#help-17

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vocal sleetBOT
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edgy sundial
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I don't really get the second activity parallelogram UVWX. The first part of the activity the KJHG that I needed to find the similar number

4.) Jh= 8 since it is its pair
5.) Lh= 6 because it is it's pair also
6.) Kh= 6+6=12 since lh is 6 and kl is also 6

But since the uvwx problem have their own number should I use the same method I used with the kjmg? This lesson is called quadrilateral thankyou!

edgy sundial
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Yes starting from number 7.)

fair thorn
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WZ and UZ are a pair (using your notation)

edgy sundial
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Oh ok do I still need to use the same method I use on the 4.) TO 6.) Activity?

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To*

fair thorn
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yes

edgy sundial
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Oh ok thankyou!

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ornate spoke
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hi, i need help on limits with sin(x) type of stuff

ornate spoke
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do i analyze the behavior of sin as it would naturally approach the (x) value?

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ex: limx->0 sin(x)/sin(sqrtx)

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i don't know if this is 0 or 2/1

fair thorn
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multiply and divide by x

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use sin x/ x = 1

ornate spoke
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so sin(x)/sin(x^2) = 1?

viral copper
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$\lim_{x \to 0} \frac{\sin x}{\sin \sqrt x}$

twin meteorBOT
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NEONPerseus

viral copper
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This is your question?

ornate spoke
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yes

viral copper
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$\lim_{\theta \to 0} \frac{\sin \theta}{\theta} = 1$

twin meteorBOT
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NEONPerseus

viral copper
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Do you know of this?

ornate spoke
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i do, but don't understand how it applies

stone terrace
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I think it would make sense to look at the taylor expansions here, have you ever done such a limit?

viral copper
viral copper
stone terrace
viral copper
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I hope you know the algebra of limits?

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The limit of a sum, difference, product, and quotient, is the sum, difference, product and quotient of the limits

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$\lim_{x \to 0} \frac{\sin x}{x} \cdot \frac{1}{\frac{\sin \sqrt x}{\sqrt x}} \cdot \sqrt x$

twin meteorBOT
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NEONPerseus

viral copper
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@ornate spoke Do you understand this?

ornate spoke
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ohhhh

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that does make sense

viral copper
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You should be able to compute this limit quite easily now

vocal sleetBOT
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vast shale
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600x+600y+200z=52000

15x+6y+kz=1170

60x+30y+10z=4100

how to find the value of k in 3x3 simultaneous equation please help

vast shale
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<@&286206848099549185>

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<@&286206848099549185>

sterile forum
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Stick to pinging Helpers only once, please.

vocal sleetBOT
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vocal sleetBOT
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silver timber
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Hi does n*sin(n) has no limit bc we dont know if sin(n) will be equal to +1 or -1 ?

peak matrix
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as n approaches infinity?

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If so, then yes, it's related to the fact you mentioned, but some functions like sin(n)/n have the limit (equal to 0 in this case) although we dont know whether sin(n) will be +1 or -1.

vocal sleetBOT
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vocal sleetBOT
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echo plaza
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ok the numerator is an arithmetic sequence, and the denominator is a geometric. how could i seperate them though? i need a hint

hard atlas
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what would you get if you differentiate sum x^k

vocal sleetBOT
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@echo plaza Has your question been resolved?

echo plaza
hard atlas
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derivative? have you not had these yet?

crisp breach
viral copper
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You can just divide the series by 3 and subtract to get a GP

echo plaza
crisp breach
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Apply the formula of gp summation afterwards

viral copper
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Although I do agree the derivative would be hella faster

echo plaza
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ah

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i see

echo plaza
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bu thanks everyone!

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vocal sleetBOT
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vocal sleetBOT
quick fjord
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you are going to have to be more specific

vocal sleetBOT
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@knotty canopy Has your question been resolved?

vocal sleetBOT
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@knotty canopy Has your question been resolved?

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@knotty canopy Has your question been resolved?

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vocal sleetBOT
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vivid gyro
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hello!
i had this question in my maths exam and i still don't know what to do. even though i know what a would have to be for the quadractic equasion to only have one x=0, i don't know how the e bit influences the result.
would be glad if someone could help me with this! thanks 🙂

vivid gyro
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not sure whether the terminology is correct, im from germany

frozen bobcat
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"exactly one x=0"? or exactly one x such that f(x) = 0?

vivid gyro
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yup, thats what i meant

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not sure if you can translate it like that but i meant zero points

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wait i think i already solved it

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.closr

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.close

vocal sleetBOT
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steep edge
vocal sleetBOT
#
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
crimson jetty
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Would you. Check. the first. time. you asked.

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Garlic gave you a hint

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asking another 10 times wont change that hint

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If youre still stuck then show your progress

vocal sleetBOT
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@steep edge Has your question been resolved?

steep edge
crimson jetty
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Then why don't you ask that directly

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You couldve asked them that rather than closing the channel the first time round

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(for reference, i dont know)

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uve opened so many channels that i cant even see the hint I was referring to

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I couldve sworn I saw Garlic send a hint related to ST being a diameter for some reason

steep edge
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I am sorry Im new

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What can I do now??

crimson jetty
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What you need to prove looks a bit loke the intersecting chord theorem to me

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Oh nvm I see why

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Thats my hint

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SFET lie on a circle

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see if you can figure out why.

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This question basically only requires you to know your circle theorems

steep edge
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What is the circle theorem??

crimson jetty
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All theorems in geometry

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that involve a circle

crimson jetty
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you need another 1-2 I think

steep edge
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Can't i solve it with trigonometry??

crimson jetty
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Probably, but I don't see the need.

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I don't know how myself.

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try some similar triangles stuff

steep edge
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Can you please try to solve it and send a pic of the solution

crimson jetty
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No we don't do that.

steep edge
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Can you tell me more about the interesting chord theorem

crimson jetty
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look it up.

steep edge
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Ok

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Ok so according to the theorem FO.OT=SO.OE how to proceed

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??

crimson jetty
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Not going to help further than the hints I gave above, gtg.

steep edge
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Do you know how to solve it

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??

hybrid flicker
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you can also solve it with a horrific amount of pythagoras's theorem

steep edge
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Can you teach me to solve it in the circle way please

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I want to learn

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I m getting it a little

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What to do next

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How to proceed??

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Please help

hybrid flicker
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the chords theorem tells you that SI¡IE = TI¡IF = r^2 - d^2, with I the intersection point, r the radius of the circle and d the distance between the center of the circle and the intersection point

steep edge
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So how can I use it here

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I suck at geometry man😭😭😭😭😭😭😭😭😭😭😭😭😭😭

hybrid flicker
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well, first of all, what is the radius here?

steep edge
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Half ST

hybrid flicker
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yes!

steep edge
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Ok!!

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What's next

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How do you know so much

hybrid flicker
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to be honest my competences in geometry problems are limited

steep edge
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Which standard are you in

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??

hybrid flicker
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i'm in engineering school

steep edge
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I am just in 10th

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Can you tell me how to proceed please

hybrid flicker
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to be honest I do not know if this whole chord theorem is going somewhere, unless you're willing to go for the leap of faith that ST and IO (O being the center of the circle) are perpendicular

steep edge
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Ok thanks for the help

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You helped me a lot

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@crimson jetty thanks to you also

hybrid flicker
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wait I can show you a solution with pythagoras

steep edge
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Ok

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Show me

hybrid flicker
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So, let's use pythagoras's theorem that ST^2 = SE^2 + ET^2

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and use pythagoras's theorem again to get ST^2 = (SR^2 - RE^2) + ET^2

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This was the first step

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our second step is to use the other right triangle in which ST is, can you find which one ?

steep edge
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SFT ?

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Or SET?

hybrid flicker
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correct !

hybrid flicker
steep edge
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Oh

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Ok

hybrid flicker
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So, can you use pythagoras's theorem on SFT?

steep edge
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ST²=SF²+FT²

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Whats next??

hybrid flicker
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alright, next we will want to get rid of the FT^2 term, because it will not be useful for us

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maybe using pythagoras's theorem on another triangle ?

steep edge
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ST²=SF²+(RT²-RF²)

hybrid flicker
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Correct !

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So, ST²=SF²+RT²-RF² = SR² - RE² + ET²

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our trick now is to write that ST² = 1/2*(ST²+ST²)

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so ST² = 1/2(SF²+RT²-RF² + SR² - RE² + ET²)

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Now, let's note that RT² = (RE + ET)²

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Can you expand that?

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Actually sorry

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Even though what I wrote is true, it will not help us here

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What WILL help us though, is that RE = (RT - TE)²

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now, can you expand that?

steep edge
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RE²=RT²+TE²-2RT.TE

hybrid flicker
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correct!

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Let's also use that RF = SR - SF

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so what is RF² ?

steep edge
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SR²+SF²-2SR.SF

hybrid flicker
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Yes!

hybrid flicker
steep edge
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Thank you so much for your help 😊😄

hybrid flicker
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no problem 👍

steep edge
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.close

vocal sleetBOT
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vocal sleetBOT
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clever quartz
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How can i find the sum of this power series

clever quartz
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i know that this is the result but i have no idea how to reach it

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a>0

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i found that the radius of convergence is R = 1/e^a

vocal sleetBOT
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@clever quartz Has your question been resolved?

clever quartz
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<@&286206848099549185>

vocal sleetBOT
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@clever quartz Has your question been resolved?

vocal sleetBOT
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@clever quartz Has your question been resolved?

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vocal sleetBOT
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sterile hollow
#

what do they mean by "compare this to the actual error you found in part a)"?

vocal sleetBOT
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@sterile hollow Has your question been resolved?

sterile hollow
#

<@&286206848099549185>

sullen estuary
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find the approx using t10 then find the actual error by |actual value - approx|

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in part b find the difference between that and error found using Et

sterile hollow
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i found the results

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im just confused with what they mean by compare

vocal sleetBOT
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@sterile hollow Has your question been resolved?

sullen estuary
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i assume compare as in how similar they are

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are they super accurate to each other or are they not

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is one signifcantly bigger than the other, etc..

sterile hollow
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ah alright

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ill take note of that, thank you very much 🙂

vocal sleetBOT
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versed knoll
vocal sleetBOT
versed knoll
#

How do you prove that segment ad is parallel to segment bc?

vocal sleetBOT
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@versed knoll Has your question been resolved?

versed knoll
#

<@&286206848099549185>

cursive turret
#

what does AD || BC mean for the (four) angles at D?

vocal sleetBOT
#

@versed knoll Has your question been resolved?

cursive turret
# versed knoll Pareller

if this should be an answer to "what does AD || BC mean for the (four) angles at D?" I do not understand it.

versed knoll
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So ab is parallel to dc and angle a is congruent to angle c

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This stuff is given

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And now you’re trying to prove that ad is parallel to bc.

vocal sleetBOT
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cobalt fiber
#

h

vocal sleetBOT
cobalt fiber
#

am i doing this right

cobalt fiber
#

<@&286206848099549185>

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so 7.5 rev/min is angular velocity and 188.5in/min is linear velocity?

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help please

viral copper
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youre right

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,calc 60*pi

twin meteorBOT
#

Result:

188.49555921539
viral copper
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yes

cobalt fiber
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So angular velocity is literally just the rev/unit

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Nothing else needed

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And then v=rω to solve for linear velocity

viral copper
cobalt fiber
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So like in this case it’s rev/min

viral copper
#

$\bar{\omega} = \frac{\Delta \theta}{\Delta t}$

twin meteorBOT
#

NEONPerseus

viral copper
cobalt fiber
#

Is that the angular velocity

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This is for precalc

vocal sleetBOT
#

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left grotto
vocal sleetBOT
left grotto
#

Last part of question 6

icy flower
#

,rotate

twin meteorBOT
vocal sleetBOT
#

@left grotto Has your question been resolved?

vocal sleetBOT
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fallow solstice
#

n(U) = 200
n(A’ and B’ and C’) = 25
n(A’ and B and C’) = 15
n(A and B) = 20
n(A and B’ and C) = 10
What is n(A) n(B) n(C)

fallow solstice
#

This is a 3 circle venn diagram

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i can’t seem to figure it out

vocal sleetBOT
#

@fallow solstice Has your question been resolved?

vocal sleetBOT
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modest cedar
vocal sleetBOT
modest cedar
#

For part a, how would I find the slope?

tall ore
#

Are you struggling to show dy/dx = that thing, or is it that you don’t know how to get gradient or tangent from the differentiated equation

modest cedar
#

Honestly both

vast shale
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Damn

modest cedar
#

Fr

vocal sleetBOT
#

@modest cedar Has your question been resolved?

mental junco
#

for part a: the equation of tangent is y = mx + c

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to find m: just substitute (-1, 1) in the dy/dx given in the question
to find c: just substitute (-1, 1) in your new equation that you get after getting m

mental junco
# modest cedar

part b is basically asking you to find all points where dy/dx is undefined,

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so you will just say that this happens when 3y^2 -x = 0

modest cedar
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Okay thank you so much

mental junco
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welcome

modest cedar
#

Oh so for part b would it come out as coordinates?

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Like (0,0)

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?

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Wait nvm it states that in the problem

vocal sleetBOT
#

@modest cedar Has your question been resolved?

vocal sleetBOT
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desert hornet
#

$$\sin^x(x) = e^{x\cdot\log\sin(x)}$$

twin meteorBOT
#

kheerii

desert hornet
#

absolutely not

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no downloads

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show me your work

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$\sin x^x \ne \sin^x(x)$, but otherwise you're correct

twin meteorBOT
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kheerii

crimson jetty
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the hell is this file

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please delete

#

looks like a suspicious file like it is

vocal sleetBOT
#
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gaunt panther
vocal sleetBOT
gaunt panther
#

need some help on iii plz

#

the intersection point of the planes is (1, -2, 0)

#

ive done this so far

#

these r the formulas in the formula booklet

vocal sleetBOT
#

@gaunt panther Has your question been resolved?

rugged orchid
#

How did you get a point

gaunt panther
#

u find a point

#

from the point u then find a line

#

i think

rugged orchid
#

Part b doesn’t find a point it finds an angle

#

Oh no that’s part ii

gaunt panther
#

yh

rugged orchid
#

Ah

#

Well that point doesn’t necessarily have to be the shortest

gaunt panther
rugged orchid
#

Well the intersection of 2 plane should be a line you can just find

#

So x-2y-5=2x+3y-z+4 describes a line in 3d that satisfies to be on plane 1 and plane 2

#

You just need to find the shortest path from point A (4,0,-1) to this line

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crimson sedge
vocal sleetBOT
crimson sedge
#

wouldn't you have to make the equation into cartesian equation first?

vast shale
#

Well, it's not a polar integral

#

But the integral is fine

crimson sedge
#

so is $\int y\frac{dx}{dt}$ a rule?

twin meteorBOT
#

yomiko

crimson sedge
#

nvm i found a video on it

#

.cflose

#

.close

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tranquil lodge
#

I put 22=39x-5x^2 into Desmond but I’m not sure which number is the right one

lime gorge
#

Hmmm

#

DesmondhmmCat hmmCat

#

Yea so show what u got

crimson sedge
#

what did you get t as

tranquil lodge
#

I’m not sure if it’s 0.612 or 7.188 or

dense stump
#

"Find all values of t"

tranquil lodge
#

So 0.612

#

And another one

dense stump
#

You said both lol

tranquil lodge
#

oh

#

So if they get rounded

#

To nearest hundredth

#

Would it be 0.61 and 7.19

dense stump
#

For this kinda question, you should prob think of a rocket. it's gonna go up and back down and therefore hit 22 feet at 2 different times

dense stump
tranquil lodge
#

YESSSSIR

#

thx lads

dense stump
#

np

lime gorge
#

Model rocket

open cave
#

Model rocket

#

Model. Rocket.

lime gorge
#

Look first 2 words Xd

dense stump
#

pretend I said nothing

open cave
dense stump
lime gorge
#

Me when blighter blights isleep

crimson sedge
vocal sleetBOT
#

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crimson sedge
vocal sleetBOT
crimson sedge
#

where did i do wrong

#

this is the rest of the working out

silk comet
#

why not substitute u = cos(t) in your first line?

crimson sedge
#

$\int 2sin^3t dx$ \ $y = (sint)^4$ \ $\frac{dx}{dy} = 4(2sin(t))^3 \cdot -2cos(t)$

twin meteorBOT
#

yomiko

crimson sedge
#

I've done it wrong

#

i didin't compare

vocal sleetBOT
#

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limber snow
#

I have a question, I was watching a video tutorial on vector calculus. I was wondering how do you compute this. In what other do you multiply and combine like terms?

limber snow
#

.close

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echo plaza
#

oh wait

#

sorry

#

you can reopen @limber snow

limber snow
#

Np I open another one

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brazen veldt
vocal sleetBOT
brazen veldt
#

so I know that F is not conservative but G is

#

lmk if anyone knows what to do here

#

is r(t)= < -3- 4t, 0>?

#

where I am stuck is how do I approach this?

vocal sleetBOT
#

@brazen veldt Has your question been resolved?

main spade
# brazen veldt is r(t)= < -3- 4t, 0>?

The path in the diagram is not a straight line from A to B. You must first have a curve which is the line segment from (-3, 0) to (-1, 0). Then a circular curve as shown in the diagram.

#

I'd approach it like this. I'd calculate c_2 in the opposite direction since you can then use standard polar coordinates and then just take the negative of that result and add it to the line integral over the first line to get the desired result.

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#

@brazen veldt Has your question been resolved?

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haughty spoke
#

I need help

vocal sleetBOT
haughty spoke
#

So we’re doing statistic for the Central Limit Theorem to Compute a probability but the problem is that I don’t know how they get the number 0.7517 and they didn’t really fully explain on how they got to that number to find their final answer 0.2483?

paper depot
#

I don’t know how they get the number 0.7517
z-tables or calculator

#

actually no

#

they explicitly say they got it from a table

haughty spoke
#

Yeah I have a table that my professor gave me and it doesn’t have that exact number

paper depot
#

show me your table

haughty spoke
#

This is the table

vocal sleetBOT
#

@haughty spoke Has your question been resolved?

cyan marsh
#

Hey, I have questions relating to logics gates, algebraic expression and standard deviation if any can help!

vocal sleetBOT
#

@haughty spoke Has your question been resolved?

vast shale
cyan marsh
#

oh okay ill send now!

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dusky glacier
#

anyone can help to solve this problem?

vocal sleetBOT
dusky glacier
#

which option should choose then?

paper depot
#

okay i did NOT mean to send a super react on that one

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@dusky glacier Has your question been resolved?

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quasi cypress
#

.open

#

.open

#

if abc = 1, prove this statement

vocal sleetBOT
#

@quasi cypress Has your question been resolved?

quasi cypress
#

<@&286206848099549185>

cerulean compass
#

I think you can prove by induction here

quasi cypress
#

how tho?

cerulean compass
#

Or you can just simplify it

#

like a/b+c/d=(ad+cb)/bd

quasi cypress
#

i still dont understand

cerulean compass
#

Then all the inverses should just cancel out

quasi cypress
#

if u would mind, can u prove with steps?

cerulean compass
#

For now combine the fractions

#

Into one

quasi cypress
#

im not getting that much of an insight, sorry

#

alright wait

#

b/ab+1+b + c/bc+1+c + a/ac+1+a

#

what should i do now

cerulean compass
#

Into 1 fraction

cerulean compass
#

Since you would also have to apply to the other side

#

Well I guess it could work

cerulean compass
quasi cypress
#

oh

#

alright

#

thats why i was confused

#

how do it do it then?

cerulean compass
#

I would substitute in abc in from 1 and try to simplify

quasi cypress
#

wait nvm i understand now

#

thank you

#

.close

vocal sleetBOT
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unreal sparrow
#

Did i answer this correctly?

vocal sleetBOT
#

@unreal sparrow Has your question been resolved?

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paper depot
#

troll

lost yarrow
#

please dont waste helper time with shitposts

paper depot
#

how old are you

lost yarrow
#

.close

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restive fulcrum
#

i need help with series of tasks involving this function

vast shale
restive fulcrum
#
  1. Domain
  2. Odd or even?
  3. N0
  4. Vertical horizontal and oblique asimptote
  5. Local extremes, intervals of monotony
  6. Points of inflexion, concavity and convexity
  7. Make a graph
flat whale
#

doing 7 will help you do the rest

restive fulcrum
#

on the graph the function doesnt matter only the points asked of me

flat whale
#

oh

restive fulcrum
#

domain is x=/=3 right?

flat whale
#

how did you get that

restive fulcrum
#

the number in the bottom of fraction musnt be 0

flat whale
#

do you know how to solve x^2 = 9?

#

there are two solutions

restive fulcrum
#

i get -x^2=-9

#

isnt that just x=3

flat whale
#

x^2 crosses 9 at two different x

restive fulcrum
#

so how do i get the solution

flat whale
#

do you know how to plot x^2?

#

or algebra rules for square root?

restive fulcrum
#

not quite

restive fulcrum
#

so its 3 and -3?

flat whale
#

yes

restive fulcrum
#

just different +/-?

#

alright so is it odd or even?

flat whale
#

check the definition of odd and even and see if your function satisfies one of them

restive fulcrum
#

i know even means its symetrical to y and odd and its symetrical to the centre

#

someone told me easiest way to check is just to input f(0) and if the functions arent the same after input its odd is that true?

flat whale
flat whale
restive fulcrum
#

so if input f(0) or f(-x) and its not the same as the base function its odd?

flat whale
#

i don't know how you conclude that

flat whale
restive fulcrum
#

i dont understant that well, if you were to solve this how would you

flat whale
#

check that equation

restive fulcrum
#

so -x^2/9-x^2 must be equal to f(-x)?

flat whale
#

if it's odd, yes

restive fulcrum
#

so its odd in this case

#

oh wait nvm

#

its even

#

so next for horizontal asimptote i got 1/8 is that correct?

#

<@&286206848099549185>

restive fulcrum
#

how so

flat whale
restive fulcrum
#

isnt it lim->1 of the function

flat whale
restive fulcrum
#

thats how we solved it in class

flat whale
#

H.A. stands for horizontal asymptote

flat whale
restive fulcrum
flat whale
flat whale
restive fulcrum
#

the number i decide my limit to go towards

flat whale
#

the problem decides it for you

flat whale
restive fulcrum
#

sorry i cant understand it

#

is a= f(x)=0?

flat whale
#

you did that in part 1

flat whale
restive fulcrum
#

so a=3?

flat whale
#

that's one of the VAs yes

restive fulcrum
#

ok so for the other 2 asimptotes i just plug in infinity and lhopital it till it gives me a normal number?

restive fulcrum
#

horizontal asimptote is just pluging infinity in right?

#

and oblique asimptote is just pluging infinity into f(x)/x which gets me K and then i get L by inputting infinity into f(x) -Kx

#

y=kx+l

#

.close

vocal sleetBOT
#
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cinder oyster
vocal sleetBOT
cinder oyster
#

Hello

#

Before i do anything here should i get rid of that 2 infront of the X

thin vale
#

that you should

ornate seal
#

Factor out coefficient of x^2 you meant

vocal sleetBOT
#

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vast shale
#

Is my graph correct

vocal sleetBOT
formal pond
#

clean your screen bro

rugged bolt
#

@vast shale Yes its good

vast shale
rugged bolt
#

Think about it

vocal sleetBOT
#

@vast shale Has your question been resolved?

vast shale
rugged bolt
#

Doesn't matter if I know or don't know, did u think?

potent stirrup
vast shale
#

What

potent stirrup
#

stop questioning the integrity of helpers, else try to follow the steps advised.

vocal sleetBOT
#

@vast shale Has your question been resolved?

vocal sleetBOT
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vast shale
#

This whole page

vocal sleetBOT
rose raft
#

all?

vast shale
#

well

#

okay maybe the first one

#

to start

#

how in the name of god do I find the central angle measure

#

idek what that means

trail mesa
vast shale
#

OH

#

TYSM ❤️❤️

trail mesa
#

your welcome

vocal sleetBOT
#

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shell magnet
vocal sleetBOT
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@shell magnet Has your question been resolved?

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vast shale
vocal sleetBOT
vast shale
#

I got this

#

Is this correct?

sullen estuary
#

that looks right

vocal sleetBOT
#

@vast shale Has your question been resolved?

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tiny trench
#

Hi so

vocal sleetBOT
tiny trench
#

Ive been doing some factoring and stuff today

#

i was doing some basic stuff and all of a sudden a number is infront of the X

#

2x^2+7x-4

#

Like its not starting with x^2

#

like perfect sq

#

rather it has a number so Im not sure how i would start that one

rugged vortex
#

You'd have to think about factors of the leading coefficient. More so, I'd like to deal with the positive factors of it

#

So in this case, your leading coefficient is 2, whose positive factors are 1 and 2

#

Since we only have two factors, we don't need to fret: it implies that 2x^2 + 7x - 4, if factorable, can be broken down into (2x + a)(x + b). If you foil this out:

2x^2 + (2b + a)x + ab = 2x^2 + 7x - 4

This also implies:

2b + a = 7
ab = -4

#

In words, find two factors that multiply to -4, but the sum of one plus double the other equals to 7

tiny trench
#

:think:

cinder oyster
#

I do on my paper and show right after

#

if u want

tiny trench
#

na its ok i am trying to do it and ill show

#

Oh i forgot to mention

#

THat part of this is to find the domain

#

Let me upload the picture of my work

#

Looks good?

#

And by the way

#

The domain how woukd it be

#

it says to write in interval not

#

like this one?

summer lichen
#

,rotate

twin meteorBOT
summer lichen
#

,w find the roots of 2x^2 + 7x -4

tiny trench
#

Oh man i make a mistake

#

and i see it

#

i took out a positive 4

#

and wrote it as a negative later on

#

i think

#

should be x+4 ah man

summer lichen
#

I would have grouped them differently

#

maybe as (2x^2 + 8x) + (-x -4)

#

but it should be the same either way

tiny trench
#

I really have to stop making this tiny mistakes

#

Mid term tomorrow and i constantly do these things

#

IM gonna redo every problem on taht test like 3 times

summer lichen
#

so what did you get for your answers?

tiny trench
#

I take picture and make upload

summer lichen
#

okay

tiny trench
#

New domain i make a arrow next to it

summer lichen
#

why'd you write the domain with all those unions?

tiny trench
#

the equestion make me put in interval notation only

#

Oh that not how i do it?

summer lichen
#

That is the correct notation, but you don't need the unions.

tiny trench
#

Oh

late ingot
#

if you think about it, you can simplify the intervals you got to (-inf, +inf) as the domain.

tiny trench
#

Ah that is good idea

#

Would be easier thanks

late ingot
#

conveys the same information.

#

no need for more than one interval here since there are no restrictions requiring it.

vocal sleetBOT
#

@tiny trench Has your question been resolved?

vocal sleetBOT
#
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hasty drum
#

I have a point estimator $\hat{\mu }=\frac{n\overline{Y}}{n+\lambda }$. I have shown that this is unbiased when $\lambda = 0$. I used $E\left[\overline{Y}\right]=\mu$ to show this. My next goal is to show the bias and MSE of $\hat{\mu }=\frac{n\overline{Y}}{n+\lambda }$ when $\lambda > 0$. I calculated the bias to be $\frac{n}{n+\lambda }\mu -\mu$ and the MSE to be $\left(\frac{n}{n+\lambda }\right)^2\cdot \frac{\sigma ^2}{n}+\left(\frac{n}{n+\lambda :}\mu :-\mu :\right)^2$. My next goal is to show that for some $\lambda$, $MSE[\hat{\mu}] < MSE[\overline{Y}]$. I have run into issues here. Thanks! 🙂

twin meteorBOT
#

catnwaffles

vocal sleetBOT
#

@hasty drum Has your question been resolved?

hasty drum
#

<@&286206848099549185>

vocal sleetBOT
#

@hasty drum Has your question been resolved?

vocal sleetBOT
#

@hasty drum Has your question been resolved?

vocal sleetBOT
#

@hasty drum Has your question been resolved?

rapid swift
#

well, actually lemme ask

#

what do you think the MSE of [Y bar] is?

hasty drum
#

I think I solved it with lambda = sigma^2/mu^2 by taking the derivative of the RHS with respect to lambda, setting it equal to 0. That lambda is sigma^2/mu^2. Then it is a simple argument to show the inequality holds for that

rapid swift
#

you can actually get away with not solving that minimization problem I think

#

if you evaluate the derivative of the MSE wrt lambda for the shrunk estimator at 0, you'll find that it's not zero

hasty drum
rapid swift
#

I mean the estimator you're given here

#

I called it "shrunk" because the thing is shrinking it

#

okay yeah

#

so if you compute the derivative of the MSE, you get

#

$- \frac{2 \mu^{2} n \left(\frac{n}{\lambda + n} - 1\right)}{\left(\lambda + n\right)^{2}} - \frac{2 \sigma^{2} n}{\left(\lambda + n\right)^{3}}$

twin meteorBOT
#

Saccharine

rapid swift
#

then if you substitute lambda = 0

#

this simplifies to

hasty drum
#

Why are we substituting lambda = 0?

rapid swift
#

well I'm calculating the derivative at 0

#

$- \frac{2 \sigma^{2}}{n^{2}}$

hasty drum
#

ah alright

twin meteorBOT
#

Saccharine

rapid swift
#

you get this

#

this is always negative by assumption

#

so suppose we say that M(x) is the MSE of the estimator at lambda = x

#

we know that M(0) = MSE[Y bar], since the estimator coincides with Y bar if lambda = 0

#

and further, we know that M'(0) < 0

#

so therefore, by some real analysis proof that you can do, there exists an x such that M(x) < M(0)

#

or you can just say it's intuitively obvious

#

I believe the rigorous proof will require some sort of epsilon-delta argument or possibly the mean value theorem

#

but it's an obvious fact in a sense

hasty drum
#

So $\lambda =\frac{\sigma ^2}{n}$ is incorrect?

twin meteorBOT
#

catnwaffles

rapid swift
#

honestly not sure. I didn't actually evaluate for that

hasty drum
#

NervousSweat math stats is killing me

rapid swift
#

I just gave an argument that doesn't actually rely on picking a specific value for lambda

#

because I could imagine that computing the MSE for specific lambda is just annoying to do

hasty drum
#

Luckily I only need a 45 on the final to pass this class

rapid swift
#

basically you know that the MSE is decreasing at lambda = 0

#

so therefore, you can just make lambda = some small number, and you know the MSE will go down

#

more formally, you know that M(0) = MSE[Y bar], and M'(0) < 0, so therefore, you know there's some x such that M(x) < M(0) = MSE[Y bar]

hasty drum
#

Yeah I just used optimization + inequalities to show it

#

your way is a lot betterhype

rapid swift
#

I think your particular value of lambda does work, because it's the value that produces the minimum MSE

#

but you don't really need that

#

whatever floats your boat I guess

#

your way is more direct

hasty drum
#

thank you! what book did you use to learn? C&B?

#

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brisk flume
#

how do I find the derivative of this function?

brisk flume
#

I dont know where to even start

hushed pewter
#

You can start by simplifying $x/\sqrt{x}$

brisk flume
#

so x ^ 1/2

twin meteorBOT
brisk flume
#

and i would bring that up to the numerator yes

hushed pewter
#

Yup. Then use power rule

brisk flume
#

when do i involve the -3x into the equation?

#

+*

#

helloo?

hushed pewter
#

Take derivative of both terms separately

#

(f+g)'(x)=f'(x)+g'(x)

brisk flume
#

i dont understand

#

ive yet to see that method in class

hushed pewter
#

Ah you may want to look it up then. You need it here unless your just doing the basic f(x+h)-f(x) stuff

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quaint sphinx
#

Just wanna ask if my work is correct

vocal sleetBOT
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@quaint sphinx Has your question been resolved?

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normal loom
#

Can we apply binomial formula to anything??, for example 7^1/5 so we write it as (1+6)^1/5 now the question is the Binomial expansion valid on non integral powers

normal loom
#

If not then what is the formula for fractional powers

peak matrix
#

Im pretty sure it works, but it gives infinite sum

normal loom
#

Oh ok then i will look into it

#

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normal loom
#

How do i define Sine function for reflex angles using polygons/triangles etc

#

This is what i mean ,

#

How do i find Sin A in third case ??

dull bear
#

.reopen

vocal sleetBOT
#

✅

dull bear
#

Before you lose your channel lol

normal loom
#

Thanks

normal loom
#

But still

#

Can somebody answer this catshrug

vocal sleetBOT
#

@normal loom Has your question been resolved?

vapid current
#

360 - A will be in 4th quadrant

#

If A is less than 90 degree

#

Sin is negative in 4th quadrant

#

So -sinA

normal loom
#

So we can find negative of Sin A but not Sin A for reflex angles

vapid current
#

Sin(360-A) = - SinA

normal loom
#

Yep i thought of that earlier too but still i dont understand how we cannot directly find Sin A if A is reflex

#

I gotta consult to more people

#

Thanks for help tho!

#

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#
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vocal sleetBOT
#
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faint marsh
#

I need help with my math homework cause I've been stuck on a problem for half an hour
I'm on independent study atm so it's difficult for me to follow some parts
Here's the problem and an example of the graphic when I input an answer

astral pilot
#

(3X+1)(3X+1)

sullen thunder
#

what about: $(x+9)(x+\frac19)$ ?

twin meteorBOT
faint marsh
#

it has to be a quadratic expression with only integers

astral pilot
faint marsh
#

that worked thank you very much!

#

didnt think about changing the x lol

astral pilot
#

.close

faint marsh
#

well a but whatever

#

ty

astral pilot
faint marsh
#

.close

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inland gyro
vocal sleetBOT
sudden compass
#

<@&268886789983436800>

sullen thunder
#

<@&268886789983436800>

sterile forum
#

👍

inland gyro
#

not sure how not sure how to start this

hybrid fossil
#

u sub

inland gyro
#

what do i do from here

viral copper
#

You didn't change the limits

inland gyro
#

what do you mean?

rough barn
outer warren
#

in the process of substitution,
u = x - a
for your new lower bound, when x=3, u = ?

vocal sleetBOT
#

@inland gyro Has your question been resolved?

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vocal sleetBOT
#
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half summit
#

I got -52/25, is it right?

vocal sleetBOT
half summit
#

-2.08 in decimal

#

$$ \frac{13n^8}{25m^3} $$

twin meteorBOT
#

rynite

half summit
#

but I first simplified the expression to that

#

then plugged the numbers

torpid talon
#

yeah that looks right

half summit
#

alr, thanks

#

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#
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tiny trench
#

pls anyone no one wanna answrr me 🥲

tiny trench
#

this is for quadratic form

#

ula

strange crater
#

What is your question

tiny trench
#

Basically

#

When i was doing quadratic formula this part

#

B^2 for me was 9 and -4ac = to -12

#

so in the square root

#

would it be 9 - - 12

#

which basically is 21

strange crater
#

What do you think?

tiny trench
#

to be honest thats what i did in my test

#

so i believe yes

strange crater
#

And why are you doubting it?

tiny trench
#

because i make mistakes like this too much 🥲

strange crater
#

It's just arithmetic. It would be 21, yes

tiny trench
#

.close thnx

vocal sleetBOT
#
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vast shale
#

A is the point (-5,2). B is the point (7,-2). C is the point (-2,5)
b) find the equation of the line perpendicular to line AB and passing through point C <@&286206848099549185>

strange crater
#

!15m

vocal sleetBOT
#

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.

#

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.

vast shale
#

<@&286206848099549185>

#

help me

#

A is the point (-5,2). B is the point (7,-2). C is the point (-2,5)
b) find the equation of the line perpendicular to line AB and passing through point C

vocal sleetBOT
#
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feral sentinel
#

why divide by (5n) and not just (5)?

vocal sleetBOT
feral sentinel
#

use u = cos^(n-1)(5t) and dv = cos(5t)dx

#

I get v = sin(5t)/5

#

where did the n come from?

strange crater
#

The exponent for cosine

feral sentinel
#

but when integrating by parts, uv doesn't have an n term in the denominator

#

uv = cos^(n-1)(5t) sin(5t)/5

#

did i miss a step?

strange crater
#

isn't it $uv - \int v du$?

twin meteorBOT
#

cwatson

tawny lily
#

i know the pythagore

feral sentinel
#

so we just look at the uv part?

pale widget
#

You need more than just the uv part. You should do the entire integration properly and then match the pieces instead of trying to do only the minimum necessary

feral sentinel
#

both terms hav 1/n has a constant and i have no clue where it came from

vocal sleetBOT
#

@feral sentinel Has your question been resolved?

vocal sleetBOT
#

@feral sentinel Has your question been resolved?

vocal sleetBOT
#

@feral sentinel Has your question been resolved?

feral sentinel
#

unless there's an error with the solution

#

.close

vocal sleetBOT
#
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pale widget
#

There comes a critical step when people give you advice that you need to follow it instead of just assuming there is an error and the suggestion is irrelevant.

vocal sleetBOT
#
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feral sentinel
feral sentinel
#

.close

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eternal glacier
vocal sleetBOT
eternal glacier
#

Both of these are the same right?

dusk dew
#

No

#

X doesn't go up to the exponent

#

It stays beside e with and the x would be raised to negative 1

eternal glacier
#

I thought +x in exponent is multiply by x? Wouldn’t -x in exponent be divide by x?

spiral inlet
#

$e^{2-x} = \frac{e^2}{e^x}$, not $\frac{e^2}{x}$

twin meteorBOT
#

tatpoj

dusk dew
eternal glacier
#

Oh right.. ty

fiery raptor
#

Wow genius

eternal glacier
#

So 2^(2+1) would be 2^3 = 8?
Or also 2^2 * 2?

dusk dew
#

2^2 all times 2

#

Or u mean 2^(2*2)

eternal glacier
#

All of these are correct?

dusk dew
#

Yeah

eternal glacier
#

Ty

#

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#
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near carbon
vocal sleetBOT
near carbon
#

Could someone help me with he second part of the question pls

#

I’m not sure how to answer

rose raft
#

!status

vocal sleetBOT
#
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
near carbon
#

1

#

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covert salmon
#

linear algebra question

vocal sleetBOT
rose raft
covert salmon
#

This is true right?

untold helm
#

It's right

covert salmon
#

Why?

dull bear
#

,w [[0,1], [0, 0]] * [[0, 1], [0, 0]]

dull bear
#

,w [[0,1], [0, 0]] * [[1, 0], [0, 0]]

dull bear
abstract anvil
#

Good counterexample

covert salmon
#

How did u think of that so quick?

#

Like what came to your mind?

dull bear
#

It just felt wrong and usually counterexamples can be simple like that, there was one that was similar and the counterexample there was similar

#

of course set A, B, C as appropriate and of course they satisfy all they ask haha

covert salmon
#

ty

#

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#
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vocal sleetBOT
#
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solemn spear
vocal sleetBOT
solemn spear
#

im not exactly sure what this is asking

#

the options are less than or equal to

#

and greater than or equal to

#

whats the relationship between x and f(x)? and what does that mean for the derivative function?>

chrome hornet
#

Derivative at a point is the slope of the function at that point now put conditions and find slope at each point

solemn spear
#

yes i know derivative is slope

#

what does it mean if the x and f(x) are less than or greater than 0 ?

chrome hornet
#

See the graph on -ve x side

#

If they are asking for x<0

#

If for f(x)<0

#

Then see the graph of -ve y axis

solemn spear
chrome hornet
#

Negative

solemn spear
#

idk what you mean

chrome hornet
#

For f(x)<0 you have to check for 3rd and 4th quadrants slope

solemn spear
#

you mean 2 and 3?

#

cause thats where its on the negative side of x

chrome kite
#

for x>0 u check 1 and 4; for f(x)>0 u check 1 and 2

#

f(x)=y

solemn spear
#

damnit how could i forget that

#

ok