#help-23

1 messages · Page 89 of 1

marsh walrus
bold ferry
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wait so it works if we do 1 + cos(theta) = 1 - cos(theta)

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and then for the left side

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we flip the signs

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-1 - cos(theta + pi)

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= -1 + cos(theta)

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set that = to 1 - cos(theta)

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and that works out

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but what if we do it the other way?

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1 + cos(theta) = 1 - cos(theta)

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we do the stuff on the right side

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1 - cos(theta)
= -1 + cos(theta + pi)
= -1 - cos(theta)
1 + cos(theta) = -1 - cos(theta)
2 = -2 cos(theta)
cos(theta) = -1

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wtf am i doing wrong?

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should i write this on paper

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this is getting very lengthy lol

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oh no his sleeping pills kicked in bleakkekw

safe radishBOT
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@bold ferry Has your question been resolved?

safe radishBOT
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desert cedar
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“The equation x2 = -1 has real solutions.”

desert cedar
#

Would that be true or false?

stray socket
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Graph x^2 and y = -1 and see if they intercept on the Cartesian plane

bold ferry
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or try finding the square root of -1 KEK

safe radishBOT
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@desert cedar Has your question been resolved?

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river yoke
#

Each number in a list is obtained as follows: The first two numbers are 2 and 3; then each number is the units digit of the number obtained by multiplying the previous two in the list. For example the first 5 numbers in the list are: 2,3,6,8,8. What number appears in position 2023?

spiral bane
river yoke
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2,3,6,8,8,4,2,8,6?

spiral bane
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keep going

river yoke
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2,3,6,8,8,4,2,8,6,8,8,4,2,8,6,8,8,4,2

spiral bane
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okay so clearly a pattern

river yoke
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yep 6,8,8,4,2,8

spiral bane
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yeah

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that should be all you need to find the 2023rd term

river yoke
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How?

spiral bane
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well you know that the 3rd term is 6 right

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also the 9th term is 6

river yoke
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I dont get it, I mean what is the relation there, both are divisors of 3? but 2023 is not

spiral bane
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so you can use the fact that 3 + 6n will be 6

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so the start of the pattern

river yoke
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Yes, but how do that helps?

river yoke
spiral bane
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Like if you know term 2022

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Go to the next number in the pattern

river yoke
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Is it 4?

spiral bane
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idk i didnt solve it

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I got 2

river yoke
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Im dumb I guess

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lol hehehe

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But how?

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May you elaborate a little bit?

spiral bane
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okay so

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3rd term is 6

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9th term is 6

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2019th term is 6

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becuase (2019-3) % 6 = 0

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so

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2020th is 8

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2021th is 8

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etc

river yoke
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I get it now, thanks!

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.close

safe radishBOT
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flint beacon
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I need help with this please

verbal vault
safe radishBOT
verbal vault
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.close

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bold temple
#

I forget how to do 1b with variables on both sides. Help?

desert pasture
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transpose

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for instance, re-write it as 7n-2n=16+4

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so 5n=20

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ergo, n=4

bold temple
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Damn I don’t remember that at all

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I’ll brush up on this topic

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Thanks

desert pasture
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transpose is just a fancy word for performing teh same operation on both sides

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instead, you could say, subtract 2n from both sides

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then add 4 to both sides

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which is what you're doing here

desert pasture
bold temple
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Ok

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Thanks

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.closw

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.close

safe radishBOT
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peak crane
peak crane
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.close

safe radishBOT
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west lily
#

Need some help with Complex Exponentiation

safe radishBOT
west lily
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how would you find (z1)^7

split ether
#

Consider rewriting z1 in polar coordinates

west lily
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haven't learnt all of those yet

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i think the expectation for us atm is to just do it step by step

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like this was what the professor did during lecture

safe radishBOT
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@west lily Has your question been resolved?

west lily
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.close

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gritty glacier
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Find $\sin [\arccot {\cos (\arctan 1)}]$

flat frigateBOT
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bettim

gritty glacier
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Is it $\frac{1}{\sqrt{2}}$

flat frigateBOT
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bettim

thin bridge
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no

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how are you getting that

gritty glacier
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So

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Arctan 1 is pi/4

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Nvm

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I took hypotunes as base

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Mb

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.close

safe radishBOT
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gritty glacier
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.reopen

safe radishBOT
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gritty glacier
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Wait no

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So

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Cos of pi/4 is 1/√2

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I entered this in a triangle

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I got base and opposite to be 1

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And hypote5to ne root 3

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Hypotenuse is root 2

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Now cot is

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1

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Arccot is pi/4

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Sin of that is 1 by to2

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Root2

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@thin bridge

thin bridge
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I got base and opposite to be 1
you don't really care about the triangle where cos(pi/4) is 1/sqrt(2)

gritty glacier
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So what do I do

thin bridge
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you're interested in a right triangle where cot(theta) = 1/sqrt(2)

gritty glacier
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So theta is pi/4 ?

thin bridge
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no

gritty glacier
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Okay sry right

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Opposit dis root 2

thin bridge
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you determined that arctan(1) is pi/4
and that cos(pi/4) is 1/sqrt(2) right?

gritty glacier
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Ye

thin bridge
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applying that your expression simplifies to

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$\sin(\arccot(\frac{1}{\sqrt{2}}))$

flat frigateBOT
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ℝamonov

gritty glacier
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Okayy

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Now what should I do

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Convert to rad?

thin bridge
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no

gritty glacier
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Wait

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It doesn't give a regular angle

thin bridge
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let $\theta = \arccot(\frac{1}{\sqrt{2}})$ \
(do NOT make any attempt to determine the numerical measure of $\theta$) \
draw a right triangle where $\cot(\theta) = \frac{1}{\sqrt{2}}$

flat frigateBOT
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ℝamonov

gritty glacier
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So opposite is root 2 , base is 1, hypotenuse is root 3?

thin bridge
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yeh,
and what's the sin of theta in that triangle

gritty glacier
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$\sqrt{\frac{2}{3}}$

flat frigateBOT
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bettim

gritty glacier
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Thanks

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.close

safe radishBOT
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light harness
#

Hello, limx->pi/3 sin(3x)/1-2cos(x)

I did that and got 0, am I correct?

lean otter
gritty glacier
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You means x tends to 0?

lean otter
light harness
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My bad

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X means to pi/3

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I got confused with another exersise

lean otter
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x means to? Don't you mean x tends to?

gritty glacier
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Direct substitution

light harness
gritty glacier
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Wait

brave wolf
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doesnt seem correct

light harness
gritty glacier
light harness
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Hm

lean otter
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Probably wrong... sin(3pi/3) is 0, and 1-2cos(pi/3) is also 0, and since they're both trig-based I would be surprised if the limit was 0 because that'd mean sin(3x) shrinks faster than 1-2cos(pi/3)

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@light harness Can you show your workings?

light harness
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Give me a sec

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It's the B) one

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Sen = sin

lean otter
flat frigateBOT
lean otter
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Since when does it actually rotate the way I asked it to

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Anyways

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How did you get that 2cos(x)=2cos^2(x)-1?

light harness
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Isn't that an identity?

lean otter
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Close enough

light harness
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Oooooh

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I see I see

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So what do I do with the 1-2cosx?

gritty glacier
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Again you wrote the question wrong,?

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Was is 2cosx or cos2x

light harness
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2cos

gritty glacier
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Then how can you use the formula?

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In denominator in second step

light harness
gritty glacier
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Ye

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Your step is incorrect ig

light harness
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So whats the correct thing?

gritty glacier
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2cos²x-1 is not correct formula for 2cos x

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Afaik there isn't any formula for 2cosx

light harness
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So, for this problem what am I supposed to use or do?

safe radishBOT
#

@light harness Has your question been resolved?

safe radishBOT
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south linden
safe radishBOT
south linden
#

could someone help me understand what is going on in this question?

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im not entirely sure how to solve?

faint seal
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did you understand what the top part means

south linden
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i think it may mean i use that in the limit instead of the e^3x^3

faint seal
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but did you understand what it MEANS

south linden
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not quite

faint seal
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how would you represent e^(x^2) using that expansion?

south linden
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series of (x^2/n!)^n right?

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if im understanding right

faint seal
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well

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what about the power of n

south linden
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oh right i forgot about that

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i currently have this

faint seal
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the power of n doesn't cover the denominator

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just the numerator

south linden
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oh yeah cant read lol

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alright so ive fixed that

faint seal
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try writing out the first few terms

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in that summation

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remember that 0! = 1

south linden
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i have a strong feeling it may be the terms to the right of it?

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but will write some quickly

faint seal
south linden
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so its that but opposite signs

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so assuming the first 3 terms cancel

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i now rewrite the summation starting at 3?

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possibly like this

faint seal
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well

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you can't just assume it

south linden
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):

faint seal
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but you're right

south linden
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ok yeah i did the first two

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so assuming the pattern

faint seal
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notice that after n=3, all the resulting terms will have a power of x greater than 9

south linden
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yup

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so degree num>denom

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or would there be some cancellation i could do?

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i dont think so

faint seal
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*except for the first term

south linden
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right first term is same degree

faint seal
#

correct

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so all the later terms are going to tend to 0

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since x goes to 0

south linden
#

would it not be inf in this case?

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since the numerator is increasing in exponents?

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oh

faint seal
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why would it be infinity

south linden
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as x goes 0

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sorry

faint seal
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yes

south linden
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read wrong

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so the overall limit would just be 0

faint seal
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so you only have to consider the first term of the summation

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which would be?

faint seal
south linden
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oh

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oh right

faint seal
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remember the first term will have the same degree

south linden
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first is same deg

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it will be that

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which is

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one second

faint seal
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should be -9/10

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I believe

south linden
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maybe i messed up

faint seal
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show your work

south linden
faint seal
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yes

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that's the same as -9/10

south linden
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oh wait

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/3

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yeah

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ok makes sense

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so would there be a way to show all other terms tend to 0, or is it sort of trivial by showing deg P >deg Q

faint seal
#

you can take an x common in the other terms

south linden
#

ok

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thank you

#

.close

safe radishBOT
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mystic ledge
#

Hey! Why is Pi an irrational number when its clearly depictable in 22/7, a form of p/q where q is not 0?

brave wolf
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pi=3.141592653589... 22/7=3.142857142857...

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so they are not same

hollow prawn
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fun fact; there are better fractional round-offs too like 355/113 approximation is accurate to six decimal places

marble hamlet
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High school students can't handle that big of a value

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Since 22/7 is mostly used in highschools

elfin yew
#

i used pi

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in hs

safe radishBOT
#

@mystic ledge Has your question been resolved?

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safe radishBOT
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obtuse widget
#

i just need help on what type of shape this is, dont need help solving for variables

wheat osprey
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How do I solve this

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(Ignore my writing beside the question)

obtuse widget
#

<@&286206848099549185>

obtuse widget
#

is it a square

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or rhombus

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i cant tell by the diagnols

granite tiger
obtuse widget
granite tiger
#

More likely a rectangle

obtuse widget
#

a rectangle has congruent diagnols

granite tiger
#

Well, if the diagonals cannot be touched

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Then it is likely a trapezoid

obtuse widget
#

oh

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ok thx

#

.close

safe radishBOT
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fair leaf
#

how do I turn this into a better equation that I can plug into a calculator and solve for. I have a duct tape solution using a spreadsheet that is just awful.

fair leaf
spiral bane
fair leaf
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solving for Pn

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a is some constant I insert

spiral bane
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okay so

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I think it would be best to write out some terms

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its not the simplest sequence that you can figure out in your head

fair leaf
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like right out what P(2) would look like?

spiral bane
#

yeah

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P3, P4, etc

fair leaf
#

assuming a is 55

spiral bane
#

okay dont do that

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do it by hand

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the whole point is that you dont simplify anything

cold scaffold
#

I need help

spiral bane
#

so that you can see the pattern

cold scaffold
#

Can you help me plz?

spiral bane
#

no

fair leaf
spiral bane
#

😔

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thats not what I meant

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keep a as a variable

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dont write any other decimals aside from 0.1 and 0.001

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in fact

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set 0.1 to a variable

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and 0.001 to another

fair leaf
#

like this ?

spiral bane
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okay thats a lot better

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but now plug in P2, P3

fair leaf
#

what does that mean

spiral bane
#

well you still have a recursive sequnce here

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you want to not have any value of P be dependent on other values of P

fair leaf
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I don't get how you can remove P(2)

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if you replace it with something else isn't that just still P(2) with a different name?

spiral bane
#

the whole point here is that you want to find an explicit function

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so for example P3

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you dont want P2 in there

fair leaf
spiral bane
#

you want to use P(3) = (z + q(a^2/z) + q(a^2/((z + q(a^2/z)))

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you want P(n) to be a function of just z, q, and a

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$P(3) = (z + q(a^2/z)) + q(a^2/((z + q(a^2/z)))$

flat frigateBOT
spiral bane
#

hmm actually idk anymore

fair leaf
spiral bane
#

yeah

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I think I got it

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instead of z + q(a^2/z)

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nope nvm

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the issue is that there are two places to use z

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so it gets really confusing

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cause then you get an infinite fraction

safe radishBOT
#

@fair leaf Has your question been resolved?

wheat osprey
spiral bane
#

@wheat ospreythis channel is occupied

wheat osprey
#

Ahh

wheat osprey
wheat osprey
#

Idk 😐

wheat osprey
fair leaf
#

<@&286206848099549185>

spiral bane
#

is this hw

fair leaf
#

solving for Pn, a is some constant I insert

spiral bane
#

or your own question

fair leaf
#

my own question

spiral bane
#

it may not be solvable by hand

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I was trying to solve it algebraically

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if its your own question ig you can just do what you were doing before and plug into excel/sheets

safe radishBOT
#

@fair leaf Has your question been resolved?

spiral bane
#

@fair leaf

safe radishBOT
#

@fair leaf Has your question been resolved?

safe radishBOT
#

@fair leaf Has your question been resolved?

spiral bane
#

@fair leaf I responded to you

safe radishBOT
#

@fair leaf Has your question been resolved?

safe radishBOT
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hallow quartz
#

my tired brain can't comprehend. how do u go from top to bottom?

hallow quartz
#

more context

empty gyro
#

,w (k^(1/3))/(k^(3/2))

hallow quartz
#

ok yeah 1/k^7/6 was what i got

hallow quartz
empty gyro
empty gyro
#

That would be my guess

hallow quartz
#

yeah, i divided by k^1/3, in order to get it in a format of a P-series test

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and i got 1/k^7/6

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which converges

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and that's what the text book says

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so i guess this explanation has a typo or smth then

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.close

safe radishBOT
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lament hazel
#

In which case A and B can have infinite common multiples?

lament hazel
#

Where a and b are whole numbers

quasi bison
#

are you sure you asked exactly the question you wanted to ask?

quasi bison
#

"Let a, b ∈ Z. When do a and b have infinitely many common multiples?"

lament hazel
#

Yes

quasi bison
#

the answer is: whenever they are both nonzero

lean otter
#

Well well look who it is again

quasi bison
#

and i am not convinced there wasn't some kind of mistake

lean otter
#

A pair of positive integers always has infinite common multiples

lament hazel
quasi bison
#

||inb4 it turns out that yes there actually was a mistake in wording||

lament hazel
quasi bison
#

reframed, you say.

#

are you 100% certain you did not make a mistake when reframing it?

#

can you show the original?

lament hazel
#

I just wanted to see a general case of this, as the answer of this is infinite but i wrote 3

faint seal
#

Any two non zero whole numbers will have infinite common multiples

#

I think you gave the answer 3 since you thought it was common factors

lament hazel
#

That is what i thought

faint seal
#

But even if it was common factors, 3 is not the fight answer

lament hazel
#

Its 2

#

1 and 3 right?

lean otter
#

Nay, 2 doesn't divide 15

#

It's actually one you might not've thought of

lament hazel
#

3 and 1*

lean otter
#

lament hazel
#

Yes

#

So 2 points more to mention in my notes

#

1 is the factor of all numbers

#

And number of non zero whole nos will have infinite common multiples

lean otter
safe radishBOT
#

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fallow knoll
#

Did I get the surface area for this shape correct

fallow knoll
#

*The top side of the rectangular prism isn’t considered

cold thunder
#

What do you meen by the topside

#

Can you color it...?

fallow knoll
#

The side between the two shapes

#

And don’t worry about the top 2 equations

cold thunder
#

Okk

fallow knoll
#

Why is it w^2/4

cold thunder
#

Wait

#

The top triangle is isocele right ?

fallow knoll
#

No I just drew it weird

#

The slant heights are equal

#

I think you forgot to include the bottom side as well

#

Actually it could be isosceles

#

Because I’m optimising it to have the lowest surface area

cold thunder
#

Ooooh I see

fallow knoll
#

I just wanted to check if my formula was right

cold thunder
#

I think its correct

#

Just add wl to what I wrote ig

fallow knoll
#

Yeah cause w/2 all squared is same as w^2/4

cold thunder
#

Yup

fallow knoll
#

Alright thanks

#

.close

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cold thunder
#

@fallow knoll just wondering because you said you want the smallest area what if it an equilateral triangle ?

frank glen
#

Hmm

#

If optimizing for lowest surface area then the triangles are preferred to be turned closer into the flat rectangular surface

safe radishBOT
#

@cold thunder Has your question been resolved?

cold thunder
#

But then he won't have a lowest area for the rectangle ( roof) ?

fallow knoll
#

I don’t really think it matters if I get the smallest one possible

#

Just my working out

#

For that specific shape

cold thunder
#

okkk

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peak lily
#

hey

safe radishBOT
peak lily
#

i've been working on this problem: , for all positive integers d, there exists an integer n such that ⌊(n+1)/d⌋ = ⌈n/d ⌉

#

<@&286206848099549185>

dry trench
#

are you asking for values of n?

peak lily
#

it's a proof, and i'm asking for the steps

dry trench
#

or both n and d

peak lily
#

don't want solution

#

i'm proving whether it's true

dry trench
#

sorry then

peak lily
#

all good

safe radishBOT
# peak lily <@&286206848099549185>

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

zinc token
#

which is the solution.

dry trench
#

@peak lily do you know mathematical induction?

zinc token
#

Is this proposition even true?

supple shore
#

Hum yes I'm not sure it's even true

#

Like if I take d=1 it's impossible ?

safe radishBOT
#

@peak lily Has your question been resolved?

peak lily
#

no

supple shore
#

No what ?

#

@peak lily

#

Maybe it's more something like for all positive integers d>2

peak lily
#

.close

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opaque pasture
safe radishBOT
opaque pasture
#

I need help solving this. I don't know where to start, I am not skilled in algebra. I will need step by step help from the beginning.

hexed dune
#

@opaque pasture f(2)

#

means

#

put 2

#

where x is

opaque pasture
#

3*2

#

?

hexed dune
#

yh

#

but obv the rest aswell

opaque pasture
#

-1.4

#

how do I get it as the fraction

eternal fjord
#

Replace all the x with 2. f(x) means a function that takes in a value and assigns it to x (in this case).

opaque pasture
#

i just did that..

wraith locust
#

Solve it

opaque pasture
#

-1.4

#

is what I got

opaque pasture
wraith locust
#

change it to fraction form

opaque pasture
eternal fjord
#

6 - 8 + 3 all over 5

quasi bison
safe radishBOT
# eternal fjord 6 - 8 + 3 all over 5

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

wraith locust
#

-1.4 is -14/10

#

Then simplify

opaque pasture
tall bough
#

how did u get to 1.4

opaque pasture
#

-1.4

tall bough
#

how did u get it

eternal fjord
#

Lexa show your work

wraith locust
#

Maybe the calculator does not have fraction form. It gives the answer in linear or decimal form

opaque pasture
#

3x2-2x2^2+3/5

#

that is what i input

wraith locust
#

use parenthesis when typing math equations hehe

eternal fjord
#

All of that is over 5, not just the 3

tall bough
#

thats not -1.4

opaque pasture
#

it is for me

tall bough
#

then keep living in that delusion

wraith locust
#

use parenthesis

opaque pasture
wraith locust
#

That's why

opaque pasture
wraith locust
#

Use parenthesis

opaque pasture
#

@tall bough fuck off nerd

alpine path
#

Chilll

eternal fjord
#

Wrap the top part of the fraction with parenthesis

opaque pasture
#

alr

tall bough
#

theres no really need to use a calculator for this

eternal fjord
#

Like (…..) / 5

opaque pasture
#

so

opaque pasture
#

alr I got the answer right

#

thanks @eternal fjord

#

and u can @tall bough suck my dick

#

.close

safe radishBOT
#
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tall bough
#

😆

eternal fjord
#

But yes you don’t need a calculator. Just try 32 - 22^2 + 3 then put that all on top of 5

wraith locust
eternal fjord
#

Aww it messed up my *

safe radishBOT
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broken yew
broken yew
#

.close

safe radishBOT
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tall bough
#

Theyre too young to be my friend

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wet gust
#

so

safe radishBOT
wet gust
#

i got this problem

#

ive done steps a-d but the last step is confusing

#

im given 251.3g mass with a string that is 1.3m long and a speed of 1.3

#

its a pendulum swinging in a circle motion

#

i have to calculate the centripetal acceleration with fc=mac=mV^2/r

#

using the last part i get centripetal acceleration = .33

#

i find the tension with t=m((v^2/r)+g) and get 2.8N

#

the last problem wants me to determine the centriepetal force acting on the mass

misty coral
wet gust
#

t=.2513(1.3^2/1.3+9.8) = 2.8

#

my bad wrong part

#

.2513*(1.3^2/1.3)=.33

misty coral
#

so that would be the centripetal force

wet gust
#

that is centrieptal acceleration isnt it ? or are they the same thing

misty coral
#

no not the same thing, if we say Σ F = ma_r = mv^2 / r , then a_r = v^2 / r

wet gust
#

Fc is centripetal force Ac is centripetal acceleration

#

and im at the Fc=Mac im just confused ngl

misty coral
wet gust
#

i did it backwards

misty coral
#

yep

wet gust
#

lol oopsies

#

thanks

#

so the Ac

#

is just V^2/R correct ?

misty coral
#

yes

wet gust
#

ugh i went and confused myself again

#

so no.1 says calculate the centripetal acceleration of the mass

#

is the answer to that just V^2/R ?

misty coral
#

yes

wet gust
#

and the Fc is m(V^2/R)

misty coral
#

yes

wet gust
#

okay thanks so i now have ac = 1.3 t = 2.8 and fc = .33

misty coral
#

what are you doing for the tension?

wet gust
#

t=m((v^2/r)+g)

wet gust
misty coral
#

I would disagree I think

wet gust
#

did i calculate wrong ?

#

thats the formula it gives me to use for tension

misty coral
#

oh sorry I see the mass is factored out

#

sure

#

👍

#

and im assuming this is when the pendulum is at the lowest point?

wet gust
#

okay thanks for the help greatly appreciated and yes

#

.close

safe radishBOT
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fresh finch
#

Name a segment that is a radius. How long is it?
Show or explain your reasoning.

fresh finch
#

I'm confused, and don't know where to start.

#

I need help ASAP.

mortal topaz
#

If diameter is 15=2r , then radius is 7.5 cm AC=AD

fresh finch
#

but its asking for the radius

bold ferry
#

Radius is half of the diameter

twin bough
#

you have to measure with the ruler the radius

#

(i dont speak english very well..)

fresh finch
#

But it asking for one of them

bold ferry
twin bough
mortal topaz
#

Radius is the same from the center point

bold ferry
#

the diameter of 15cm is given, so radius is half

fresh finch
#

half of 15?

bold ferry
#

yes

#

15 / 2

fresh finch
#

Divided?

twin bough
fresh finch
#

so the answer is 7.5

mortal topaz
#

Yes

fresh finch
#

ok.

#

thank you

twin bough
#

u´re welcome

fresh finch
#

Wait

twin bough
fresh finch
#

Its asking to my work

twin bough
fresh finch
#

how can i show my work

river sky
#

Look

#

Diameter = 15cm

#

Diameter/2 = radius

#

15/2 = radius

#

7.5= radius

#

Simple

#

That's all the work

#

That you need

twin bough
#

you have to measure with the ruler the radius, like if is the G or something else

river sky
#

Every segment there is a radius too

#

AC=AD=AE=AG=AB = 7.5cm

fresh finch
#

ok.

river sky
#

Indicating they all are radii

fresh finch
#

one more thing

fresh finch
#

Name a segment that is a diameter. How long is it?

#

This is the last question

river sky
twin bough
#

the middle point?

river sky
#

A is Mid Point generally

fresh finch
#

Ooh

#

So it would be C-D conneting

twin bough
river sky
fresh finch
#

But its asking how long is it

river sky
#

CD is 15

twin bough
river sky
#

It's given

#

Right below CD it's written 15

#

Meaning

#

CD is 15cm

fresh finch
#

Ok.

#

Thank you

river sky
#

Alright

twin bough
river sky
#

.close

safe radishBOT
#
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latent tendon
#

I feel like this is more of a "am i reading the problem correctly for a mathematical problem", so heres my question. There are the equations given to me: (1st page) and these are the data given to me (page 2) so is ra, r1 rb, r3 and c is c1
Image
Image

latent tendon
#

I assume so because

safe radishBOT
#

@latent tendon Has your question been resolved?

safe radishBOT
#

@latent tendon Has your question been resolved?

safe radishBOT
#

@latent tendon Has your question been resolved?

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pulsar spade
safe radishBOT
pulsar spade
#

This is what I've done so far. I just wanted to know if I'm going about the problem correctly, as this is the first question of the assignment.

safe radishBOT
#

@pulsar spade Has your question been resolved?

safe radishBOT
#

@pulsar spade Has your question been resolved?

safe radishBOT
#

@pulsar spade Has your question been resolved?

safe radishBOT
#

@pulsar spade Has your question been resolved?

spiral bane
#

see if you can just get a online calc to do it

#

like wolframalpha

safe radishBOT
#

@pulsar spade Has your question been resolved?

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frosty granite
#

For part c u get x squared =144

safe radishBOT
frosty granite
#

I’m confused about why x would be -12 rather than 12 given the domains

safe radishBOT
#

@frosty granite Has your question been resolved?

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frosty granite
#

.reopen

safe radishBOT
#

frosty granite
#

<@&286206848099549185>

alpine path
#

The function goes from the domain of g to the range of f.

frosty granite
#

okay hm

alpine path
#

Still confused about something?

#

Better explanation maybe:

If x^2 = 144 (what you said) Is the answer.

x has two possible answers. Check if both these values plugged in g, give a value that is in the domain of f. If both happen to fall in the domain of f, then both values are correct. Since both values can be chosen to get f(g(x)) = 17.

#

@frosty granite

#

Always be careful when squaring roots though, since you might get an answer that is not a real number, when plugging that number back into the square root.

frosty granite
#

yeah that makes way more sense

alpine path
#

good luck!

frosty granite
#

.close

safe radishBOT
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upbeat swan
#

Is TREE(3) closer to TREE(2) or to TREE(4)?

safe radishBOT
tall bough
#

difference between tree(3) and tree(4) is way larger than the difference between tree(2) and tree(3)

upbeat swan
#

Why

tall bough
#

The sequence of TREE(n) grows incredibly quickly as n increases

safe radishBOT
#

@upbeat swan Has your question been resolved?

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gritty glacier
#

$\arctan ( 1-x), \arctan (x) , \arctan(1+x)$ are in AP , find $x^3 +x ^2$

flat frigateBOT
#

bettim

upbeat swan
#

.close

gritty glacier
upbeat swan
#

Sry lol

#

I thought it was my channel

gritty glacier
#

its okay :3

#

<@&286206848099549185>

lean otter
gritty glacier
#

arithmetic progression

lean otter
#

That means that

arctan(1-x) + arctan(1+x) = 2 arctan (x)

gritty glacier
#

yes

#

i did that

lean otter
#

Have you seen something about formulas of the sum of the arc?

#

arctan(x+y) in terms of arctan(x) and arctan(y)

gritty glacier
#

$\arctan x + \arctan y = \arctan (\frac{x+y}{1-xy})$

flat frigateBOT
#

bettim

gritty glacier
#

this?

lean otter
#

Formulas like that

gritty glacier
#

in terms of arctan x and arctan y?

#

np

#

nop

lean otter
#

I would try to consider this to write arctan(1+x) + arctan(1-x)

#

Considering 1+x instead of x and 1-x instead of y

gritty glacier
#

im getting $\arctan(\frac{2}{-x^2})$

flat frigateBOT
#

bettim

gritty glacier
#

is that right?

lean otter
#

Maybe arctan(2/x²)

gritty glacier
#

so xy would be (1-x)(1+x)

#

that is (1+x-x-x^2)

#

no?

#

so 1 - xy would be -x^2

lean otter
#

we have that

2 arctan(x) = arctan(x)+arctan (x)

So 2 arctan x = arctan (2x/(1-x²))

gritty glacier
#

you told to consider the other two arctans

lean otter
gritty glacier
#

we have to take the - sign inside oh got it

#

so it is x^2 only

#

right?

lean otter
#

In the denominator yes

gritty glacier
#

tahnks got it

#

is the final answer 1?

lean otter
#

So we have

arctan(2/x²) = arctan(2x/(1-x²))

#

Do you agree?

gritty glacier
#

e

#

ye

#

i did it all

#

i got

#

$x^3 + x^2 = 1$

#

right?

flat frigateBOT
#

bettim

lean otter
#

Right

#

That is it

gritty glacier
#

thnks

#

.close

safe radishBOT
#
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gritty glacier
#

helo

safe radishBOT
gritty glacier
#

find $\frac{dy}{dx}$ if $ 2x+y =\sin y$

flat frigateBOT
#

bettim

gritty glacier
#

i got $\frac{2}{\cos y-1}$

#

but answer says wrog

flat frigateBOT
#

bettim

jade magnet
#

i think is -2 not 2?

gritty glacier
#

how?

jade magnet
#

oh nvm i just did it the other way around 💀

gritty glacier
#

💀

#

is the -1 in denominator right?

#

it is given as -3

jade magnet
#

i got -2/1-cos(y) which is the same so i dont know lol

thin bridge
#

can you show what you're entering into the system

gritty glacier
#

nvm the pdf's fuked up i guess

thin bridge
#

thought you were entering that into some online thing and that came out as wrong

gritty glacier
#

also $2x + 3y = sin x$

flat frigateBOT
#

bettim

gritty glacier
#

im getting

#

$\frac{1-x\cos x}{x}$

jade magnet
#

through what steps?

gritty glacier
#

wait

#

wrong ques

#

it is 3x not 3y

#

so no y terms

#

so dy/dx is 0?

#

.close

safe radishBOT
#
Channel closed

Closed by @gritty glacier

Use .reopen if this was a mistake.

safe radishBOT
#
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restive palm
#

i need help here

safe radishBOT
final plinth
#

D=0

misty coral
#

what are the conditions for the discriminant if the function touches the x -axis at one point

misty coral
#

apply that here then

#

what are your a,b,c values?

restive palm
#

a = 1
b = -k + k
c = 8

#

?

misty coral
#

I would say no.

obsidian oracle
#

That would just make b = 0

misty coral
#

your a value is the coeff of your x^2 term, your b value is the coeff of your x, and then c is the rest of the jargan , just constants

restive palm
#

oh

#

a = 1
b = 0
c = 8

#

like that?

misty coral
#

k still exists

obsidian oracle
#

But the coefficient in x isn't 0, is it?

restive palm
misty coral
#

yes.

#

that makes b?

restive palm
#

b = 0?

misty coral
#

no.

obsidian oracle
restive palm
#

oh k

misty coral
#

close

restive palm
#

um

#

x?

#

wait no

#

1?

obsidian oracle
#

You want to write ax² + bx + c

#

So far we have a = 1

#

C = k+ 8

#

So that's x² + bx + k + 8

restive palm
#

the coefficient of x in b is k right?

misty coral
#

not just k

obsidian oracle
#

That would make it x² + kx + k + 8

restive palm
#

-k?

misty coral
#

yes

obsidian oracle
#

Yes!

restive palm
#

ah nice

#

let me solve now

#

so the eq looks like

-k - 4(1)(k+8)^2

#

just to make sure

#

oh one sec

#

wait what's wrong here

misty coral
#

what do your notes say the discriminant is given by

restive palm
#

b-4ac^2?

misty coral
#

no, did you refer back to your notes

restive palm
#

oh I think I wrote it wrong

misty coral
#

its given by b^2 - 4ac,

restive palm
#

alr thanks

#

so the eq after simplifying is k^2-4k+32

#

?

lean otter
#

k^2-4(k+8) =/= k^2-4k+32

misty coral
#

^

restive palm
#

is that the same?

lean otter
#

Not equal bro

restive palm
#

ohh

lean otter
#

What is negative 4 times k? what is negative 4 times 8?

restive palm
#

oh -32

lean otter
#

keep going you almost have the solution.

restive palm
#

so the answer is 4 and -8

#

for D

lean otter
#

???

restive palm
#

right?

lean otter
#

(k+4)(k-8) is indeed the factor but not the roots

misty coral
#

the factors would be (k+4)(k-8) = 0 yes

lean otter
#

If we are looking for k we need to find the roots.

restive palm
#

another q sry lol

misty coral
#

wait

#

you havent finished this one

restive palm
#

-4 and 8?

misty coral
#

alr sure KEK

lean otter
#

Broooo

restive palm
#

lol

misty coral
#

I think you could do this one on your own

lean otter
#

𝐁𝐎𝐌𝐁𝐀𝐒𝐓𝐈𝐂 zoomEyes

restive palm
#

the answer is +-9?

#

o wait 3

lean otter
#

My dumbass set it equal to (x-a)^2 and then had to undergo 2 variable changes.

restive palm
#

lol

misty coral
restive palm
#

3 and -3?

misty coral
#

yes

restive palm
#

ah great

#

thank you all

#

ill close now

#

.close

safe radishBOT
#
Channel closed

Closed by @restive palm

Use .reopen if this was a mistake.

#
Available help channel!

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Remember:
Ask your math question in a clear, concise manner.
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.

frank musk
#

Can someone help me/tell me what is missing in my proof?

frank musk
#

I've been told it does not cover all cases, but I don't see it.

#

The proposition I'm trying to prove is

#

Show that no number n with n ≅ 3 (mod 4) can be written as a sum of two integer squares

white hollow
#

present your proof

frank musk
#

Is it visible?

white hollow
#

yes that's essentially the proof

#

actually I don't see a problem with it

#

let me check again

frank musk
#

The feedback I got was

#

"The assumption that m and n have to be odd and even respectivly does not cover all cases."

white hollow
#

uhh

#

I don't understand that feedback, what you wrote seems perfectly fine

#

(odd, odd) (odd, even) (even, odd) and (even, even) are the possibiltiies for m and n and you covered all of them

frank musk
#

Yeah that's what I thought as well. I'm not sure what's wrong

#

if anything is wrong at all. I was only given 50%

white hollow
#

I believe whoever gave you that feedback is mistaken

frank musk
#

Is there any cases at all where this doesn't apply?

white hollow
#

perhaps they expected you to explain why both m and n having the same parity does not work

frank musk
#

But why give me that feedback then?

white hollow
#

it does cover all cases

#

I don't know why they gave you that feedback

frank musk
#

It spesifically said that id doesn't cover all cases, which is weird

white hollow
#

the only perceivable issue I can come up with is what I just mentioned

white hollow
frank musk
#

Ok, thanks!