bounds on the number of prime terms used, because the (term - 1) will swallow the tail end of the prime terms

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Maybe that could be useful to figuring this out?

safe radishBOT
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@steep yacht Has your question been resolved?

steep yacht
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Mm You could keep breaking down the primes terms I wonder If some pattern emerges

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If you take it to its extreme, all primes would 3*n - (n - 1) = 2n + 1. Because you can keep breaking the primes down in to 3s

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Would this be sufficient to prove all primes are (p + q) - 1

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<@&286206848099549185>

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Does this make any sense?

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wait no it doesn't it would imply that (p + q) - 1 = 2n + 1, which would imply that p + q = 2n which is goldbach.

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so all primes and (p + q) - 1. then p + q = 2n. because of the recursive nature of the problem

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<@&286206848099549185>

safe radishBOT
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@steep yacht Has your question been resolved?

steep yacht
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Man if it's not out of a text book it's really hard to find people to help on this server

left gyro
safe radishBOT
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@steep yacht Has your question been resolved?

steep yacht
left gyro
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its not filled with discord mods

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these people (as far as Ive heard) go outside

steep yacht
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hahah ok fair, yeah i'm scared to ask question there as my math "education" is barely at a high school level

left gyro
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they have problems at all levels but I think most of the people there arent as high up as you think they are

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theyve seen big problems and failed them, thats why theyre presumably here and not souring high on their own

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the average textbook problem is much easier than a difficulty 1 problem on there

safe radishBOT
#

@steep yacht Has your question been resolved?

safe radishBOT
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versed smelt
#

This is engineering math integration but this is the basic integration practice and im stuck :<

versed smelt
#

This is my working so far, i tried to re-write the equation after expanding the brackets but got stuck

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this is the answer

lime dust
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Look for a way to make that 16 disappear from inside the sqrt

versed smelt
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like turn it into 4^2?

lime dust
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That u have already but u can’t take out cause u have a subtraction

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Si u need to make x^2 = 16u^2

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To take common factor the 16

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How do u achieve this?

versed smelt
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uhh ive got no clue

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:<

fringe kernel
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hi

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i can help you

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hold up

fringe kernel
versed smelt
#

yeah

radiant crypt
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He knows the solution, doesnt know the steps glassescat

versed smelt
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wait yeah i need the steps to it

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sorry

fringe kernel
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im assuming that you know the formula of integral of 1/root(a2-x2)

versed smelt
#

ohhh wait i understand

fringe kernel
#

thats good

versed smelt
#

i think i confused myself when i re-wrote it like this

fringe kernel
#

yea probably

versed smelt
fringe kernel
fringe kernel
versed smelt
#

right okok

#

.close

safe radishBOT
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nova field
#

how do i do this question? is it a quadratic formula one?

analog kelp
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what do you think

nova field
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i have no idea

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is it something abt y = mx + c?

analog kelp
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have you taken calculus

analog kelp
nova field
analog kelp
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ok so stationary points are closely related to the derivative, theyre either the points that make your derivative function equal to zero or is undefined

nova field
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Ok

analog kelp
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start by taking the derivative and check for the points that make the function equal to zero or is undefined

nova field
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i got the derivative but how do i check for the points that make it undefined or zero?

analog kelp
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check if the function is undefined at any points in its domain

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if the domain is R then there are no points satisfying the undefined condition

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just by looking at it, the domain is gonna be just R because its a normal quadratic function

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if you wanna check if the function is equal to zero, just set it to zero and factorize

nova field
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ah alright i think i rmb how to solve it now

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Thanks

analog kelp
#

np

nova field
#

.close

safe radishBOT
#
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lunar bolt
safe radishBOT
lunar bolt
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Need helo on 2. A

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Very confused

timid scroll
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Soh cah toa

lunar bolt
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10 x tan(31)

obsidian oracle
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Degrees or radians?

lunar bolt
obsidian oracle
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And this is wrong

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Toa = opposite adjacent

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a is neither

lunar bolt
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can you teach me the steps to solve question a

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please

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stuck on this for 30 minutes

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the teacher gave the answer already which is 19.4 but im trying to know how to find it out

obsidian oracle
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You know one side, you want to know the other

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Compared to the angle you know

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What's the side you know?

lunar bolt
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10

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adjacetn

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or is it opposite

obsidian oracle
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It's not adjacent to the angle

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Adjacent = touches the angle

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It's opposite

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As it doesn't touch the angle

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What's the side you want to know?

timid scroll
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H is always opposite the right angle triangle
O is always opposite the angel
A is the 3rd one

lunar bolt
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so a

obsidian oracle
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Ok

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You will then use sides :

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Opposite hypothenuse

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So which formula?

lunar bolt
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soh

lunar bolt
obsidian oracle
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Yes i saw the first time

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Then use it

lunar bolt
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but i dont have the hypotenuse

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how am i suppsoed to find it

obsidian oracle
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Write down the formula

lunar bolt
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10 x soh(31)

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?

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10 x sin (31)

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=

obsidian oracle
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Not ×

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sin(31) = 10/a

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Opposite/hypothenuse

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That's why soh is in this order

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Now you can find a

lunar bolt
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so is it sin (31) divided by 10??

obsidian oracle
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No

lunar bolt
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im actually so confused this method worked for other questions but not this one

obsidian oracle
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sin(31) = 10/a

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rewrite this as a = ...

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How do you put a "on top"?

lunar bolt
obsidian oracle
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How do you put a on the numerator?

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Instead of the denominator?

lunar bolt
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swap it

obsidian oracle
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Ok sure

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So swap numerator and denominator on both sides

lunar bolt
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wdym by that

obsidian oracle
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I mean

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If x/y = c/d, you write y/x = d/c

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Swap it

lunar bolt
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talk a bit more simple please, my brain is a bit foggy today

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oh yeah

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how do i do that with my equation though

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since its only sin 31 and 10

obsidian oracle
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sin(31)/1 = 10/a

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Now swap

lunar bolt
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what do i swap

obsidian oracle
lunar bolt
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so 31 sin 1 and a/10

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?

obsidian oracle
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???

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1/sin(31)

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a/10 = 1/sin(31)

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Now write a =...

lunar bolt
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i just started trig man

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im young

obsidian oracle
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Sure

lunar bolt
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a/10 = 1/sin31 = 1/0.515

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=1.942

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where does the 1 and the 0.515 come from?

obsidian oracle
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From what we did

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0.515 is just you plugging in sin(31)

lunar bolt
obsidian oracle
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sin(31) = 0.515

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You just did that in your calculator

lunar bolt
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oh yeah mb

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my calculator was on rad

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instead of deg

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where does the 1 come from btw?

obsidian oracle
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when we swapped

obsidian oracle
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Dividing by 1 does nothing

obsidian oracle
lunar bolt
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so basically a/10 and =1/sin31

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is the same right

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@obsidian oracle

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okay i got it

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thank you

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very much

safe radishBOT
#

@lunar bolt Has your question been resolved?

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rich meteor
#

.

safe radishBOT
rich meteor
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I think RHS is incorrect

patent flame
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why do you think so

rich meteor
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because if i put the formula a+b whole square on lhs,it’s in +

sleek wolf
#

that's correct
now you need to express that in a formula

rich meteor
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sin^2^2 + cos^2^2 +2sin2cos2

patent flame
rich meteor
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no idea

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sin2+cos 2 =1

patent flame
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consider (sin^2(theta)+cos^2(theta))^2

patent flame
rich meteor
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where am i supposed to bring - from

patent flame
rich meteor
patent flame
#

exactly

sleek wolf
patent flame
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and now expand the brackets

rich meteor
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im left with 1+2sin2cos2

sleek wolf
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sin⁴(theta) + cos⁴(theta) = 1 - 2 sin²(theta)cos²(theta)
sin⁴(theta) + cos⁴(theta) + 2 sin²(theta)cos²(theta) = 1

rich meteor
#

nooooo

sleek wolf
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you can solidly do that

rich meteor
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my teacher said no

sleek wolf
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then they're wrong, really

rich meteor
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she said i have to get same on both sides

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like 1-2sin2cos2=1-2sin2cos2

rich meteor
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sin 4 +cos 4

sleek wolf
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no :(

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you cannot erase 2sin²cos² like that!

rich meteor
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ok

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could u do it my way

sleek wolf
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you have to converge to my way to do it your way

rich meteor
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im not used to it

sleek wolf
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sin⁴(theta) + cos⁴(theta) + 2 sin²(theta)cos²(theta) = (sin²(theta))² + (cos²(theta))² + 2 sin²(theta)cos²(theta)
can you rewrite it for me...?

sleek wolf
sleek wolf
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and its numerical value is?

rich meteor
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1

rich meteor
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can u tell me how to get the - sign pls😭😭

rich meteor
sleek wolf
#

you do this:
sin⁴(theta) + cos⁴(theta) = sin⁴(theta) + cos⁴(theta) - 2 sin²(theta)cos²(theta) + 2 sin²(theta)cos²(theta)

sleek wolf
sleek wolf
# rich meteor (sin2+cos2)^2

group sin⁴(theta), cos⁴(theta) and 2 sin²(theta)cos²(theta) together to get 1 as calculated here
we end up with 1 - 2 sin²(theta)cos²(theta)

rich meteor
#

huhhh….

warm patio
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Can you handle with simple Variables to make it easier

sleek wolf
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substitute sin²(theta) as a and cos²(theta) as b ;)

rich meteor
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that’s so complicated

warm patio
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(X + Y)² = x² + 2xy + y² ( adding -2xy both sides)
(X+Y)² -2xy = x² + y²

sleek wolf
rich meteor
sleek wolf
warm patio
rich meteor
#

uhhh

#

ok thanks

#

.clode

#

.close

safe radishBOT
#
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safe radishBOT
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spice narwhal
#

I think I miss out something here with this one.

spice narwhal
#

Of course, I am not going to find the cube of a 3x3 matrix. At least, I assume that, since a matrix with elements a,b,c,d,e,f,g,h and j would be a cumbersome task when cubing.

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But I don't know where to begin with this problem.

split ether
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For nxn matrices you have det(AB) = det(A)det(B) and det(kA) = k^n det(A)

spice narwhal
#

Hm, in that case, I have two questions

  1. What is the "B" matrix here?
  2. What is the "n" in k^n?
split ether
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The part "For nxn matrices" should answer both questions

spice narwhal
#

Ohhhh so det(AxAxA) + i^3 det(A)

split ether
#

Yeah

spice narwhal
#

Yeah, didn't fully realise the nxn connection to what you said

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Makes a ton of sense! Thanks!

#

Have a good day.

#

.close

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bold acorn
#

I don't understand with the statement in the yellow line

#

Can someone explain to me

safe radishBOT
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untold topaz
#

Can someone tell me how they got e^2 ?

safe radishBOT
sharp flicker
#

so since the lim as x -> 0 can approach 0 from either the positive or the negative side you have to consider those scenarios

#

in those scenarios you will see something interesting happen to ln(1+x) and x

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just plugging in 0 for x wont always work especially in cases where a numberr is being divided by x

frigid locust
#

e^(2/x)ln(1+x) = e^(ln(1+x))^2/x = (1+x)^2/x = ((1+x)^1/x)^2 = e^2

humble helm
untold topaz
#

Thanks gais ! ||Suffering silently||

#

🫂

#

.close

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cerulean sluice
#

Two fair dice are thrown simultaneously. The random variable D is the difference
between the smaller and the larger score, or zero if they are the same. Tabulate the
probability distribution of D! can someone help me explain this probability and distribution?

dusk gyro
#

you can start by counting the total number of possible cases

wanton basin
#

First, difference can actually be expressed as sum if you change the faces of the second dice: x - y = x + (7 - y) - 7 = x + y' - 7

#

Second (minuand) dice: 1 -> 6, 2 -> 5, …, 6 -> 1

For example,
Dice [4] - Dice [5] = Diff [-1]
Dice [4] + Dice' [2] - 7 = -1

wanton basin
cerulean sluice
#

i fopund it

safe radishBOT
#

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sleek hornet
#

intergrate this using by parts?

safe radishBOT
sleek hornet
#

u= 2x-x²
dvdx = e^(x/2)

#

?

lean otter
#

ILATE = Inverse Logarithmic Algebraic Trigonometric Exponential. Whatever function is later in this sequence, is the one that is set as dv

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so, here we have an algebraic function and an exponential one

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so $\dd{v} = e^{\frac{x}{2}}$

flat frigateBOT
lean otter
#

and $u = (2x - x^2)$

flat frigateBOT
sleek hornet
#

ok

#

got the answer

#

tqvm

#

.close

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autumn fjord
#

How is set difference generally defined for countable inifinite sets? For example, can I consider that the difference of two inifinite sets might give a finite set? For example, the difference of the set of all natural numbers with the set of natural numbers greater than 10. Can I consider the result to be a finite set (numbers 0 to 10), or is it simply undefined?

safe radishBOT
#

@autumn fjord Has your question been resolved?

safe radishBOT
#

@autumn fjord Has your question been resolved?

past pelican
#

There is no problem for infinit sets

#

$$ A \setminus B = { x \in A \mid x \notin B } $$

flat frigateBOT
#

A shot

past pelican
#

@autumn fjord

autumn fjord
#

Thanks @past pelican

past pelican
autumn fjord
#

I get that there might be a finite number of elements that are in A but not in B. Thus the difference of two infinite sets can be finite

#

At least I think that's what you're saying

past pelican
#

Yeah

autumn fjord
#

.close

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compact python
#

Is Sx or ox the standard deviation?

safe radishBOT
compact python
#

dumb question but i cant seem to find the answer

timid mason
#

they both are

#

Sx is the standard deviation of a sample
So is the standard deviation of the population

compact python
#

i meant to ox, the one bellow Sx

desert juniper
#

it's the other way around. Sx is of the sample, ox is the one from the pop

compact python
#

theyre different numbers so im kinda confused

timid mason
compact python
#

so ox is the standard deviation of everything and Sx is the standard deviation of a specific group?

desert juniper
#

ox (it's actually a sigma, not an o) is the standard deviation, assuming that the data you're entered is the full population.
sx is the standard deviation of the sample, which assumes that the data you're entered is just a portion of the full pop

#

sx = sqrt(n/(n-1)) ox

compact python
#

ahhh i see

#

thank you so much soraka

#

ill ace my math exams

#

.close

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opaque pasture
#

how can I solve for this

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opaque pasture
#

how can I solve for this

lean otter
#

,, a = \f{\Delta v}{\Delta t}

flat frigateBOT
lean otter
#

also open a new help channel

lean otter
#

the velocity from time 0-8 is obviously growing at a constant rate, so the acceleration is constant. So pick any two points on that range and find the slope and thats ur max acceleration

opaque pasture
#

.cloes

#

.close

#

okahy

safe radishBOT
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opaque pasture
safe radishBOT
hardy lion
#

do you know what a minute is

opaque pasture
#

1 radian would be 60 mins

hardy lion
#

no

mellow wedge
#

....no

opaque pasture
#

o

hardy lion
#

1 degree is 60 mins

mellow wedge
#

angular displacement is like, d(theta)/dt

hardy lion
#

convert rad to deg and deg to min

hardy lion
mellow wedge
#

1.5 radian is like 85.94 degrees

#

so like 90 degrees right angle approx

opaque pasture
#

5156.4

#

mins

opaque pasture
#

then it should be 5156.4 mins

opaque pasture
mellow wedge
#

how much is that in degrees?

opaque pasture
#

85.94 degrees

mellow wedge
#

then you can just differentiate it

opaque pasture
#

what

#

@hardy lion

mellow wedge
#

okay, were not talking about differntiation to find angular acc or smg, sorry

#

i just check rn

opaque pasture
#

im not sure if the final answer would be 85.94 or 5156.4 mins

hardy lion
#

the second one

opaque pasture
#

they said to convert to rad to degree to min

mellow wedge
#

if we would be talking about acceleration, we'd use like 3rd eqn for vel and thn find an eqn and differentiate it

hardy lion
#

pun intended lol

opaque pasture
#

i missed the pun

mellow wedge
#

same here

hardy lion
#

the second one

opaque pasture
#

whats the pun 😭

#

what else is second??

hardy lion
#

anyway

mellow wedge
#

oh......haha i dont get it

opaque pasture
#

thats not a pun if its onyl one thing that has two options

#

or it went over my head

hardy lion
#

5k-ish sounds aboht right

opaque pasture
#

k

#

This would be angular velocity = angle turned/ time taken pi radians by five, so angular velocity would be 0.628 rad/s

flat frigateBOT
#

Result:

0.628 rad / s
opaque pasture
#

,calc 12 * 0.628

flat frigateBOT
#

Result:

7.536
opaque pasture
#

,calc 7.536 * 5

flat frigateBOT
#

Result:

37.68
opaque pasture
#

Is this right way to solve this?

#

/close

#

.close

safe radishBOT
#
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noble gate
#

What does this mean by simplify be removing factors of 1?.

hardy lion
#

lets say we had 4/6

#

a factor of 1 would be 2/2

#

by removing 2/2 you get 2/3

#

basically "simplify"

#

thats what they shouldve wrote

noble gate
#

oh. man that is really helpful.

#

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shadow spade
safe radishBOT
shadow spade
#

how do I solve for IVP if I can't solve for y?

patent flame
#

when x = 0, y = 2 just plug that into your equation

shadow spade
#

I don't need to solve for y?

stray steppe
#

when you put x=0 and y=2 you get the value of C

shadow spade
#

okay

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junior smelt
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cobalt monolith
#

is this correct?

safe radishBOT
cobalt monolith
#

if someone could explain altitude it would help me a lot as well, thank you!

cloud lichen
#

since this is an equilateral triangle the imaginary line will split the side into two equal pieces

#

Like this

#

that imaginary line is our altitude

#

We have a 30-60-90 triangle

#

so the altitude will be equal to 5[root]3

#

equilateral triangle has the same altitude at any corners

cobalt monolith
#

okay thank you so much 🙂

safe radishBOT
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coarse breach
#

Hi, this is an example problem for finding the directional derivative of a point on a gradient given a direction. I dont understand how the last step multiplies out to the answer, where does 8 * 5 come from?

safe radishBOT
#

@coarse breach Has your question been resolved?

coarse breach
#

<@&286206848099549185>

sand pasture
#

looks like a dot product

#

there's a mistake

#

should be 8 times 2

coarse breach
#

yeah thats what I'm thinking

#

this is in my textbook 😦

#

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sand pasture
#

I mean, how is u defined?

coarse breach
#

u is that second vector

sand pasture
#

its defined like that before?

coarse breach
#

ah

#

there we go

sand pasture
#

yea so with a 5

#

so result is still correct

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coarse breach
#

could someone help me understand why this isn't correct?

safe radishBOT
#

Show your work, and if possible, explain where you are stuck.

sand pasture
#

the gradient is not a sum of partial derivatives

#

its a vector of partial derivatives

coarse breach
#

i and j here are the unit vectors

sand pasture
#

cuz your function goes from R^2 to R

#

a derivative of this function must be 2 d also

coarse breach
#

here is the provided example from the book

sand pasture
#

ah okay nvm

#

wasn't seeing the i and j

coarse breach
#

I wonder if it wants me to put it in vector form though

#

I just have limited attempts...

sand pasture
#

yea I'd agree with the answer. But what are P and u for?

coarse breach
#

they're for later parts of the problem

#

this is just the first part, each are graded independently

#

ah 😐

#

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whole gale
safe radishBOT
whole gale
#

is D correct?

pure agate
#

It's the only one that is a tangent line, so yes.

whole gale
pure agate
#

Yes.

whole gale
#

ok it was right can you help with more?

pure agate
#

A and B are both secant lines.

#

And C is a normal line.

#

Ask away.

whole gale
#

is this 5?

pure agate
#

Is this a test?

whole gale
#

no

#

homeowrk

pure agate
#

Ok, can you show your work?

glacial shale
#

its right

whole gale
glacial shale
#

should be

whole gale
#

adn got y=3+4(x-1)

glacial shale
#

yeah thats right

pure agate
#

That's correct.

whole gale
#

ok

#

can you go to a different channel please

#

this is mine

pure agate
whole gale
pure agate
#

And please delete your comment.

whole gale
#

how about this one?

#

@pure agate

pure agate
#

One moment.

whole gale
#

ok thanks

pure agate
#

Looks good.

whole gale
#

how about this

pure agate
#

Looks good.

whole gale
#

this one?

#

@pure agate

pure agate
#

Sorry, working on dinner.

whole gale
#

ok

pure agate
#

Can you show your work on this one?

#

Nevermind. It's correct.

whole gale
#

ok

#

Can you help walk me through this last one?

#

but im not sure

pure agate
#

Can you show your work or at least how you approached the problem?

whole gale
#

I did f(5)-f(4)/5-4

#

and got 1.5

rich hazel
#

yo

#

i can help

whole gale
rich hazel
#

call

whole gale
#

what

rich hazel
#

ok/

#

wait

#

can we call

whole gale
#

ok

pure agate
#

That looks correct.

whole gale
#

?

#

@pure agate

#

.close

safe radishBOT
#
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jade coral
safe radishBOT
jade coral
#

is my teacher contradicting herself here?

#

she shows an area as negative whereas previously she does the absolute value of areas under the x-axis

plucky elk
#

|-negative| = positive

jade coral
#

for that integral

light shoal
#

the integral is -14

#

the absolute value of the integral is the area

jade coral
light shoal
#

but that's not what the question asks

#

it asks what is the integral

#

and that is indeed -9

safe radishBOT
#

@jade coral Has your question been resolved?

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lean otter
#

anybody can do this without any theorem from some real analysis book ?

lean otter
#

just pre-university level question

slender pendant
#

Isnt that like that famous JEE problem or idk

lean otter
#

💀

slender pendant
#

Yeah apparantly its really hard

lean otter
#

have you tried ?

slender pendant
#

No im not from india its just this is the second time i see this today

lean otter
lean otter
slender pendant
#

Apparantly there are videos on yt of solutions.

lean otter
slender pendant
lean otter
#

@lean otter found you!

#

look at the question i asked

thorny leaf
#

integration limits would be according to options

#

may be this will be lengthy , but right now I only got this method on my mind

lean otter
#

integral as limit of sum ?

#

hmm might work

thorny leaf
lean otter
#

yeah i will try this

safe radishBOT
#

@lean otter Has your question been resolved?

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gaunt nebula
#

How to approach this?

safe radishBOT
gaunt nebula
safe radishBOT
lean ruin
#

Have you tried graphing it?

gaunt nebula
#

I have tried but I get confused why y is equal to two things

lean ruin
#

They are different lines

gaunt nebula
#

Let me attempt draw

lean ruin
#

Like one line is y = x and another line is y = 8x and a third line is y = 4

#

These three lines give a figure whose area we need to evaluate

gaunt nebula
#

Something like this?

lean ruin
#

Yup

#

Now can you calculate the are using integrals?

gaunt nebula
#

Is my upper bound 4

#

And lower 0?

lean ruin
#

Yes

gaunt nebula
#

Then anti derive?

lean ruin
#

Correct

#

Maybe even combine the integrals

gaunt nebula
#

Unsure if this is right

#

But I got this

lean ruin
#

Looks right to me

gaunt nebula
#

Tyyy

#

Also what about the area portion

#

Part b

#

It’s asking for in terms of y

lean ruin
#

Write both functions in terms of x

gaunt nebula
#

Let me try

#

Y=X and y/8 = X

lean ruin
#

corrwct

#

Now try integrating

gaunt nebula
#

Is it same limits

lean ruin
#

Yes

#

Wait actually we made a mistake in the last part

#

We shouldn't have used upper limit 4

#

We should have used upper limit = 4 * 8 = 32

gaunt nebula
#

For part a?

lean ruin
#

Yes

#

My bad

gaunt nebula
#

Why is it 4x8

lean ruin
#

Wait no lets redo part a from scratch aight

gaunt nebula
#

Alr

#

What part did we fumble on

lean ruin
#

We need to calculate the shaded area yea

gaunt nebula
#

I see yeah

#

So our boundaries were 4 and 0?

lean ruin
#

First lets get the rectange alrea between 0 and 4

#

Whole rectangle

gaunt nebula
#

Alr

#

Is it 4x4

lean ruin
#

Yes

gaunt nebula
#

So whole is 16

#

And we need to remove non shaded areas

lean ruin
#

Yup

gaunt nebula
#

Do we need to re establish integrals

lean ruin
#

I think we can trivially remove the big one on the bottom by integrating x = y yea?

#

From 0 to 4

gaunt nebula
#

Ye

#

Didn’t we do that

#

Or was that not right

lean ruin
#

No the whole reasoning is flawed there tbh

gaunt nebula
#

So how would we setup the integral

#

Like that?

lean ruin
#

Does this make sense?

gaunt nebula
#

I understand all of it except the upper bound of 1/2

lean ruin
#

well the line y = 8x and y = 4x intersect where

gaunt nebula
#

Oh ok

#

Why u did 4-8x

lean ruin
#

I added the rectangle from 0 to 1/2

#

And subtracted the lower area

#

To get the upper area

#

We now can subtract that area from our total

#

This question is much simpler in y btw

gaunt nebula
#

Ok

#

So know we can anti derive?

lean ruin
#

Yup

#

Lmk what u get

gaunt nebula
#

Got this

lean ruin
#

Yup put in the limits

gaunt nebula
#

I got 7

lean ruin
#

Me too

#

Now try with y

#

You can use 0 and 4 and the functions we wrote earlier (y/8 and y)

#

Just subtract

gaunt nebula
#

I’ll try that

#

Like this

lean ruin
#

The other way around im afraid

gaunt nebula
#

Could you explain why

#

So I don’t make mistake in future

lean ruin
#

Because the bigger area is represented by the area under y not y/8

gaunt nebula
#

Oh ok

#

So this

lean ruin
#

Yup put the limits in

gaunt nebula
#

Answer is back at 7

lean ruin
#

Thats good yea

gaunt nebula
#

I appreciate this a lot man thank you

#

For bearing with me

lean ruin
#

👍 no worries

gaunt nebula
#

Have a good one

#

.close

safe radishBOT
#
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cinder pewter
safe radishBOT
cinder pewter
#

like why

safe radishBOT
#

@cinder pewter Has your question been resolved?

empty gyro
cinder pewter
empty gyro
#

There isn't a specific graph for these, no

#

It's more about intuitively understanding the definition of continuity

#

As an example, consider gas prices as a function of time.

#

Absolutely not continuous. Gas prices can change by an amount at any time, jumping around from any value to any other value

#

It could be 4.50 one moment, then instantly go to 4.70

#

It's not continuous because the price has a sudden jump

#

So, for the first one, can temperature instantaneously jump from one value to the next? Or does it move smoothly?

hybrid plover
#

"continuous functions are functions which you can graph without lifting your pencil"

empty gyro
#

more or less, yea

cinder pewter
empty gyro
#

I would agree. Temperatures changes smoothly. It may rapidly change, say if you start a fire. But that change would not be instant

#

Okay, what about the second one?

cinder pewter
#

Is it the temperature at a certain time but the distance is different each time?

empty gyro
#

Basically, it's temperature as a function of your location

cinder pewter
#

I’d say discontinuous then because the temperature could jump based on the distance

#

I’ll try the last 3 and let u know cuz I get 3 attempts anyways, ty for the help

empty gyro
#

That's hard to say precisely though.

#

On a large scale, I would argue the temp is continuous

safe radishBOT
#

@cinder pewter Has your question been resolved?

safe radishBOT
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lean otter
safe radishBOT
#

Please don't occupy multiple help channels.

lean otter
#

@cunning cloak

cunning cloak
#

Hi

#

Okay

lean otter
#

i put down left and down which are correct

cunning cloak
#

Oh this one

lean otter
#

but i just dk what im doing wrong for the first fill in blank\

cunning cloak
#

Could it possibly be right 8 units

lean otter
#

dont think so

#

cause since we switch left with right its 1/3 correct

cunning cloak
#

So we know that the left 8 units is correct

lean otter
#

indeed

cunning cloak
#

Can u try swapping them out and identifying which part of yoru answer is wrong

lean otter
#

down is correct aswell

#

reflect is whats wrong

cunning cloak
#

Is there a “flip” option

lean otter
#

compress, stretch, shift, reflect

#

i think ive tried everyone

cunning cloak
#

No what i mean is

#

Gttg sry

safe radishBOT
#

@lean otter Has your question been resolved?

lean otter
#

<@&286206848099549185>

celest juniper
#

What's your question

lean otter
#

left and down are right

#

but reflect isnt

#

even if i put shift its incorrect

glacial shale
#

is there a translate

lean otter
#

<@&286206848099549185>

karmic vine
#

ask your query

lean otter
#

it goes left 8 units and down 4 units which is correct

#

so 2/3 is correct

#

but reflect is wrong

#

i need help

karmic vine
#

wait

#

let me figure it out

lean otter
karmic vine
#

ok so

#

i used desmos for explaining

lean otter
#

so it shifts left?

karmic vine
#

no

#

yea shifts left

#

but it isnt getting reflected

#

do i make sense?

lean otter
#

yes

karmic vine
#

great

#

anything else you wanna ask

lean otter
#

uh

#

just am i typing it wrong?

#

cause its still incorrect 💀

karmic vine
#

it is kinda reflecting about the x axis and also shifting towards left

lean otter
#

hm

#

i understand what youre saying

#

just confused on what to put to fill in the blank

karmic vine
#

try writing both reflects and shifts

lean otter
#

could it be one of these perhaps

#

think its just gonna be one word

#

like compress or something

karmic vine
#

ohh

lean otter
#

yea no ones been able to tell me what it is

karmic vine
#

cant you just consult your teacher?

#

are you in university?

#

and what country are you from?

safe radishBOT
#

@lean otter Has your question been resolved?

safe radishBOT
#
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nocturne hinge
safe radishBOT
nocturne hinge
#

W = kx * x

#

k is the spring constant which I thought was found by doing 5/(0.11)^2

#

but apparently I'm supposed to use some other calculation using the natural length of 32 instead?

safe radishBOT
#

@nocturne hinge Has your question been resolved?

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half berry
#

do i pick numbers to plug in based on the limit?

pure agate
#

No. 2^- means that x < 2 which means you need to use the first case.

half berry
#

so do I plug in 2?

#

and 2^+ is the second case

pure agate
#

You evaluate the limit as x->2^- for f(x). f(x) is determined by if x <=2 or x >2.

#

For this problem, yes, you can just use x=2.

half berry
#

got it

#

.close

safe radishBOT
#
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kindred hedge
safe radishBOT
kindred hedge
#

Can anyone help me how to prove this?

#

I’m stuck for the (1/m + 1/M)^2

#

Like I don’t see how it changed to that

#

Is it I let (mM)^2 then only I can get the term I want?

left gyro
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what you do is rewrite mM to be inside the square root

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(mM) = square root of (mM)^2

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this gets moved in to be that (mM)^2 youd need to finish the simplification

safe radishBOT
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@kindred hedge Has your question been resolved?

safe radishBOT
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naive pendant
safe radishBOT
naive pendant
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Got ssstuck

safe radishBOT
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@naive pendant Has your question been resolved?

naive pendant
#

I got it!

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spark thicket
#

A floor plan has a 40: 1 scale. In the drawing, one of the rooms measures 38 inches by 1 1 inches. I need to show my answers to the nearest hundredth, even if it means I need to type zeros. I need to answer the actual dimensions would be # feet by # feet.
The area of the room would be # ft². How should I start to solve this problem?

spark thicket
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How should I start to solve this problem? This is a Proportion assignment.

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<@&286206848099549185>

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hey, help me out plz

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How should I start to solve that problem?

plucky elk
spark thicket
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yeah sorry. That's it.

plucky elk
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Or are those the dimensions of the drawing

spark thicket
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There is no drawing. That's a word problem.

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I need to solve # which are blanks

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#, means number

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Hello?

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<@&286206848099549185>

young nexus
spark thicket
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no, there is no drawing.

plucky elk
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An abstract one

spark thicket
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it's a word problem.

plucky elk
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Draw it yourself

plucky elk
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Like word problems with apples and oranges don't actually give you apples or oranges

spark thicket
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oh ok give me a minute.

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Ok, I drew a pic. Now what?

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can I send a pick? do I send a pick?

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<@&286206848099549185>

plucky elk
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1 inch = ? feet

spark thicket
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ok and then?

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what do I do with 40:1 scale?

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<@&286206848099549185>

young nexus
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1 feet in the map/plan/drawing is 40 feet in reality.

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and do not ping every 5-10 minutes.

spark thicket
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oh sorry...

plucky elk
spark thicket
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hm...

plucky elk
spark thicket
plucky elk
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,w feet in 1 inch

spark thicket
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do I convert 40in to feet?

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as well as 38, and 11?

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sorry, I still don't get what I am suppose to do? This is a Proportion problem.

plucky elk
spark thicket
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38 in is 31.6666667 ft, 11in is 0.91666667, and 40 in is 3.33333. Now what?

spark thicket
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huh?

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38?

plucky elk
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38 inches is not 31.67 feet

plucky elk
spark thicket
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oh yeah

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38 is 3.167 feet

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I used the thing.

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ok now what?

plucky elk
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You know the drawing in feet. Then convert that to real dimensions by using the scale

spark thicket
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how do I do that?

plucky elk
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1 feet in drawing implies 40 feet in real dimensions

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That's what 40:1 scale means

spark thicket
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so i mult 3.33333ft with 3.167 and 0.91666667

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i need to mult somewhere.

plucky elk
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40:1 does not mean 40 inches to 1 feet

plucky elk
spark thicket
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oh right!

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So 1 feet=40inches, now what?

#

.close

safe radishBOT
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hardy sphinx
safe radishBOT
hardy sphinx
#

not sure what to do :D.

hasty wagon
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😄

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multiply both sides by x~

hardy sphinx
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okok

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1 sec

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(3x+3x^2)/(4x^2) = x-1

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?

bleak delta
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3(1+x)/4 = x-1

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this is better

hardy sphinx
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ah

bleak delta
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you multiplied up and down by x

hardy sphinx
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oopsie

bleak delta
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(3+3x)/4 = x-1 at the end

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and linear equality

hardy sphinx
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oh

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is that it

bleak delta
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yes

hardy sphinx
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oh wait i gotta find x

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oh yeah

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forgot

bleak delta
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yes

hardy sphinx
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how do io

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go about this

bleak delta
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multiply 4 both sides

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so /4 disappears

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cancel out with 4

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and the right side is multiplied by 4 also

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3(1+x) = 4x-4

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3+3x = 4x-4

hardy sphinx
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ohhh ok

bleak delta
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subtract 3x from both sides

hardy sphinx
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i got it from here

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ty

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very much

bleak delta
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okay

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you are welcome

hardy sphinx
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.close

safe radishBOT
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tight void
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Yes

eternal carbon
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on which one?

tight void
lean otter
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The first one first please

eternal carbon
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for all of these, what you want to do is convert the given information into tangible equations you can work with

tight void
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Or

eternal carbon
tight void
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1 + C = 10

eternal carbon
lean otter
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Wait so I’m gonna give all the letters a number except for A?

eternal carbon
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i meant what i was talking about

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but that's the idea yes

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since the problem tells you A = 1, you are allowed to use that information