#help-28

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proven jay
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but how i do find it otherwise

desert steppe
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*tan(m) = x/y

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strong ferry
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strong ferry
mighty crescent
# strong ferry

From the graph, you can see the local minimum and local maximum

strong ferry
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I havent done this before can you elaborate

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I need to find out the minimums too

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@mighty crescent

mighty crescent
strong ferry
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no

mighty crescent
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Local maximum is the left one and local minimum is the right one

strong ferry
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how do I find -1 and 17

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I think I see

mighty crescent
strong ferry
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the maximum is over (-1,0) and then I plug in -1 to the function to get the second number

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ty ty

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what does this mean? @mighty crescent

empty sapphire
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the maximas are y outputs. You'd find the value by plugging them into the equation above.

In this case something like this

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,w 2(-1)^3 - 6(-1)^2 - 18(-1) + 7

glossy valveBOT
empty sapphire
#

so that's your relative maximum

strong ferry
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I got that part

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does the part I underlined mean anything?

empty sapphire
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not really, that's just the graphing window. It's says that the x values are from -5 to 5 with each tick being 1 unit and the y values are form -60 to 60 with each tick being 10 units

strong ferry
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ah ok thank you

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plain fox
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plain fox
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where am i wrong ?

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plain fox
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<@&286206848099549185> pls help

winter yacht
plain fox
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it is clear

winter yacht
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Wait, sorry

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my brightness was low lol

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Gtg sorry

plain fox
lusty vector
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i think u can use agp here

plain fox
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whats agp?

lusty vector
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arithmetic-geometric progression

plain fox
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no i need to use binomial

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plain fox
#

can someone help me with this?

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mighty crescent
lost lichen
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Hello

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Can you help with vector

mighty crescent
plain fox
mighty crescent
plain fox
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but that i cant use that , i have to use binomial

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if i could use those methods , this question was a piece of cake

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but i have to use the binomial and stuff

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civic reef
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can anyone solve?

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Please don't occupy multiple help channels.

narrow helm
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close either this or your previous channel.

civic reef
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they are both different questions

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i'll ask this later after the prev is solved then

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@atomic kayak Has your question been resolved?

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@atomic kayak Has your question been resolved?

atomic kayak
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<@&286206848099549185>

gilded panther
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yess

strong galleon
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Can someone please explain this to me?

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<@&286206848099549185>

mighty crescent
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@atomic kayak Has your question been resolved?

atomic kayak
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No

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hushed tendon
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Hey

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hushed tendon
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What am I missing here? how did she get to this?

vast fossil
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It's by definition

hushed tendon
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what happened to m+1?

narrow helm
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n+1 can be written as (n + m + 2)-(m+1)

vast fossil
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If you still don't understand, try rewriting the right hand side using the definition (a choose b is equal to a!/((a - b)!b!))

hushed tendon
#

alright thanks

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torn jolt
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torn jolt
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how do i solve this

torn jolt
vast fossil
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Express P_n(-x)

torn jolt
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basically x^k becomes (-x)^k

vast fossil
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Right, which is the same as (-1)^k x^k

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The two (-1)^k's will combine into just 1

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So you have $P_n(-x) = \sum_{k=0}^n\frac{1}{k!}x^k$

glossy valveBOT
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A Lonely Bean

torn jolt
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?

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oh

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im kind of confused

vast fossil
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By what exactly?

torn jolt
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are u saying this

torn jolt
vast fossil
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Yes, because (-1)^k * (-x)^k = (-1)^k * (-1)^k * x^k = (-1)^2k * x^k = ((-1)^2)^k * x^k = 1^k * x^k = x^k

torn jolt
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ok fine

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makes sense

vast fossil
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Now it looks like you need to use the formula for multiplying power series together

torn jolt
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what is the formula

vast fossil
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$\left(\sum_{k=0}^\infty a_kx^k\right)\left(\sum_{k=0}^\infty b_kx^k\right) = \sum_{k=0}^\infty\left(\sum_{i=0}^na_ib_{n-i}\right)x^k$

torn jolt
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omg!

vast fossil
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Oh wait it should be k instead of n

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Hold on

torn jolt
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amen!

glossy valveBOT
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A Lonely Bean

vast fossil
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So in this case we have a_k = (-1)^k/k! and b_k = 1/k!

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hmmCat Hold on P_n isn't a power series, it's a polynomial

torn jolt
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amen...this isnt calculus

sharp flame
vast fossil
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Well the formula for multiplying polynomials is not so different, it's just
[ \left(\sum_{k=0}^n a_kx^k\right)\left(\sum_{k=0}^nb_kx^k\right) = \sum_{k=0}^{2n}\left(\sum_{i=0}^ka_ib_{k-i}\right)x^k ]
As far as I remember

sharp flame
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💡

vast fossil
sharp flame
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No I meant that pattern

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I'll stop channel clogging now

vast fossil
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thonk What pattern

sharp flame
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But that's cool

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a_(i)a_(n - i)

vast fossil
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I'll show later why that works

glossy valveBOT
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A Lonely Bean

vast fossil
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So $P_n(x)P_n(-x) = \sum_{k=0}^{2n}\left(\sum_{i=0}^k\frac{(-1)^i}{i!}\frac{1}{(k-i)!}\right)x^k$

glossy valveBOT
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A Lonely Bean

vast fossil
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hmmCat Hmm

torn jolt
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amen

vast fossil
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It looks like we need to consider the cases of k being even or odd

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If k is odd, then every ith term gets cancelled with the (k - i)th term

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So we look at only even k

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I.e., $P_n(x)P_n(-x) = \sum_{k=0}^n\left(\sum_{i=0}^{2k}\frac{(-1)^i}{i!(k-i)!}\right)x^{2k}$

glossy valveBOT
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A Lonely Bean

torn jolt
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ok

vast fossil
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Now you may notice that every ith term in that sum is equal to the (2k - i)th term, we can add them up

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Except for the central term, since it is not paired with a term equal to it (since i = 2k - i for that term)

torn jolt
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ok

vast fossil
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Eh this doesn't seem to be going anywhere

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I'll let you know if I come up with the solution

torn jolt
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ill ask my professor

vast fossil
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Oh it's you

torn jolt
#

?

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.close

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misty flare
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Hey guys. I need help on how to calculate this

torn jolt
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Are you aware of sine law

misty flare
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no

willow sedge
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if two triangles are equal then ratio of corresponding sides should be equal

misty flare
#

thanks

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lucid hill
#

I want to sort n marbles into n/m bags of m marbles each. The marbles are colored, and there are c(i) marbles of color i. Bags cannot contain more than 1 marble of each color.

How many ways can I do this?

I can do it ignoring colors, but after a while I haven't found a viable solution to exclude color repetitons besides brute force. And I'm dealing with around 50 marbles, so that is not possible.

This is not related to any study or work, so I don't even know if it's possible to find a simpler solution.

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@lucid hill Has your question been resolved?

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@lucid hill Has your question been resolved?

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lucid void
#

I have this math problem that looks like this. I have to find both solutions for x. I was able to find x = 3 but it says the other solution is x = 7 and I’m not sure how they got that answer. Can anyone explain?

quaint prawn
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@rare dock snow

rare dock
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snow

gritty rose
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Square both sides, isolate the square root, then square again

vast fossil
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Could you show your work?

lucid void
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Sure I’ll show what I did to get 3

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So here’s how I got 3 and I checked it at the bottom

gritty rose
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Yea that's wrong

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,tex .freshman

glossy valveBOT
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riemann

gritty rose
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But also you didn't square the right side

lucid void
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Oh when I do that I get x = 4 which is wrong

gritty rose
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Right. It's wrong for two reasons

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But somehow they cancelled each other and got the right answer

gritty rose
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(a+b)^2 = ?

lucid void
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I should end up with 5x+1 - 3x-5 = 4 right?

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@lucid void Has your question been resolved?

gritty rose
gritty rose
gritty rose
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split saffron
#

I got this question incorrect, can someone tell me which one of these was the correct answer, and why that is the case?

split saffron
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The slices are perpendicular to the y axis, so I believe I would take the integral with respect to x, and since it is a square, I think the correct answer would have been the one above what I chose.

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torn jolt
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torn jolt
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hello, could someone explain me this please, is about variations in combinatorics, without repetition

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I don't get (n-k+1)

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the other part I get it

restive sigil
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it's basically multiplying k numbers starting from n and going down

torn jolt
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yes

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but I think they answers would be different

restive sigil
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what do you mean?

torn jolt
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mm w8

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I think there should be a parenthesis like this ((n-k)+1) or is it not necessary?

restive sigil
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not necessary, they mean the same thing

brave blaze
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(n-k)+1 is the same as n-k+1
what is your point

torn jolt
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see

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this

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ignore the R/F

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is not the same

brave blaze
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because you didnt apply the formula well

torn jolt
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why

brave blaze
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7x6x3

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you wrote this

torn jolt
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Yes

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but it's okay

brave blaze
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and whats the formula saying ?

torn jolt
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(n-k+1)

brave blaze
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before that

torn jolt
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n (n-1)(n-2)......(n-k+1)

brave blaze
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yes

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so why did you jump from 6 to 3

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you forgot something

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also its not really 3

torn jolt
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7x6x5x4x3

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?

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is not the same

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also

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I wanted to see how to get only 5

brave blaze
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if you take k = 3, you have this :
7x6x5

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not 7x6x5x4x3

torn jolt
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but you need a parenthesis

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because you could do (n-(k+1)) as well

brave blaze
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?

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n-(k+1) = n-k-1

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not the same thing with your formula

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dont put parenthesis where there is none

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or at least know how it works

torn jolt
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oh okay, I calculated it like this n-(k+1)

torn jolt
brave blaze
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sadge

torn jolt
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this is why

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I come here

torn jolt
brave blaze
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no problemo

torn jolt
#

.close

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slender pond
#

For B why doesn’t reverse chain rule work?

slender pond
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1b?

brittle steeple
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reverse chain rule?

kind jay
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Is that integration by parts?

brittle steeple
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it would be u-substitution

slender pond
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Yes I’m supposed to use that

brittle steeple
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integration by parts is reverse product rule

kind jay
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U can apply ibp many times, not only once

brittle steeple
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ye we'll need to see more work to understand what you're trying to do

slender pond
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Ok

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Why does the method I use work on the right but not for the one on the left

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@brittle steeple @kind jay

brittle steeple
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i don't know what your method is

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first you have written

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y = e^(6x^2-1)

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and then later you have written

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y = 1/2 * e^(6x^2-1)

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you are aware these are different things, right

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so y cannot equal them both

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leaden gust
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Hi, this a practice question and I need help in finding the domain and range with X intercept and y intercept, this might be easy but I’m stuck for the domain is it (0, infinty)?

quaint prawn
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no

rough tundra
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why would domain be (0,inf)? pandaHmm

quaint prawn
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the domain is all of the x-values you can put into the function

leaden gust
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This is why I’m kinda confused with domains only for this graph

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I see

quaint prawn
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looking at this, can you put in x-values of 0 or below?

leaden gust
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Yes I think so

quaint prawn
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you think so? or yes

leaden gust
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Yes

quaint prawn
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Yes, you can.

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are there any x-values that you can't put in?

leaden gust
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Yes, any value above 0?

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(Idk if I’m right)

quaint prawn
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why

leaden gust
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Wait so this graph the thing I’m confused with is it does not touch the X axis I think bcos both the arrows are in y axis as I see it, but I know I’m wrong

quaint prawn
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why does it matter if it touches the x-axis

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but clearly it does not

leaden gust
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So if it doesn’t touch the X axis at all and the domain should be the values of X axis, does this mean the domain is 0?

quaint prawn
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nope

leaden gust
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Oooo so it’s all the values

quaint prawn
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domain has nothing to do with the x-axis

leaden gust
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I see

quaint prawn
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the domain is the set of all x-values you can input into your function

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remember what functions do

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they take something in (inputs)

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and spit something out (outputs)

leaden gust
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True

quaint prawn
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so the domain is all of the possible inputs

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an easy example is something like
y=x

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what can you put into this?

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is there any limitations on what x is?

leaden gust
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Nope

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Anything

quaint prawn
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so the domain is (-inf, inf)

leaden gust
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From negative to 0 and above

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Yep

quaint prawn
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and another good example is

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y=1/x

leaden gust
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Ooo

quaint prawn
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can we put everything into this?

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or is there something tricky

leaden gust
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1/c is not a fixed value so it depends on the value of X

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So I think we can

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Yes

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We can

quaint prawn
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what about x=0

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if f(x)=1/x what is f(0)?

leaden gust
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It’s 1

quaint prawn
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1/0 = 1?

leaden gust
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Oh no , it’s 0

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My bad

quaint prawn
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1/0 = 0?

leaden gust
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Anything divided by 0 is 0

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So yes

quaint prawn
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no

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you can't divide anything by zero

leaden gust
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Wait so no result?

quaint prawn
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exactly

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1/0 is undefined

leaden gust
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I see

quaint prawn
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you can't put x=0

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so 0 isn't in the domain

leaden gust
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that’s why I got my answer wrong

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Bcos I put 0 as domain

quaint prawn
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No

leaden gust
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And 0 cannot be domain

quaint prawn
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No

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The domain of a function, depends on the function

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for y=x

leaden gust
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Yes

quaint prawn
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x can be 0

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0 is in the domain of y=x

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but for y=1/x

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it is not

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it depends on the function

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so 0 is in the domain of some functions, and not in the domain of some other functions

leaden gust
#

makes sense so it depends on the function

quaint prawn
#

Yes

leaden gust
#

Got it

quaint prawn
#

Rinz let me show you a quick example of something

leaden gust
#

Yes please

glossy valveBOT
#

Austin

quaint prawn
#

what is the solution of this?

leaden gust
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2x= X, so 2x-x = -x , x=0?

quaint prawn
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x=0, yes

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but what if you took $2x=x$

glossy valveBOT
#

Austin

quaint prawn
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and divided both sides by x

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then you would have

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$2=1$

glossy valveBOT
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Austin

leaden gust
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True

quaint prawn
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well this is clearly not true

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so how did we get this false statement?

#

can we not divide by x?

#

well

#

since x is 0

#

you can't divide by 0

#

otherwise

#

2=1

#

and other bad things

leaden gust
#

Yep true if u can’t divide by 0 then it’s 2=1

#

I see

quaint prawn
#

so how about you try this, what is the domain of $f(x)=\frac{1}{1-x}$

glossy valveBOT
#

Austin

quaint prawn
#

what x-values can you not put in?

leaden gust
#

It cannot be equal to 0

#

Bcos division by zero is undefined

quaint prawn
#

what cannot be equal to 0

#

be more specific

leaden gust
#

The 1-x cannot be equal to 0

quaint prawn
#

which means x cannot equal what?

leaden gust
#

0 so we do X=1 and solve for it

#

But

quaint prawn
#

yeah, so x cannot equal 1

leaden gust
#

X cannot be equal

#

Yes

#

So it will be

#

All real numbers except x =1

quaint prawn
#

yes

#

which you write like this

leaden gust
#

Phew

quaint prawn
#

(-inf, 1) U (1, inf)

leaden gust
#

Yep got it

quaint prawn
#

great

#

so back to your question

leaden gust
#

only u could make me understand ngl

#

Yes

quaint prawn
#

let us continue with the domain here then

#

what do you think is the domain now

leaden gust
#

Oh yes also the functions are f(-4) and f(3) for that question

quaint prawn
#

Those aren't functions

leaden gust
#

Values

quaint prawn
#

if there is more information though just send a picture please

leaden gust
#

Yes

quaint prawn
#

so I can understand what you mean better

leaden gust
quaint prawn
#

okay so

#

what it is saying is to evaluate the function at x=-4 and x=3

#

that is just another one of the things you need to do

leaden gust
#

Yes

quaint prawn
#

but let us take it one step at a time

#

starting with the domain

leaden gust
#

Yes the domain

quaint prawn
#

What do you think the domain is now?

leaden gust
#

(-inf, 1)

quaint prawn
#

no, the domain of the function in your question

#

not the example I gave

#

this is a graph of your function

leaden gust
#

Wait so it has a arrow

#

Means it can’t be infinite

#

Right

#

Nvm its@oppisite

#

Arrow means infinite

#

So domain would be

#

(2,-inf)?

#

I’m confused about this graph ngl

quaint prawn
#

No, stop for a second, I'll try to explain

leaden gust
#

Yes

quaint prawn
#

your screen is not infinitely large right

#

so you can't see all of the graph

#

the arrow just indicates that it keeps going

#

even though you can't see all of it

#

because your screen is not big enough

leaden gust
#

True

quaint prawn
#

so all the arrow means, is that the graph keeps going in that direction

#

even though the graph gets cut off on your screen

#

Now, as for the domain, remember what we are looking for.

#

Are there any x-values that you can not put into this function?

#

If there were, they would not have a cooresponding y-value on the graph

#

So what do you think is the domain?

leaden gust
#

Then it should be infinite

quaint prawn
#

By infinite, do you mean that we can put all x-values into our function?

leaden gust
#

We can put all values of X in this, yeah

quaint prawn
#

so then the way you write that is:
(-inf, inf)

#

do you understand?

leaden gust
#

Yes I have better clarity now

#

I’m not looking at what numbers the arrows are on instead what all they can have values for

#

So it’s better

quaint prawn
#

Okay great. The next part of your question asks for the range

leaden gust
#

Yes

quaint prawn
#

the range is similar to the domain

#

so, now you know that the domain is all x-values you can put in

#

the range is all y-values you can get out

leaden gust
#

Got it

quaint prawn
#

so look at your graph

#

are there any y-values your graph does not touch?

leaden gust
#

Yep

#

1

quaint prawn
#

that's true

#

it also doesn't touch anything below 1 right

leaden gust
#

Yes it does not

#

So 1 and below

quaint prawn
#

what about 1.5

#

does it touch 1.5?

leaden gust
#

Oh wait so it’s 2 and above

quaint prawn
#

Do you mean the range is 2 and above?

leaden gust
#

It doesn’t touch 1.5 or 1 or below but it touches 2 to be exact

quaint prawn
#

True

leaden gust
#

So basically the graph is intercepting 2 and going above

quaint prawn
#

it does not touch anything below 2

#

so the range is 2 or above

#

right?

leaden gust
#

Yes nothing below 2

#

Yes

quaint prawn
#

okay

#

try to write that

#

in a proper interval

leaden gust
#

So it will be (2, infi)

#

A question

quaint prawn
#

not quite

leaden gust
#

Do we write infi in front of@the number

quaint prawn
#

the open bracket means that you are excluding 2

#

it is [2, inf)

#

meaning that we are including 2

leaden gust
#

Ooo I see

quaint prawn
#

and we write infinity after the 2 because it is larger than 2

leaden gust
#

So always [, to include

quaint prawn
#

to include yes

#

so rewrite it again

#

the proper way this time

#

what is the range?

leaden gust
#

[2,infi)

#

Right

quaint prawn
#

good job

#

yes

leaden gust
#

yes got it

quaint prawn
#

The next part asks about the x-intercepts

leaden gust
#

Yes

quaint prawn
#

that is when the function touches the x-axis

#

does your function ever touch the x-axis?

leaden gust
#

It does not have X intercepts

#

Nope

quaint prawn
#

yea

#

thats correct

leaden gust
#

yes

quaint prawn
#

what about the y intercept

#

the y intercept is when your function touches the y-axis

#

does your function ever touch the y-axis?

leaden gust
#

but for y intercepts where it touches the y axis , there is 2

#

Yes

quaint prawn
#

so the y-intercept is 2

leaden gust
#

Yep

quaint prawn
#

you wrote 2, infinity

#

but it is only 2

leaden gust
#

Also a question , there can’t be more than 1 y intercepts right?

leaden gust
quaint prawn
#

there can be

#

no, i am looking at the second picture you sent

random isle
#

yo can someone help me out with interval notation

#

increasing and decreasing intervals

quaint prawn
leaden gust
quaint prawn
leaden gust
#

Now the last question

#

It asks us about values of functions

quaint prawn
#

yes it asks for f(-4) and f(3)

leaden gust
#

yes

quaint prawn
#

this is saying, what is your function when x=-4, and what is your function when x=3

#

you should be able to tell by looking at your graph

leaden gust
#

Yep

quaint prawn
#

great, all done then! good work

leaden gust
#

For the value

#

Yep other than that we are done

#

Thank you so much @quaint prawn !

quaint prawn
leaden gust
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elfin hound
#

Can someone just explain the mapping, domain and range to me? I'm aware of what all three mean but just in this context because I missed the lesson these notes are from.

elfin hound
#

Like why is it X+2 for the mapping and not X-2?

#

And how they got the domain and range

white geyser
#

are you sure those answers are right

elfin hound
#

its what the teacher did for notes

white geyser
#

are those circles on the original curve hollow or filled in

elfin hound
#

it looks hollow?

#

idk if thats important tho

#

i just wanna know why (x-2) makes it move 2 units right and not 2 units left?

white geyser
#

its important because for the domain and range you used brackets, which implies a closed interval ( including end points)

#

i've never seen mapping used in precalc context, but i assume its because they want the translations to reproduce the old function from the new one?

elfin hound
white geyser
#

if the circles are hollow it should be open interval, since those points aren't defined.

#

but its hard to tell from the picture

elfin hound
#

i just wanna know the whole x thing

#

does (x-2) not mean you're - 2 from the original x values?

#

if not

#

then does

white geyser
#

x+2 would undo the translation of the transformed function

elfin hound
#

(x+2) make it translate left?

#

but shouldn't adding make the graph go right? and taking make the graph go left?

#

thats how the x axis works

white geyser
#

g(x + 2) - 1 = f(x + 2 - 2) - 1 => f(x)

#

i think thats what they are trying to say, again, ive never seen "mapping" used in precalc, so just a guess.

elfin hound
#

i might as well ask the teacher lmao

#

i missed the lesson she went over these notes

#

i understood the earlier parts but this kinda fucked me up

#

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sly grove
#

how to convert 1/3 to base 7 (by writing 1/3 as a sum of a geometric sequence)

severe linden
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#

@sly grove Has your question been resolved?

sly grove
severe linden
#

you want limit 1/3

#

equate and solve for a (and hope it ends up being a digit)

sly grove
#

can you give an example? (also i haven't learned limit of geometric series

severe linden
glossy valveBOT
severe linden
#

You have learnt geometric series but not this?

sly grove
#

that's right

severe linden
#

odd

#

but it basically just does what it says.

#

so we want

#

I think I said it incorrectly above.

#

We do not want to solve for a, as a = 1/7

sly grove
severe linden
#

,wolf 1/(1-1/7)

severe linden
#

So if we had the number

#

1.1111111111111111111111111111111111... base 7

#

it would be 1.1666666... or 7/6

#

Let's work from here.

sly grove
#

also, there's an example problem (if you want to see it

severe linden
#

I would prefer if we focus on the problem first.

sly grove
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#
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severe linden
#

.reopen

full forumBOT
#

severe linden
#

@sly grove Did you understand my sum?

sly grove
severe linden
#

yes

#

and how you use 1/(1-1/7)

#

to clarify

#

the 1.16666 is decimal

sly grove
sly grove
severe linden
#

Just making sure

#

wpe are usually not even supposed to give away solutions bhappy

#

Anyway, now we got 7/6

#

in base 7

#

How can we get from 7/6 to 1/3 using operations

#

that do not mess up the base-7 representation in unpredictable ways?

sly grove
#

7/6 = 1 + 1/6, and then get from 1/6 to 1/3?

severe linden
#

🙂

#

1/6 to 1/3, could it be... a multiplication by 2?

sly grove
#

yeah. how would you go from there to base 7 then?

severe linden
#

Well we know

#

7/6 = 1.1111111111111111111111111111...

#

we subtract 1

#

and then we multiply by 2

#

Both are not rocket science for either fractions nor base-7

sly grove
#

(1.11111...(7) - 1) *2?

severe linden
#

yes

sly grove
#

ohhhh

#

0.11111...(7) * 2 = 0.222...(7)?

severe linden
#

Easy, right?

sly grove
#

thank you so much:))

severe linden
#

you are welcome.

#

I hope the underlaying principles became clear enough.

#

.close?

sly grove
#

sure

#

.close

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rancid gulch
#

i got to 11x = x(a+b) + 2(a+b)

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rancid gulch
#

im not sure where to go from here

#

a + b = 11

#

but what about the second part

#

2A + 2B = 0 maybe?

#

idk 😨

scenic sundial
#

how would you do it if it was 11x + 1?

rancid gulch
#

1 = 2a + 2b

#

i think right

scenic sundial
#

so how would you do it if it was 11x + 0

astral sinew
rancid gulch
#

yay!!

scenic sundial
#

it is

astral sinew
#

(11)x + (0) = (A+B)x + (2A+2B)

#

Do you see?

rancid gulch
#

yes

#

but then a = -b right

scenic sundial
#

yep

rancid gulch
#

and so (-b) + b = 11? so 11 !=0 tho

astral sinew
#

Check your factoring

#

What's the original polynomial

rancid gulch
#

does x^2 +4x + 4 not factor to (x+2)(x+2)

astral sinew
#

Yes

#

But there's a special thing you have to do with repeated factors

rancid gulch
#

oh no

astral sinew
#

You will write

rancid gulch
#

woops

astral sinew
#

11x/(x^2 + 4x + 4) = A/(x+2) + B/(x+2)²

rancid gulch
#

ohh?

#

why is that?

astral sinew
#

Might help to use actual numbers if you want the intuition. PFD is basically:
5/6 = 5/(2×3) = A/2 + B/3 = 1/2 + 1/3

rancid gulch
#

also in that case would it be 11x = A/(x+2) + (Bx + C)/(x+2)²

rancid gulch
#

okok

humble osprey
astral sinew
rancid gulch
#

oh yeah

astral sinew
#

Until you clear the denominator

rancid gulch
#

thats what i meant sorry

humble osprey
#

isnt that only for when a quadratic factor cant be broken up into smaller factors (aka it doesnt have real zeros)

astral sinew
#

Repeated roots are special

humble osprey
#

yeah but if they're real theres no need for Bx + C in the nominator

astral sinew
#

There is. Because the denominator is of degree 2

#

So the numerator can be of degree 1

#

Hopefully that makes sense q

rancid gulch
#

so what i got after separting everything was
a + b = 0
4a + 2b + c + 4 = 11
2c = 0

#

so c = 0

#

4a + 2b + 4 = 11
so 4a + 2b = 7

#

a = -b

#

-4b + 2b = 7

humble osprey
rancid gulch
#

b = -7/2

humble osprey
#

the case you're talking about is for when there are imaginary roots

#

with the real ones, A/(x+2) + B/(x+2)^2 is enough

rancid gulch
#

i got it wrong 💀

humble osprey
#

look at number 2

#

thats what you're supposed to use

rancid gulch
#

ohhh k

#

why is it a - b?

#

i mean x - a

humble osprey
#

where?

#

oh

#

its random variables, it doesnt matter

rancid gulch
#

ok sorry lol

humble osprey
#

nahh no worries, nothing to apologize for

#

anyway this is what you're supposed to have now

rancid gulch
#

so i have like 11x = A(x+2)^2 + B(x+2) right

#

so i expand to 11x = (x^2)(A) + x(4A + B) + (4A + 2B)

#

wouldnt that mean A = 0 and B = 11 ?

humble osprey
rancid gulch
#

oh wait lol

humble osprey
rancid gulch
#

yeah

#

ok one sec 😭

#

so its 11x = (a(x+2)^2 + b

humble osprey
#

dont rush, thats how most of those types of mistakes are made 😭

rancid gulch
#

wait

#

I mean

humble osprey
rancid gulch
#

11x = a(x+2) + b

humble osprey
#

yep, you got it :D

rancid gulch
#

thanks 😭

humble osprey
#

you're welcome!

rancid gulch
#

so A = 11 and B = -22

#

YES

#

IT WORKED

#

IM SO HAPPY

humble osprey
#

yep, that's correct

#

:D

rancid gulch
#

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glad whale
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glad whale
#

HOw in the world is this wrong??

scenic sundial
#

show your work maybe?

glad whale
#

Ok

wild sleet
#

7/4 + 2/4 is not 11/4

scenic sundial
#

very true

glad whale
#

wait

#

doesnt the square root of b

#

turn to b^2

#

1/2****

wild sleet
#

7/4 + 8/4 is also not 11/4

scenic sundial
#

it is b^(1/2) yes

glad whale
#

ah

#

thats the mistake i mde then

#

so it will be so then 1/2 + 5/4

#

get common denom

#

so will be 7/4?

scenic sundial
#

where did 5/4 come from?

glad whale
#

oh god im looking at

#

something else

#

i mean 7/4

#

so 7/4 + 1/2

#

9/4

#

b^9/4

scenic sundial
#

make sure you have the right parentheses, but yes

glad whale
#

Oh ok

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patent grotto
#

why can -x^2 + x + 6 simplify to (x-3)(x+2) but when its in a function y = -x^2 + x + 6 you cant

spiral vigil
#

you can

swift fulcrum
#

Why not

patent grotto
#

im putting it in online cals

#

and they say no unless im tripping

spiral vigil
#

show screenshot or something

patent grotto
spiral vigil
#

ask it to factor instead

patent grotto
#

💀 oh you right lmfao

spiral vigil
#

"simplification" is somewhat nebulous

patent grotto
#

i am tripping

#

thanks

#

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wise seal
#

I’m stuck at b. I found the limf(x) by doing g(x)=xf(x)-2x+3/x+2 etc etc but I can’t use this at b

wise seal
#

Or maybe I’m doing something wrong ?? I don’t know

#

OH nvm

#

I figured it out

#

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torn jolt
#

Hello, why are these two formulas for combinations without repetition equal
can someone show me an example like when n = 5 k = 3

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#

@torn jolt Has your question been resolved?

torn jolt
#

<@&286206848099549185>

#

i dont speak very good spanish

#

sorry

#

mm you don't need to, it's just the formulas, but I will translate

#

Non-repeating combinations
The number of combinations of n elements taken from k and k as well as groupings of the same number of elements is different, at least in one element, is calculated with the following formula:

torn jolt
#

<@&286206848099549185>

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torn jolt
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dry relic
#

A father has his wedding anniversary and birthday on the same day.
The family celebrates with a trip to London. The children pay for the musical and football match for the father. The mother pays the ticket for the football match itself, but gets a ticket for musical by the children. Tickets for the musical cost SEK 2,500 in total, while the tickets for the football match cost SEK 5,400 in total.
together. The plane tickets cost SEK 1,600 per person.

Write an expression for how much each of the children needs to pay.

dry relic
#

I might struggle with converting my expression to LaTex format, but here we go:

#

The answer, according to the book, is $2500/x + 5400/x+1 + 1600$

glossy valveBOT
dry relic
#

formatting issues... grrr

#

i personally disgree with the book's expression, though

elfin stream
#

Do $\frac{a}{b}$

glossy valveBOT
#

ItzKraken

dry relic
#

x = amount of children btw

#

The answer, according to the book is:

#

$\frac{2500}{x} + \frac{5400}{x+1} + 1600$

#

grrr

elfin stream
dry relic
elfin stream
#

Only one $ at the start, one at the end

glossy valveBOT
dry relic
#

Perfect, thanks @elfin stream !

#

Anyways, I disagree with the equation

#

I believe it rather should be $\frac{2500}{x} + \frac{5400-\frac{5400}{x+2}}{x+1} + 1600$

glossy valveBOT
elfin stream
dry relic
elfin stream
#

Hmm and so is the mother?

dry relic
#

yes, and she is getting her musical ticket paid by the children

#

everyone will pay for the 1600 SEK flight ticket,
the 2500 SEK is the cost for everyone to get into the musical. This will be split between the children

5400 is the total cost of the football match. Children split the bill for the tickets that it costs for them and the father, while the mother pays for herself

dry relic
# glossy valve **Seed**

if we were to analyse my expression above, we would see that 2500/x is logical, considering that 2500 is the bill for the entire family, which will get split by the amount of children, x

dry relic
#

the +1600 also is logical, since everyone pays for their own flight ticket

#

1600 is per person

elfin stream
dry relic
elfin stream
elfin stream
dry relic
elfin stream
#

Oh found it

dry relic
#

and we want to make it so that the children split the bill between the ticket cost for them and the father only

elfin stream
dry relic
#

we need to therefore remove the cost of the mothers ticket from the 5400, and split the difference number that we get between the children

#

how do we do that? we know that x is the amount of children, and that there is both a father and a mother. This means that 5400/(x-2) tells the cost for each ticket

#

one ticket costs in other words 5400/(x-2)

dry relic
#

and the mother pays for herself, so the amount that the children will split between themselves is 5400 minus 5400(x+2), which is the cost for the mother's ticket

#

The book however says it's just $\frac{5400}{x+1}$ and calls it a day

glossy valveBOT
dry relic
#

it's difficult to claim that the book is wrong though

#

so i'm unsure

elfin stream
#

They must be then assuming 5400 SEK doesn't include the mothers share

dry relic
#

@elfin stream it might very well be the book's perspective, in which i comment that the problem formatting was vague

#

because seconds after, another problem appears where it's told that the children pay a total of 3000 SEK, so you're supposed to make an equation

#

using my method you get no whole x-values

#

using the book's method you get 5

full forumBOT
#

@dry relic Has your question been resolved?

full forumBOT
#
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full forumBOT
#
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magic rover
#

prove that for a,b,x positive integers $\gcd(x^a-1,x^b-1)=x^{\gcd{a,b}}-1$

glossy valveBOT
#

bigpufik

magic rover
#

im trying to use euclidean algorithim

#

im getting

#

$\gcd(x^a-1,x^b-1)=\gcd(x^a-1,x^a-x^b)$

glossy valveBOT
#

bigpufik

magic rover
#

i can assume a>b

#

and try to factor x^b

#

then

#

$\gcd(x^a-1,x^b-1)=\gcd(x^a-1,x^a-x^b)=\gcd(x^a-1,x^{a-b}-1)$

glossy valveBOT
#

bigpufik

magic rover
#

then not really sure

#

.close

full forumBOT
#
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#
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prisma flame
#

how to solve $$\lim x -> 0 ( x floor(\frac{1}{x}))$$

glossy valveBOT
#

neither

prisma flame
#

i know the so,ution is 1

#

but idk how to get there

#

suppose to use basic calculus limit properties

forest panther
#

you can try to give bounds to floor(1/x) if you've seen the squeeze theorem

full forumBOT
#

@prisma flame Has your question been resolved?

#
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#
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late fable
full forumBOT
late fable
#

I don't think this is right

#

Well I know that it's "right"

#

according to the book

#

But I don't think os

#

It doesn't make sense

#

Ping if you answer please

full forumBOT
#

@late fable Has your question been resolved?

late fable
#

<@&286206848099549185>

full forumBOT
#

@late fable Has your question been resolved?

late fable
#

<@&286206848099549185> help me

#

Why aren't you responding

barren zephyr
#

<@&286206848099549185>

#

Help me

barren zephyr
full forumBOT
# barren zephyr <@&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.

full forumBOT
light sonnet
full forumBOT
#

@late fable Has your question been resolved?

late fable
#

<@&286206848099549185> HELP ME

#

PLEASE

#

HELP ME

late fable
#

<@&286206848099549185>

late fable
#

<@&286206848099549185>

torn jolt
#

what do u need

late fable
full forumBOT
#

@late fable Has your question been resolved?

late fable
#

@wicked seal

#

<@&286206848099549185>

#

Please

#

awhrre are you

torn jolt
late fable
#

Please

#

Help

late fable
#

I’m questioning the answer to the question

torn jolt
#

Look at the graph

#

Look at the control

#

You notice how hit is similar to the control

late fable
#

I know the answer is right but It doesn’t seem right

torn jolt
#

but when they say "Smahed into" yes responses are higher

late fable
#

Look at the answer choices

#

None of them say that

torn jolt
#

the one you selected says that

#

just very

#

weirdly

late fable
#

Ok

#

but it doesn’t make sense

torn jolt
#

Basically it's saying that if you use more violent words

late fable
#

That choice doesn’t make sense

torn jolt
#

they are more likely to respond yes

late fable
#

Knowing whichever treatment the subject received

#

We will always predict no

torn jolt
#

The treatment being the word choice

#

when you chose "smahed into" they were more likely to respond yes

late fable
#

But that’s not what it’s saying

#

If it said that

torn jolt
#

ReiPlush It is tho

late fable
#

Then it would be right

#

Oh wait

late fable
#

Like no matter what word choice

#

We will always predict no

#

wdym

late fable
torn jolt
#

ReiPlush I think you're confusing most likely response with prediction

late fable
#

I’m not

#

I think you are

full forumBOT
#

@late fable Has your question been resolved?

full forumBOT
#
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#
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After 15 minutes, feel free to ping <@&286206848099549185>.
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wispy bay
#

Hello, how do I get the 1st term of an arithmetic sequence when I'm given only with the 3rd and 17th term?

wispy bay
#

I've tried using the arithmetic equation but I keep on getting wrong/invalid answers

#

at a loss here right now

mighty crescent
wispy bay
#

it's really messy but okay

#

here I tried substituting the nth term and n with 8

mighty crescent
#

,rotate