#help-13

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twilit bison
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okay

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we don't need to add 11 to 13

ember kindle
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thats what the video said i needed to do

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so

twilit bison
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is the problem in the video different?

ember kindle
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no

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its the same problem

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but different numbers

twilit bison
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are you able to share the video or does it require an account or something?

ember kindle
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im unable to share it and any screen recording apps i use do not take in any sound

glad peak
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If you are on windows you can use snipping tool

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Also, are you sure it said to add them and not subtract?

ember kindle
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that just takes screenshot

glad peak
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Yes it does

frigid dust
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all you need is a screenshot

ember kindle
frigid dust
#

but you can take a picture of the formula in the video

ember kindle
#

theres limited space yk

frigid dust
#

does it show it at any point in the video?

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take a screenshot at that moment

ember kindle
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but thank you for ur help . ive already gotten the answer

frigid dust
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alright

twilit bison
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sorry i can't help without more info

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i can't understand 11+13

cedar kilnBOT
#

@ember kindle Has your question been resolved?

cedar kilnBOT
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maiden wave
#

I need help.

cedar kilnBOT
maiden wave
#

How do you do this question. I am trying to find the answer.

digital cliff
#

do you have any ideas?

maiden wave
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I am given the slope intercept and the points

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slope intercept is y=mx+b

digital cliff
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yup

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then what

maiden wave
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Then you need to put the y intercept into a fraction

digital cliff
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im not sure what that means

maiden wave
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You're finding B first.

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Since we need the b to finish this equation.

digital cliff
#

you do, i agree with that much, i just dont get what putting 'the y intercept into a fraction' means

maiden wave
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That what I thought I should do.

digital cliff
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im speaking about the wording, the phrase doesnt mean anything how you worded it

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but are you just saying to replace b with the given intercept?

maiden wave
#

Yeah.

digital cliff
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thats the way to go indeed

maiden wave
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YAY.

digital cliff
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now what?

maiden wave
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Now we need to find the slope

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since we have the B value and also the intercept.

digital cliff
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how would we do that?

maiden wave
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Just replace the B value with the intercept.

digital cliff
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we already did that, no?

maiden wave
#

yeah.

digital cliff
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im asking how we can find the slope after

maiden wave
#

We need to know the Y values and the X values.

digital cliff
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do we have any?

maiden wave
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Y1 is the intercept

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and y2 is just -9

digital cliff
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youre throwing around the word intercept a lot

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but it doesnt apply

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intercept is where one thing meets another, typically when talking about a line, its where it crosses the axes

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(-3,-9) is just a point

maiden wave
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-3 is a X value and -9 is a Y value.

digital cliff
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it is

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when x=-3, y=-9

maiden wave
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Now we need the other X and Y.

digital cliff
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youre thinking too much here

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you dont need the formula m=(y1-y2)/(x1-x2)

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you already have y=mx-75/7

maiden wave
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yes

digital cliff
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just plug the point into it

maiden wave
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The X value is just -3.

digital cliff
#

uh, si?

maiden wave
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And the M value is just 4/7.

digital cliff
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,w (-9+75/7)/(-3)

digital cliff
#

you have a sign issue, but otherwise alright

maiden wave
#

So the answer is -4/7x-75/7

digital cliff
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y=, si

maiden wave
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Thank you.

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๐Ÿ‘

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I have one more actually.

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They didn't give me the X or Y

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The X and Y are positive though.

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But they are not whole numbers.

violet flume
#

.close

cedar kilnBOT
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narrow owl
#

Hi

cedar kilnBOT
narrow owl
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i have a test and i wanna know if theres ways to know what methods i need to use to solve

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how i can tell the methjod i need to use

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the topics are direct/indirect variation word problems

dire geode
#

just do problems

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help channels are for specific problems or topics

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worthy tusk
cedar kilnBOT
worthy tusk
#

what is the appollonius median theorem and when is it used-?

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wrong chat

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.close

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worthy tusk
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ok wait maybe i lied my friend was not useful ;-;

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allow me to resend!

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what is the appollonius median theorem and when is it used?

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-sigh- if only i can understand the foreign language of maths

proud vigil
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gilded widget
#

HELLO

cedar kilnBOT
gilded widget
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My attempt

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can anyone suggest me ways to find ab+bc+ca

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hello

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<@&286206848099549185>

dull oxide
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!15m

cedar kilnBOT
#

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.

gilded widget
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oh my bad

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hello

proud vigil
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uh.

gilded widget
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can anyeone help

proud vigil
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i think this is solvable just using a sum and noting the expansion of (a+b+c)^2

gilded widget
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like i did get to a point where a^2+b^2+c^2 =(138- (ab+bc+ca))/2

proud vigil
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hmm.

gilded widget
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wait i m wrong

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um tihis

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is correct

proud vigil
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maybe do some subtraction.

gilded widget
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nah it's not working

proud vigil
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II-III and then I+(II-III) would seem to work to get all the squared terms cancelled

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ab+2b^2+bc-ac

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ah, yeah

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thats a bit annoying.

gilded widget
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okay so the key here is to find

dull oxide
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,rccw

gilded widget
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ab+bc+ca

wraith daggerBOT
gilded widget
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hello

earnest idol
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i did solve it but i feel there can be a shorter way

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its nothing difficult just manipulation of many equations

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oh theres a beautiful geometric way as well using cosine rule

cedar kilnBOT
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@gilded widget Has your question been resolved?

gilded widget
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i did find that solution

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but i do not understand

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the cosine rule

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like isaw it on quora

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u apparently hav to use cosine rule then

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heron rule or smth like that

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h3i

cedar kilnBOT
#

@gilded widget Has your question been resolved?

cedar kilnBOT
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vague blade
#

Power is 14

cedar kilnBOT
slate lintel
#

u-sub

vague blade
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Can you explain more?

proud vigil
slate lintel
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i'd go e^x but yeah

proud vigil
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oh its

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can i spoil

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,texsp ||$\int(\frac{u^2-1}{2u})^4\cdot\frac{1}{u}du$||

wraith daggerBOT
vague blade
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The power is 14, not 4, does that change something?

proud vigil
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mb i misread

cedar kilnBOT
#

@vague blade Has your question been resolved?

vague blade
proud vigil
#

now its just working it out algebraically

vague blade
#

I'm kinda bad at this and understanding math at english, can you explain how exactly to do it algebraically?

cedar kilnBOT
#

@vague blade Has your question been resolved?

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cedar kilnBOT
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vapid radish
#

I need assistance for the formula to determine the primative function of this function

vapid radish
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could be rewritten as 4*x^-0.5 I think

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or just 4 * 1/x^0.5

fallen moat
vapid radish
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Well, the answer is supposed to be 8*sqrt(x) so im wondering if its just rewritten or if theres some other formula

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,w integral 1/x^0.5

fallen moat
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do you recall the power rule?

vapid radish
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?

fallen moat
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lemme grab

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Note that for
f(x) = x^n
then it's antiderivate F(x) is
F(x) = x^(n+1) / (n+1) +C

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so for this situation,
f(x) = 4 * x^(-0.5)
F(x) will be
4 * x^(-0.5+1) / (-0.5+1) +C

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and also, for any af(x) where a is a constant
it's antiderivate will be aF(x)+C

vapid radish
#

so since its divided by 0.5 it becomes 2 * 4 * x^0.5 which is 8squrtx?

fallen moat
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yep

vapid radish
#

I get

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it

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Thanks so much

fallen moat
#

Cheers!

vapid radish
#

.close

cedar kilnBOT
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jaunty river
#

Little help?

cedar kilnBOT
undone star
jaunty river
undone star
#

sure

jaunty river
undone star
#

ok nice

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do the first 2 terms resemble the last 2 terms?

jaunty river
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No becuase of the 7

undone star
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they look pretty close but not quite there

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ok what can u do to simplify the first 2 terms?

jaunty river
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take x^2 out

undone star
#

ok nice so what does that look like now?

jaunty river
#

but i dont have the other part

undone star
#

and then u arranged it to

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$x^{2}(x-7) + ? = 0$

wraith daggerBOT
#

Dootud

undone star
#

what are we missing from before?

jaunty river
#

x-7

undone star
#

ok right so it now looks like?

jaunty river
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or with parentheses if you wnat

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i have a mental note of the =0

undone star
#

can you group them somehow now?

undone star
jaunty river
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they are both (x-7)

undone star
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ok right

jaunty river
#

I think theres a step regarding that but im not sure what it is

undone star
#

hmm how about this

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what u have above is the same as writing

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$x^{2}(x-7) + 1(x-7)=0$

wraith daggerBOT
#

Dootud

jaunty river
#

ohhh

undone star
#

does that look a little bit more familiar?

jaunty river
#

(x^2 + 1) has to be used right

undone star
#

ye ye

jaunty river
#

wait

undone star
#

๐Ÿ‘ u on the right track

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what does that leave u with now?

jaunty river
#

Yes thank you

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oh wait

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I think there is one part i have a question on

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yea i didnt get it right

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I have to solve for all real number solutions and I'm not sure how to do that

undone star
#

so we are solving $(x^{2}+1)(x-7)=0$

wraith daggerBOT
#

Dootud

jaunty river
#

don't you have to separate the x^2

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into two different thingies

undone star
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(x+1)(x+1) isnt the same as x^2+1

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try expanding it

jaunty river
#

oh your right

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so now what?

undone star
#

ok so remember when we are solving, we just need to find when that expression is 0

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so that is just the same as finding when either
x-7=0
or
x^2+1 = 0

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because 0 x (any number) = 0

jaunty river
#

oh it uses the i doesnt it

jaunty river
undone star
jaunty river
#

no not becuase of you

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I just got stuck

undone star
#

what im trying to say is that, as long as one of the brackets is equals to 0

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then whats in the other bracket doesnt matter

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because 0 x (anything) is just 0

jaunty river
#

when was 0 being multiplied?

undone star
#

so we are now just solving separately
when is x-7=0
and when is x^2+1=0

jaunty river
#

or is it just that we only need to use one

undone star
wraith daggerBOT
#

Dootud

jaunty river
#

Right

#

I separated the (x-7) and made it equal 0 and got positive 7

undone star
#

for the left hand side to =0, it occurs when
(x-7)=0
or
when (x^2+1)=0

undone star
#

thats a good start

#

ok lets think about x^2+1=0, do u see any problems with this

jaunty river
#

is it because i isn't a real solution

undone star
#

yes

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good

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the quesiton only wants real solutions

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and i is imaginary

jaunty river
#

thats why we didnt use the other ones answer right

undone star
#

so that means the only solution we have is x=7

jaunty river
#

ok great

#

thanks

#

you actually made it seem really simple

undone star
#

u got there by urself pretty much

#

๐Ÿ‘

jaunty river
#

thanks man, have a great day

undone star
#

u2

jaunty river
#

.close

cedar kilnBOT
#
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cedar kilnBOT
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vestal sandal
cedar kilnBOT
vestal sandal
#

This correct or nope

cedar kilnBOT
#

@vestal sandal Has your question been resolved?

glad peak
vestal sandal
#

what?

glad peak
#

Are they linearly independent

#

Is what I meant to ask

#

More specifically, is the third column lin indep

vestal sandal
#

A2 all columns are linearly independent

glad peak
vestal sandal
#

Omg I wrote it wrong ๐Ÿ™‚

vestal sandal
#

So the dimension is 2

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Of U2

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And the basis is the first two columns

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For u2m

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?

glad peak
#

Mhm sounds about right

vestal sandal
#

thank you so much

#

btw

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it is just the first two columns as it is right

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for the basis

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of U2

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and U1 to

glad peak
#

Yes, a valid basis will be, for any a and b, { a(c_1), b(c_2) }

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Except a, b = 0

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So a = b = 1 would just be the two columns

vestal sandal
#

Perfect amazing

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thank you so much

#

.close

cedar kilnBOT
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vestal sandal
#

.reopen

cedar kilnBOT
#

โœ…

vestal sandal
#

@glad peak

#

Is part c correct same question

glad peak
vestal sandal
#

what i did is Ax = b where b is 0

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and A

#

i got

#

via

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a1u1 + a2u2 = b1w1 + b2w2

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where u1 and u2 are the columns of the basis of u1

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and w1 w2 are columns of basis u2

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a1 a2 b1 b2

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are the coefficents

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which forms the x

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a1u1 + a2u2 -b1w1 -b2w2 = 0

glad peak
#

Yeah this sounds correct so far

vestal sandal
#

A matrix is comprised of u1 u2 -w1 -w2 x is a1 a2 b1 b2

#

and then equals to 0

#

and i found x

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and the x I gave above

#

so its correct?

glad peak
#

You can check by seeing if the basis you found is an element of both subspaces

#

If it is then you know you didnโ€™t make any computational errors

vestal sandal
#

right so if i could form the vector using u1 u2's basis vectors

glad peak
#

Yes

vestal sandal
#

right perfect thank you so much

#

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dusky cape
#

$2x^2 +x-3 =0$

cedar kilnBOT
wraith daggerBOT
#

Simon James B

dusky cape
#

$delta = 1^2 - 4 * 2 *(-3) \newline delta = 1 +24 = 25$

wraith daggerBOT
#

Simon James B

dusky cape
#

$x1 = (-1 +5) = 2$

wraith daggerBOT
#

Simon James B

dusky cape
#

$x2 = (-1-5)/2 = -3$

wraith daggerBOT
#

Simon James B

dusky cape
#

what am i doing wrong here? because these are not the right answers

#

the correct answers are supposed to be -3/2 and 1

#

did i get delta wrong or..:(

upper ruin
dusky cape
#

ok

upper ruin
#

You forgot that the quadratic formula has 2a in the denominator

#

In this case 4

dusky cape
#

omg

#

i am used for a to always be one so i always forget 2a ๐Ÿ˜ญ

upper ruin
#

Well if a is usually 1, you should be used to dividing by 2

dusky cape
#

OH i FORGOT to divide it all?

#

omg

#

thanks i got it now

#

.close

cedar kilnBOT
#
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vapid radish
#

It said to use a calculator and describe the answer. It became infinity so I assume that means it lacks a value because the graph is unlimited?

vapid radish
#

aka it grows forever when x gets closer to 1/2

#

?

odd verge
#

,w Plot y=tanฯ€x

wraith daggerBOT
frigid dust
#

,w int tan(pi x)dx from 0 to 1/2

frigid dust
#

yup

#

mby they meant from 0 to 1?

vapid radish
#

0 to 0.5

#

so youre right

slate lintel
frigid dust
#

but cant you use symmetry and just say its equal to 0?

#

,w int tan(pi x)dx from 0 to 1

vapid radish
#

so whats the conclusion chat? is it continously growing therefore lacks a value when going closer to 1/2?

odd verge
vapid radish
#

which means it doesnt touch each other because its a tan graph?

frigid dust
#

,w tan(pi x) dx from -1/2 to 1/2

frigid dust
#

๐Ÿค” that does converge but from 0 to 1 doesnt?

round geode
#

Probably due to the fact that from 0 to 1 is crosses an asymtote

odd verge
#

,w int tan x

wraith daggerBOT
frigid dust
#

but you can just use u-sub to convert it into the same integral but from -1/2 to 1/2, no?

vapid radish
#

quick question . is the 4 the answer or just implying that the righthandside is 4 times bigger?

frigid dust
#

its the same thing

#

since 4 doesnt depend on x you can keep it outside of the integral

vapid radish
#

oh nvm i didnt see the lefthandside 4 ๐Ÿ˜ญ

cedar kilnBOT
#

@vapid radish Has your question been resolved?

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oblique cliff
cedar kilnBOT
frigid dust
#

!status

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

whats the question? is it how many values x has within 0 to 360degrees?

oblique cliff
#

yes and ive checked the awnser but i dont understand how to get to it

vapid radish
#

so like 30 deg + 0 times 180 then 60 deg + 0 times 180 then repeat untill its larger than 360

oblique cliff
#

so 30, 60, 210 and 240, man i went about it so wrong

vapid radish
#

which you stop

#

yeah

oblique cliff
#

thanks

#

!close

vapid radish
#

np

oblique cliff
#

.close

cedar kilnBOT
#
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cedar kilnBOT
#
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sterile quarry
#

This more of a physics question but yeah

sterile quarry
#

As we say physics is juste applied maths

#

So itโ€™s for question b

#

I know it is in French but all there is to know is that weโ€™re trying to find the differential equations pour the mouvement of the ball

#

This is what I did

#

But in the answers they do something completely different but the answers are very similar and only change by a factor of a constant

#

So the question is where did I go wrong/ why canโ€™t we do what I did

cedar kilnBOT
#

@sterile quarry Has your question been resolved?

cedar kilnBOT
#
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devout shadow
#

hi can someone help me check if this is correct

cedar kilnBOT
#

@devout shadow Has your question been resolved?

sterile quarry
#

wtf heโ€™ll nah

#

.reopen

fresh patio
cedar kilnBOT
#

@devout shadow Has your question been resolved?

cedar kilnBOT
#

@devout shadow Has your question been resolved?

river heart
#

i swear if 1 person says helpersbleak bleakkekw

cedar kilnBOT
#

@devout shadow Has your question been resolved?

cedar kilnBOT
#
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steep wyvern
#

hi

cedar kilnBOT
dim tiger
#

hi

#

so whats the question

pallid parrot
#

show me your question

steep wyvern
#

1 min

frigid dust
#

!da2a

pallid parrot
#

i could translate it for him

cedar kilnBOT
#

No need to ask โ€œCan I askโ€ฆ?โ€ or โ€œDoes anyone know aboutโ€ฆ?โ€โ€”itโ€™s faster for everyone if you just ask your question! See https://dontasktoask.com/

dim tiger
steep wyvern
dim tiger
#

aha ok i understand the question

pallid parrot
#

Find a simplified form of the summation

dim tiger
#

although i am not sure if i will be able to answer it

#

but let me try anyway

steep wyvern
pallid parrot
#

kยฒ + k = k(k+1)

#

so substitution into this equation

#

k!(k(k + 1) + 1)

#

if you expand this it will be

#

k! * k(k + 1) + k! * 1

#

since you're multiplying by everything inside the parenthesis

#

ุงูˆ ุจุชุถุฑุจูŠ ู…ุถุฑูˆุจ ุงู„ k ููŠ ูƒู„ ุดูŠ ููŠ ุงู„ู‚ูˆุณ

steep wyvern
#

yeah I will try ,thank you

#

where r u from

pallid parrot
#

egypt

pallid parrot
steep wyvern
#

nice to meet u

pallid parrot
quasi current
pallid parrot
#

nice to meet u 2

pallid parrot
#

sometimes it can be inaccurate

steep wyvern
quasi current
dim tiger
#

ok so try this

dim tiger
#

by expanding and separating the sums

#

after that use $k^2=(k+1)^2-2k-1$

wraith daggerBOT
steep wyvern
#

thank u so much

dim tiger
#

try it and if anything isnt clear or if you are stuck somewhere along the way tell me

steep wyvern
#

@dim tiger and then

pallid parrot
#

id distribute

steep wyvern
pallid parrot
dim tiger
#

what i said was like this

pallid parrot
#

just like how a(b+c) = ab + ac

steep wyvern
pallid parrot
#

what do you feel like doing choose it and ill help

dim tiger
#

$\sum_{k=1}^n k!(k^2+k+1)=\sum_{k=1}^n k!k^2+\sum_{k=1}^n k!k+\sum_{k=1}^n k!$

wraith daggerBOT
dim tiger
#

from here work with the first sum

dim tiger
#

and then distribute and simplify

pallid parrot
#

you could simplify the k equation first then use the sum

dim tiger
#

after that you will get a subtraction of 2 summations

#

which cancels out things

#

and leaves you with the closed form that you are looking for

steep wyvern
#

tysm

pallid parrot
#

also before you cancel put in numbers to test and see which is cancelled

#

and after you cancel try numbers and check if they're the answer

#

that's pretty much it

dim tiger
#

try that and then if you have questions about it you can tell me

steep wyvern
#

I complete?

dim tiger
steep wyvern
#

on side 1 or 2

#

or both

#

@dim tiger

dim tiger
#

on the right hand side of the last equation in the last line

steep wyvern
#

@dim tiger

dim tiger
#

maybe you meant another thing idk but what is written here is incorrect

#

you need () around (k+1)^2-2k-1

#

since all of this is multiplied by k!

steep wyvern
#

yeah

#

@dim tiger

#

like that?

#

@dim tiger

dim tiger
#

yes

#

now distribute that

#

and separate it into 3 sums

steep wyvern
#

in the right side

#

@dim tiger

dim tiger
#

yes

steep wyvern
#

@dim tiger

#

Yes ?

#

@dim tiger

dim tiger
#

almost everything is correct

#

$-\sum_{k=1}^n k!(-1)$ should be $-\sum_{k=1}^n k!(1)$ instead

wraith daggerBOT
dim tiger
#

after you do this simplify as much as you can

#

so if there are things that will cancel out and so on

steep wyvern
#

@dim tiger

#

@dim tiger

#

Where r u

#

@dim tiger

dull oxide
#

don't ping spam

dim tiger
#

i am here

steep wyvern
dim tiger
steep wyvern
dim tiger
steep wyvern
#

Cuz I tag so much

dim tiger
steep wyvern
#

Sorry

#

Yes I forgot 1

dim tiger
#

you had $\sum_{k=1}^n k!(k+1)^2-\sum_{k=1}^n k!(2k)-\sum_{k=1}^n k!+\sum_{k=1}^n k!k+\sum_{k=1}^n k!$ and then $-\sum_{k=1}^n k!+\sum_{k=1}^n k!=0$ but you forgot $\sum_{k=1}^n k!k$

wraith daggerBOT
steep wyvern
dim tiger
#

alright

#

you can simplify more

#

why

#

because $\sum_{k=1}^n k!(2k)=2\sum_{k=1}^n k!k$

wraith daggerBOT
dim tiger
#

so what happens to $-\sum_{k=1}^n k!(2k)+\sum_{k=1}^n k!k$?

wraith daggerBOT
steep wyvern
#

Now I can @dim tiger

dim tiger
steep wyvern
#

1 min

dim tiger
#

alright take your time

steep wyvern
#

@dim tiger

dim tiger
#

ok you forgot k! in the first term of the right hand side but thats just a typo

#

so from here

dim tiger
#

$\sum_{k=1}^n k!(k+1)^2-\sum_{k=1}^n k!k=\sum_{k=1}^n k!(k+1)(k+1)-\sum_{k=1}^n k!=$ ??

wraith daggerBOT
dim tiger
#

k!(k+1)=?

steep wyvern
#

K!2k

dim tiger
#

no

steep wyvern
#

Yes that's wrong

#

๐Ÿฅฒ

dim tiger
#

k!=k(k-1)(k-2)...(3)(2)(1)

#

so now if you muliply that by k+1 what do you get

steep wyvern
#

K!k+k!

dim tiger
#

hmmm let me ask you in another way

#

what is (k+1)!

dim tiger
steep wyvern
#

But I didn't understand (3) (2)(1)

dim tiger
#

i meant that they are multiplied

#

what is k!

steep wyvern
#

So (k(k_1)(k_2).....(3)(2)(1))(k+1)

dim tiger
#

and what is k(k-1)(k-2)...(3)(2)(1)

steep wyvern
#

K! ๐Ÿ˜ญ

dim tiger
#

alright great

#

so (k+1)!=??

steep wyvern
#

(K+1) (k-1)(k-2).....(3)(2)(1)

#

?

dim tiger
#

so write (k+1)! in terms of k!

steep wyvern
#

(K(k-1)(k-2)....(3)(2)(1))((k+1)(k-1)(k-2)....(3)(2)(1))

#

?

dim tiger
#

(k+1)!=(k+1)k(k-1)(k-2)...(3)(2)(1) and k(k-1)(k-2)...(3)(2)(1) so (k+1)!=??

steep wyvern
#

(K+1)!=k!

#

No

#

(k+1)!=k!(K+1)

steep wyvern
#

@dim tiger

dim tiger
dim tiger
steep wyvern
#

@dim tiger

steep wyvern
#

@dim tiger

#

And now?

dim tiger
#

ok

#

so now is the last step

#

write some of the first terms of each of these sums

#

and notice that a bunch of terms cancel

#

write down what remains

#

and that will be your closed form

steep wyvern
#

yes I will try and tell u

dim tiger
#

ok

steep wyvern
#

that's right

#

?

#

@dim tiger

dim tiger
wraith daggerBOT
dim tiger
#

the left hand side is wrong by the way

steep wyvern
#

k!to !

dim tiger
#

i am only paying attention to the right hand side

dim tiger
steep wyvern
#

what should i do now

fallen heath
#

$\sum_{k=1}^n k!(k^2 + k + 1) = \sum_{k=1}^n k!\cdot [(k+1)^2 - k] = \sum_{k=1}^n (k+1)^2 k! - \sum_{k=1}^n k\cdot k! = \sum_{k=1}^n (k+1)\cdot (k+1)! - \sum_{k=1}^n k\cdot k!$

wraith daggerBOT
fallen heath
#

It's a one-liner. Can you proceed from here @steep wyvern ?

steep wyvern
#

will try

fallen heath
#

Write down terms from both the Sum and you'll know what to do next

steep wyvern
#

The same result here

#

@dim tiger

#

@fallen heath

fallen heath
#

Yes, I can see that

#

You need to use that relation by writing terms of both the sums and noticing if you can maybe simplify

steep wyvern
#

Can I do that??

#

@dim tiger

#

@fallen heath

fallen heath
#

No

#

How'd it go from $\sum_{k=1}^n (k+1)\cdot (k+1)! - \sum_{k=1}^n k\cdot k!$ to $\sum_{k=1}^n (k+1)\cdot (k+1)! - 2\sum_{k=1}^n k\cdot k!$

wraith daggerBOT
steep wyvern
#

Or

fallen heath
#

The one before was correct.. you're just supposed to write out the terms, as in

(2โ€ข2! + 3โ€ข3! + ... + (n+1)(n+1)!) - (1โ€ข1! + 2โ€ข2! + ... + nโ€ขn!)

steep wyvern
#

That's correct

#

?

fallen heath
#

No

steep wyvern
#

So

twilit bison
steep wyvern
#

I wanna complete this

steep wyvern
twilit bison
#

yeah you're almost there

#

$\sum_{k=1}^{n} (k+1)\cdot (k+1)! = \sum_{k=2}^{n+1} k\cdot k!$

wraith daggerBOT
fallen heath
#

You reached here this @steep wyvern And that is correct. Now to proceed from here, you need to write out each term of the sum

twilit bison
#

there's probably different ways to do it if you don't want to change index

steep wyvern
#

After this I should write out each term of the sum

frigid dust
#

,rcw

wraith daggerBOT
steep wyvern
#

But how

dim tiger
#

so what does $\sum_{k=1}^3 k$ mean for example

wraith daggerBOT
dim tiger
#

it means 1+2+3

steep wyvern
#

Yes

dim tiger
#

so basically what you do is that you start from the point you set

#

in this case k=1

#

substitute this value in what is inside of the sum

#

then add the next term which will be substituting k=2 instead of k=1

#

and repeat the process till you reach the upper limit of the index that you set

#

so for example $\sum_{k=1}^n k^2=1^2+2^2+3^2+\cdot\cdot\cdot+n^2$

wraith daggerBOT
dim tiger
steep wyvern
#

And the Solution should be 1 side

dim tiger
#

so how do you write $\sum_{k=1}^n (k+1)!(k+1)$ term by term

wraith daggerBOT
steep wyvern
#

I didn't understand how to write term by term because of this (k+1)!(K+1)

dim tiger
#

substitute k=1

#

thats the first term

#

then add the next term

#

you get the next term by substituting k=2

#

so what do you get if you substitute k=1

dim tiger
steep wyvern
#

(1+1)+(2+1)!(1+1)+(2+1)

#

?

dim tiger
#

how did you get that

steep wyvern
dim tiger
steep wyvern
#

I didn't understand ๐Ÿฅฒ

dim tiger
#

my question is like this : what is the value of (k+1)!(k+1) for k=1

steep wyvern
#

And n=?

dim tiger
#

there is no n here

dim tiger
steep wyvern
#

It's 4?

dim tiger
#

think of this as independent of anything above

dim tiger
#

what is its value for k=2 ?

steep wyvern
#

18

dim tiger
#

thats right

#

ok so $\sum_{k=1}^2 (k+1)!(k+1)=??$

wraith daggerBOT
steep wyvern
#

22

#

ุŸ

dim tiger
#

great

#

so now $\sum_{k=1}^n (k+1)!(k+1)=??$

wraith daggerBOT
dim tiger
#

just write it as a sum of terms

dim tiger
# wraith dagger

so you said that this is 22 . why? because it is 4+18 or in other words it is (1+1)!(1+1)+(2+1)!(2+1)

dim tiger
steep wyvern
#

Yes

dim tiger
#

write it as (1+1)!(1+1)+(2+1)!(2+1)+???

#

only write the first few terms then ... and the last few terms

steep wyvern
#

+(n_1+1)!(n-1+1)+(n+1)!(n+1)

#

?

dim tiger
#

you forgot a term between these 2

#

what comes after (n-1)!(n-1)?

#

is it really (n+1)!(n+1)

steep wyvern
#

Only n?

dim tiger
#

wdym by only n

#

you mean only n instead of n+1

#

so n!n?

steep wyvern
#

No

dim tiger
#

then what did you mean

steep wyvern
#

no I was wrong

dim tiger
#

ok so what is your correction

steep wyvern
#

why

#

cuz

#

10 before it 10-1

#

for exemple

dim tiger
#

is n-1=(n+1)-1??

steep wyvern
#

no

dim tiger
#

nvm i misread mb

steep wyvern
#

so what

dim tiger
#

what you wrote is correct

steep wyvern
#

yeah

dim tiger
#

alright so $\sum_{k=1}^n (k+1)!(k+1)=(1+1)!(1+1)+(2+2)!(2+2)+\cdot\cdot\cdot+(n-1+1)!(n-1+1)+(n+1)!(n+1)$

wraith daggerBOT
dim tiger
#

now do the same process for $\sum_{k=1}^n k!k$

wraith daggerBOT
steep wyvern
#

(1.1 )+(2.1+)....(n-1!.1)+(n!.1)

dim tiger
#

??

steep wyvern
#

no wait

#

(1!.1)+(2!.2)+....(n-1!.n-1)+(n!.n)

dim tiger
#

alright

steep wyvern
#

nd then

dim tiger
#

now $\sum_{k=1}^n (k+1)!(k+1)-\sum_{k=1}^n k!k=(1+1)!(1+1)+(2+1)!(2+1)+(3+1)!(3+1)+\cdot\cdot\cdot+(n-2+1)!(n-2+1)(n-1+1)!(n-1+1)+(n+1)!(n+1)-[1!1+2!2+3!3+\cdot\cdot\cdot+(n-1)!(n-1)!+n!n]=(1+1)!(1+1)+(2+1)!(2+1)+(3+1)!(3+1)+\cdot\cdot\cdot+(n-2+1)!(n-2+1)(n-1+1)!(n-1+1)+(n+1)!(n+1)-1!1-2!2-3!3-\cdot\cdot\cdot-(n-1)!(n-1)!-n!n=??$

wraith daggerBOT
steep wyvern
#

yeah

#

can we complete tmrw plz

#

you really helped me

#

thank u so so much

dim tiger
#

you still need one step

#

just simplify this now

#

notice that almost all of the terms cancel

#

only 2 terms remain

#

work out which 2 remain and you are done

#

with this i am done

#

think about it when you want

#

and i am sure you will get the answer

steep wyvern
#

thank u

#

so can i send tmrw

dim tiger
#

sure np

steep wyvern
#

tysm

cedar kilnBOT
#

@steep wyvern Has your question been resolved?

#
Channel closed

Closed by @steep wyvern

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

cedar kilnBOT
#

Please don't occupy multiple help channels.

#
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Send your question here to claim the channel.

Remember:
โ€ข Ask your math question in a clear, concise manner.
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โ€ข After 15 minutes, feel free to ping <@&286206848099549185>.
โ€ข Type the command .close to free the channel when you're done.
โ€ข Be polite and have a nice day!

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

dapper lotus
#

can someone explain how we get Z here?

cedar kilnBOT
dapper lotus
#

is it given? is there a way of calculating it?

clear umbra
#

normal table

dapper lotus
clear umbra
#

normal distribution table

dapper lotus
clear umbra
#

you have 95% confidence right

dapper lotus
#

yes

clear umbra
#

whats the alpha value for it

dapper lotus
#

could you explain to me like i have no idea what i'm talking about

#

what is an alpha value

clear umbra
#

this your first time learning this?

dapper lotus
#

yes

clear umbra
#

alpha is just 1 - confidence

#

95% is 0.95

#

so alpha = 1-0.95 = 0.05

dapper lotus
#

okay

clear umbra
#

and this is a confidence interval

#

there will be two sides

#

so you'll need to divide it by 2

dapper lotus
#

i divide 0.05 by 2?

clear umbra
#

yes

novel veldt
dapper lotus
dapper lotus
clear umbra
#

0.05/2 is 0.025 correct

#

?

clear umbra
dapper lotus
clear umbra
#

now do you have a normal distribution table

dapper lotus
clear umbra
#

do you know the normal distribution

dapper lotus
clear umbra
#

?????

dapper lotus
#

what is the normal distribution

#

i don't know man

#

describe it

clear umbra
dapper lotus
#

no

#

i do not

clear umbra
#

oh dear lord

fresh patio
#

Normally distribute deez nuts

novel veldt
#

bro just assume its given

clear umbra
fresh patio
dapper lotus
#

i am so cooked

clear umbra
#

why are you learning confidence intervals when you dont know what a normal distribution is

dapper lotus
#

do you know how to use R? cause i know we're meant to be using that but the professor does not show us how that is involved in the "getting Z process"

clear umbra
#

i havent used R in months lol

dapper lotus
# clear umbra i havent used R in months lol

me neither i basically passed the entire subject and then got told a month later "yo by the way you missed this one midterm (i dislocated my leg at the time) and you need to retake it, oh and by the way if you fail this you fail the whole subject"

#

the first half of the subject is R and excel and data analysis

#

second half is all discrete math

#

and i already passed all the discrete math shit

#

and a good majority of the data anlysis shit

#

this is the only thing i don't understand

clear umbra
#

take this

dapper lotus
#

along with the rest of the"equation sheet" but this is the most relevant thing

clear umbra
#

then just use that and dont care how you get it

#

but thats not what your question was is it

dapper lotus
#

dude i'm running off no hours of sleep right now

#

i appreciate your help a lot though

#

i'm going to leave for now, and assume that Z is given

#

thank you for your help

#

if i need more i'll rejoin

#

.close

cedar kilnBOT
#
Channel closed

Closed by @dapper lotus

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cedar kilnBOT
#
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dense shoal
#

Could someone help here? I am very confused because there is no x approaching sign

dense shoal
#

Is the question just wrong?

livid hound
#

they probably intend
limit for x to inf

dense shoal
#

Becuase you need a limit?

livid hound
#

poorly worded question

dense shoal
#

Should I just assume x-->+inf?

livid hound
#

yes

dense shoal
#

okay thanks

dense shoal
livid hound
#

wrong

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why do you think it's dne

dense shoal
livid hound
#

no

dense shoal
#

Oh, so its -1?

livid hound
#

you can attain the value,
the limit will indeed be -1

dense shoal
livid hound
#

yes

dense shoal
#

okay thank you so much!!

cedar kilnBOT
#

@dense shoal Has your question been resolved?

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Channel closed

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#
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livid cipher
#

I have a set of parametric equation: x=2t+1 and y=2-t, when I graph it, I can't find the limitation and I just have a continious line, so how do I find the limitation?

livid cipher
#

I know I am supposed to use the orginal parametric and graph x vs t graph and y vs t graph

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but even if I graph it, I still don't know what the limit is

dire geode
#

Limit of what as what

livid cipher
#

like on the x and y coords on the x vs y graph

#

which will be the graph I am trying to get

dire geode
#

Do you want a graph or do you want a limit of something

livid cipher
#

I want the graph, but the graph, which is a line, won't be continious, and I want to figure out from which point to which is the graph

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because it will have some limitations because of t

dire geode
#

What limitations are there on t

livid cipher
#

well, you can check on desmos

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but i will put a screenshot here

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actually nvm

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im being dumb

dire geode
#

Where did the requirement 0<= t <= 1 come from

livid cipher
#

yea

#

i just saw that

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i think desmos did it automatically

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i didn't see it until now

#

mb

#

.close

cedar kilnBOT
#
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cedar kilnBOT
#
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livid cipher
#

quick question, in parametric, does x^2+y^2=t^2?

swift olive
#

What was the original question?

livid cipher
#

the one I just asked

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in parametric, does x^2+y^2=t^2

crimson sedge
#

wdym parametric?

livid cipher
#

parametric equation

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because in polar

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x^2+y^2=r^2

swift olive
#

Correct

#

The parametrization of a circle would be
x = rcos t
y = rsin t

crimson sedge
#

the question is poorly asked to be honest. If you can express x and y as functions of a parameter (probably just one), you can find lots of parametrizations

livid cipher
#

.close

cedar kilnBOT
#
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cedar kilnBOT
#
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Remember:
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โ€ข After 15 minutes, feel free to ping <@&286206848099549185>.
โ€ข Type the command .close to free the channel when you're done.
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delicate yacht
#

@livid cipher assuming that you meant the previous parametrisation,

$x=2t+1$ and $y = 2-t$, then

$x^2+y^2= (2t+1)^2+(2-t)^2 = 5t^2 + 2t + 5 $

... so, no, it isn't just $t^2$... and it wouldn't be a single circle anyway

because $t$ takes multiple values.

wraith daggerBOT
cedar kilnBOT
#

@delicate yacht Has your question been resolved?

delicate yacht
#

Hopefully @livid cipher will see thus comment, even though the bot thinks I am asking a question...

#

So...

#

.close

cedar kilnBOT
#
Channel closed

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cedar kilnBOT
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dim gulch
#

the last part

cedar kilnBOT
feral juniper
#

!status

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

can you show it?

dim gulch
#

i got 3400pi

#

but cant figure why its wrong

dim gulch
#

can u find the right answer please

feral juniper
#

do you know what is meant with similar in this context?

dim gulch
#

i understood

#

i did...

sly swan
#

idk

dim gulch
#

$$ 4000\pi - 1000\pi + 20^2\pi $$
$$ = 3400\pi $$

sly swan
#

can u explain what similar means

dim gulch
#

@feral juniper

#

which should be correct right

wraith daggerBOT
sly swan
#

does it mean same ratios?

dim gulch
feral juniper
sly swan
feral juniper
#

so @dim gulch what is the ratio of s to r

feral juniper
dim gulch
#

i am talking about last part

#

in the second pic

feral juniper
#

I know

dim gulch
feral juniper
#

you want to derive that r = 20cm

dim gulch
#

ik how

sly swan
#

wait hades

dim gulch
#

but do the calc the surface area

sly swan
#

which one do u need help with

#

the first pic or the second pic?

dim gulch
#

the one i sent

sly swan
#

i see