#help-13

1 messages · Page 261 of 1

vernal kite
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oh whoops

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alr

wicked mantle
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..

vernal kite
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x^2

wicked mantle
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How about AB?

vernal kite
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1+x+x^2

wicked mantle
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Do you know how to assume two terms that one is greater than the other( a>b)?

vernal kite
#

nope

wicked mantle
# vernal kite nope

Assume a-b>0
If the case is not valid, then the answer will be on the other side

vernal kite
#

does it have something to do a+b > c
b + c > a
c + a > b

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or is that different

wicked mantle
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Different

vernal kite
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alr

vernal kite
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its a perfect square

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x^2 + x + 1 - 3x > 0

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oh wait no

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no it isnt

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whoops

wicked mantle
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I guess yk what to do next, right?

vernal kite
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factorise

wicked mantle
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yessss

vernal kite
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x = 1

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which is larger than 0

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so therefore ab is larger than 3qr

wicked mantle
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Valid, the assumption was true

vernal kite
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what does it mean in the second part

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determine when equality occurs

wicked mantle
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Draw the pic of the graph first

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Of that arquatic function

vernal kite
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x int is 1

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y int is 1

wicked mantle
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yep

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When x=1

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The equality becomes true

vernal kite
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could it also be x is larger than or equal to 1

wicked mantle
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There is only one condition that equality is true

vernal kite
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ohhhhh

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i get what u mean

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alrlr

wicked mantle
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Any questions left?

vernal kite
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for now nope

wicked mantle
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Alr

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Gl fam

vernal kite
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oh wella cttually

wicked mantle
#

Type
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wicked mantle
vernal kite
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i have one mroe

wicked mantle
#

Sure

vernal kite
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the things not sending gimme a sec

wicked mantle
#

Okay

vernal kite
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so with this question, i’ve proved the 4 triangles, how can i prove it’s a rhombus now

wicked mantle
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First, prove that the four sides of the "unknown" graph are the same

vernal kite
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so ps, pr, sr and rq?

wicked mantle
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Second, prove that the diagonals of the "unknown" graph are vertical to each other

wicked mantle
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I just realized that you don’t need second part lol

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The first part is just enough

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gl, ping me when you’re done

vernal kite
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@wicked mantle does it hjave something to do with pythag?

wicked mantle
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Pythag?

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yes

vernal kite
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pythagoras theorem

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so (so)^2 + (po)^2 = (sp)^2

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and if we replicate that in all four triangles

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each side of the rhombus is the same

wicked mantle
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yep

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Correct

vernal kite
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so would i say since all sides are equal

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therefore pqrs is a rhombus

cedar kilnBOT
#

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glossy vale
#

When writing a sequence, do u need to write it by order or by most to least? If there is a repeat term, do u write it twice?

dire geode
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and for what purpose

glossy vale
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We have an assignment which asks us to find the first 5 terms of a sequence whose general term is insert formula

dire geode
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depends on the formula

glossy vale
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I believe I posted the exact assignment yesterday

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I'm just confused as to how I should write the sequence

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See the terms are supposed to be -2, 1, 0, 1, 32 do I write it that way or does it have to be least to most? So, -2, 0, 1, 32 no repeated terms?

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@dire geode

dire geode
glossy vale
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Oh its an=(n - 3)^n

dire geode
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for what n

glossy vale
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Depends on which number of a sub so 1, 2, 3, 4, 5

dire geode
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yea then your answer should be in order of n = 1, 2, 3,...

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a1, a2, a3, ...

glossy vale
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Okay, got it. Thanknyou!

#

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cedar kilnBOT
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crimson sedge
cedar kilnBOT
queen canyon
#

Please help I don’t understand how to get these two answers I’m grade 10

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I’m stuck on where to even start I k no w these will be on test and forget. Everything else was easy with conjugated but I think this is similar where u multiple by both denominator and numerator but after that I don’t know

crimson sedge
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.close

cedar kilnBOT
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hearty arch
cedar kilnBOT
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gray oasis
cedar kilnBOT
gray oasis
#

Help me understand a.)

dire geode
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,rotate

wraith daggerBOT
dire geode
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which equation doesn't make sense first

gray oasis
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The first one below a

cinder shard
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its just poor working out. f(x) = cos, f' = -sin

They should have wrote f(x) = cos on that line, OR f'(x) = d(cosx)/dx

dire geode
gray oasis
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Where?

dire geode
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f'(x) = cos x is wrong

gray oasis
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Why?

wraith daggerBOT
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riemann

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riemann

gray oasis
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Yes

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f'(cosx) = -sinx right?

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@dire geode

dire geode
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$f'(x) = (cos(x))' = -sin(x)$

wraith daggerBOT
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riemann

gray oasis
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Ah okay okayy

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How about for the second line?

dire geode
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m = slope

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slope at a point = derivative at a point

cinder shard
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the function 'm' is not defined.

When you write f(input) that is the function named f, and an input you are passing to it.

You seem to not understand function notation fully. Scratching up on that should help you

You should write f'(pi/2) instead and calculate. Then say let the tangent be y, g(x) or another name and define it as y=mx+c. Then say that the gradient of the tangent, m, is equal to f'(pi/2).

gray oasis
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Where did -1 came from?

cedar kilnBOT
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@gray oasis Has your question been resolved?

dire geode
#

in particular that one

cedar kilnBOT
#
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open mauve
cedar kilnBOT
#

@open mauve Has your question been resolved?

open mauve
#

@old ridge

cedar kilnBOT
#

@open mauve Has your question been resolved?

open mauve
#

<@&286206848099549185>

delicate yarrow
#

<@&286206848099549185>

crimson sedge
delicate yarrow
#

their question still hasnt been answered

cedar kilnBOT
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@open mauve Has your question been resolved?

open mauve
#

<@&286206848099549185>

crimson sedge
open mauve
crimson sedge
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that is different person

open mauve
open mauve
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<@&286206848099549185>

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So... anyone?

cedar kilnBOT
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@open mauve Has your question been resolved?

spice pilot
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@open mauve

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i got u

open mauve
#

You can help?

cedar kilnBOT
#

@open mauve Has your question been resolved?

cedar kilnBOT
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royal loom
#

$g^{(n)}(x)=p_n(1/x)e^{-1/x}$ for $x>0$ and some degree $2n$ polynomial $p_n$

wraith daggerBOT
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Austin

royal loom
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I am trying to prove this by induction but I keep getting stuck on the degree part at the end

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the base case I've done

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suppose it is true that g^(m)(x)=p_m(1/x)e^(-1/x) where that polynomial is degree 2m

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then

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g^(m+1)(x)= (p_m(1/x))' * -1/x^2 + 1/x^2 e^(-1/x)

flint plinth
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are you going to make us guess what g might be bleakkekw

royal loom
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g doesn't matter

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but it's e^(-1/x)

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for x>0

flint plinth
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well what are you trying to prove then

royal loom
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just this statement about g

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okay maybe g does matter

flint plinth
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"g doesn't matter"

royal loom
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but like it's fine

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XD

royal loom
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and then multiply by the 1/x^2 and it will give 2m+3

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which I don't want

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it should be 2m+2

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but I don't see a mistake hmmcat

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$$g(x)=e^{\frac{-1}{x}} \quad x>0$$

wraith daggerBOT
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Austin

royal loom
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$$g'(x)=\frac{1}{x^2}e^{\frac{-1}{x}}$$

wraith daggerBOT
#

Austin

royal loom
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Suppose $g^{m}(x)=p_m\left(\frac{1}{x}\right)e^{\frac{-1}{x}}$ where $p_m$ is degree $2m$

wraith daggerBOT
#

Austin

royal loom
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Then $$g^{m+1}(x)=\left(p_m\left(\frac{1}{x}\right)\right)'\cdot \frac{-1}{x^2} + \frac{1}{x^2}e^{\frac{-1}{x}}$$

wraith daggerBOT
#

Austin

royal loom
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and I have no idea how this new thing is supposed to match up with the degree we want

cedar kilnBOT
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@royal loom Has your question been resolved?

royal loom
#

.close

cedar kilnBOT
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cedar kilnBOT
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drifting dove
#

"A woman’s necklace of pearls broke while (rule 2).
A third of the pearls rolled onto the floor,
one-fifth was scattered on the bed,
she herself retrieved one-sixth,
and her lover picked up one-tenth.
If only six pearls remained on the string,
how many pearls did the necklace have?"
Found this in my book

drifting dove
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Seems like algebra, but im not sure where to start

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The name of the poem is elementary arithmetic

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So... 💀

dusty path
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So for this question, you will be adding fractions. Start off by taking all of your fractions and adding them. From there, you can obtain the lowest common denominator. From there, solving this is a matter of adding the numerators, then simplifying your final fraction (if possible, which it should be due to the context of the question involving whole objects).

drifting dove
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Idk whar that means

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Domeone help

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<@&286206848099549185>

dusty path
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I apologise for not answering for a while. So you understand that this is a fractions problem, right?

drifting dove
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No

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This is a necklace problem

dusty path
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Well yes, it is a necklace problem involving fractions.

drifting dove
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Sure

tepid sail
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go on please

dusty path
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You have your set of fractions. To get the total number of beads, you must add the fractions, and in order to add fractions with different denominators, as shown in the problem, you want to make all the fractions have the same denominator.

drifting dove
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What denomonator

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I try 60

dusty path
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The denominators of all of your fractions. You want to make the denominators of all fractions the same denominator.

drifting dove
#

Or maybe 30

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I got 24/30

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Waitt

cedar kilnBOT
#

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bold ermine
#

what's a factor theroem

cedar kilnBOT
spice kraken
#

factor theorem states that if (x-a) is a factor of f(x), f(a) = 0

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acoustic helm
#

hello

cedar kilnBOT
acoustic helm
#

there was a test question i wasn't able to solve, i cant remember all the components but it goes like this:

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the equation of asymptotes of a hyperbola are y=± (4/3)x

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However, the focal points are (0,10), (0, -10)

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The part that confused me was the focal points

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because i thought the focal points would be: a^2 +b^2 = c^2 ---> ±√(a^2 +b^2) = c

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but it doesnt work in this case

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Please and help and thank you!

#

.close

cedar kilnBOT
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vague falcon
#

Whats 1+1?

sharp lotus
vague falcon
#

Whats up?

sharp lotus
#

consult Whitehead and Russell

vague falcon
#

nah i do t need that i need 1+1?

dire geode
vague falcon
#

No actually

slate lintel
vague falcon
#

I dint

slate lintel
#

.close

solid juniper
cedar kilnBOT
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mossy pivot
cedar kilnBOT
mossy pivot
#

Whered i go wrong

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og question

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my answer

spice kraken
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it's not (4sint)(3cost)

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don't use product rule

mossy pivot
#

oh

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ohh

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wait chain rule

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idk hwy i did product rule

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wait

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wait yeah then how do i get g'

spice kraken
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g'(t)=8(4sint+3cost)^3(4sint+3cost)'

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now just find derivative of 4sint+3cost

mossy pivot
#

ohhh

spice kraken
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wait Ityped wrong

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lemme fix

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ok

mossy pivot
#

got it

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4cost-3sint

spice kraken
#

yep

mossy pivot
#

.close

cedar kilnBOT
#
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granite hare
cedar kilnBOT
granite hare
#

I'm working on this discrete math problem

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and I know I have to find the least common multiple of the two numbers, but I'm not really sure why that works

slate lintel
#

it might help you to write down the times that each of them return to the start

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like the first one returns at 2:04, 2:08, ...

fair geyser
#

some numbers are common multiples of 4 and 6
for example 300 is 75×4 and also 50×6
the first number like that is the least common multiple

granite hare
#

and then i would notice that they both meet at 2:12

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and 12 is the LCM of 6 and 4

slate lintel
#

and if you keep listing them out

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you'll see that they meet at every common multiple of 6 and 4

granite hare
#

so they'd meet again at 24

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then 36

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i think i see now

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thank you both

#

.close

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wary tangle
#

could anyone help me with this question? ive got no idea where i go from here💀thanks in advancee :)

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vernal kite
#

for question 2, is there anything that i’ve done wrong so far? i’m not sure what to do after the last step i did

vague rapids
#

how did u write angle DEA =150?

vernal kite
#

co interior angles

tender wharf
vernal kite
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180 - angle edc

vernal kite
vague rapids
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are those parallel

vernal kite
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nope

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i was wondering why

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but is dec 30 degrees still?

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i mean

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angle edc

tender wharf
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yes

vernal kite
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but we cant find angle dea

vague rapids
#

what I'd suggest is start from the Left most of the diagram

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assume angle HBG to be x

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then by using properties of triangles, try to label each angle in terms of x until you get to angle GDE

vernal kite
#

would angle hbg + angle hgb = angle hgf

vague rapids
#

no

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that would be equal to angle GHF

vernal kite
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ohhh alr

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so angle ghf is 2x then

vague rapids
#

well you don't need to ask "if that is equal to that"

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Just keep in mind that sum of all angles in a triangle is 180 degrees and sum of angles of a linear pair is 180

vernal kite
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i got angle bed = 8x

vague rapids
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well that is not what you should get

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check your working

vernal kite
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so ghf = 2x

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fgd = 4x

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and then angle bed = 8x

vague rapids
#

are you sure?

vernal kite
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i can't solve it

vague rapids
#

This aint nothing too hard

vernal kite
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how is it not 4x

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2x+2x

vague rapids
#

well 180= angle HGB+ angle FGH+ angle FGD

vernal kite
#

6x - 180

cedar kilnBOT
#

@vernal kite Has your question been resolved?

green mulch
#

X is 4.2 something

vernal kite
#

no

green mulch
#

X is 6

vernal kite
#

yes

green mulch
#

U got it?

vernal kite
#

nope

green mulch
#

Should I explain?

vernal kite
#

yes please

green mulch
#

Just a sec

cedar kilnBOT
#
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vernal kite
#

.reopen

cedar kilnBOT
#

green mulch
#

So now in EBD 4x + x + 150= 180

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5x = 30

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So x = 6

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Ask me if I don't understand anything

vernal kite
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how is angle fgd = 3x

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isn't the sum of two opposite interior angles = one exterior angle

green mulch
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Let fgd be y

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Then x + 180-4x + y = 180

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Solve for y and u would get y = 3x

green mulch
#

Got it?

vernal kite
#

is y just 180 - 4x + x?

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oh wait nvm

green mulch
#

Yeah...

vernal kite
#

yea i get it

green mulch
#

Btw which grade question is this

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I just wanna know

vernal kite
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grade 10

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or year 10

green mulch
#

Ohh

vernal kite
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im in australia

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this is tuition homework

green mulch
#

Noice

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I am in grade 9 htw

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Btw*

vernal kite
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in aus?

green mulch
#

In India

vernal kite
#

oh wow

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thats like

green mulch
#

We love maths for some reason

vernal kite
#

year 12 here

green mulch
#

Oh

#

I didn't know that

vernal kite
green mulch
#

How old are u btw?

vernal kite
green mulch
green mulch
vernal kite
#

yea it is

#

im gonna close this channel

#

thx for the answer

green mulch
#

Npp

#

Byee

vernal kite
#

cya

#

.close

cedar kilnBOT
#
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cedar kilnBOT
#
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crimson sedge
#

in the derivation of $\ds\vj T = \dv[\vj r]s$

wraith daggerBOT
crimson sedge
#

we can say the following:

#
\begin{align*}
\vj T &= \4{\dv*[\vj r]t}{\3{\8{\dv*[x]t}^2+\8{\dv*[y]t}^2+\8{\dv*[z]t}^2}} \qq \0r{\8[\bigg]{s = \int_\alpha^\beta\3{\8{\dv[x]t}^2+\8{\dv[y]t}^2+\8{\dv[z]t}^2}\dd t}} \\
&= \4{\dv*[\vj r]t}{\dv*[s]t}
\end{align*}
wraith daggerBOT
crimson sedge
#

but the problem is that u have to makea beta vary right? hmmCat

hollow trail
#

usually you would define it as s = integral from alpha to t of some dummy variable

crimson sedge
#

right

#

and i guess u have to place some conditions

#

like the curve has to be simple and smooth

#

(smooth: continuous and not 0. simple: does not cross itself)

hollow trail
#

i don't think it necessarily needs to be simple

crimson sedge
#

since the integral is like directed

#

@sacred grail you said something about this like 2 years ago to mexd can u tell me again

sacred grail
#

idk what the question is Xd

crimson sedge
cedar kilnBOT
#

@crimson sedge Has your question been resolved?

#
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azure marsh
cedar kilnBOT
azure marsh
#

Part d

#

I dont know how to derive the middle expression

spice kraken
#

integral represent area

azure marsh
#

yep

#

integral gives the first and last expression

#

i was thinking rectangles

spice kraken
#

yes

azure marsh
#

sum of rectangles gives middle

#

but i tried

#

didnt get anywhre

spice kraken
#

what did you get

azure marsh
#

so 1/2 + 1/3 +1/4 +.......... 1/k is the sum of the rectangles

#

after that no idea how to simplify it

spice kraken
#

??

#

how'd you get recipricols

azure marsh
#

im dumb

#

sorry

#

i get it

#

ln(k!)

#

is sum of rectanfles

#

got it thanks

#

.close

cedar kilnBOT
#
Channel closed

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azure marsh
#

Part bi

#

I get the gradient but not sure how to use part a

cedar kilnBOT
#
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split raven
#

help how do i solve for this?

cedar kilnBOT
spice kraken
#

parallel mean same slope

#

perpendicular mean slopes multiply to -1

split raven
#

ohh

#

but how do i solve it? turning it to sif? solving one by one?

spice kraken
#

yes find the slope and see if it meet the requirement

split raven
#

is letter b right for no.7? @spice kraken

spice kraken
#

I don't think so

split raven
spice kraken
#

what are the slopes you calculated

split raven
#

x - 2y = 2
-> y = 1/2x - 1

a. y = 1/2x - 5/2
b. y = x + 1
c. y = -2x + 3
d. y = -2/3x + 3

spice kraken
#

the slope is 1/2

split raven
#

oops

spice kraken
#

b has slope of 1

split raven
#

what

spice kraken
#

y = 1/2x - 1 has slope of 1/2

split raven
#

yea

#

if perpendicular it has to be -1/2 but none of the slopes in the choices are

spice kraken
#

we want the slopes to multiply to -1

#

we would actually want -2

#

since -2/2=-1

split raven
#

yea

#

so what now

spice kraken
#

well which option has slope of -2

split raven
#

c

cedar kilnBOT
#

@split raven Has your question been resolved?

cedar kilnBOT
#
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cloud igloo
#

2x + y = 1000
how do I find the highest possible value of xy?

cloud igloo
#

ping me if you respond, I am not having this chat open

earnest socket
#

solve for one in terms of hte other

cloud igloo
#

what does f(z,y) mean? I have only worked with equations with 3 unknowns on paper

raw gulch
raw gulch
cloud igloo
# raw gulch

I dont fully understand whats being done here, can you explain it step by step?

#

oh wait

raw gulch
#

find coordinates its vertex

#

then you get where x is reched and value fo max that is all

cloud igloo
#

I came to the answer x = 250 and y = 500, is that correct?

raw gulch
#

right, i was not calculatin the est in my mind, so if yo wroe correct then all is ok

#

maximum si reached at x = 250 and its max value = 500

#

\thsi way , it shud be written in an exercise book

cloud igloo
#

alright, ty

#

.close

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#
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abstract wolf
#

hey I needed some help with this question

proud vortex
#

so

#

avery

#

the tank has a 1cm thick wall

#

to find the volume of the material

#

u need 2 radii

#

one is 1m

abstract wolf
#

ummm

proud vortex
#

other is 1m + 1cm

abstract wolf
#

👀

proud vortex
#

now you apply the regular formula for the volume of cylinder but replace r square

#

with r1 square - r2 square

#

r1 being 1m

abstract wolf
#

tho

#

😭

proud vortex
#

oops its a hemispehre

#

hmm sorry

#

wait ill solve it for ya

abstract wolf
abstract wolf
#

(im just in 9th grade :,)) )

proud vortex
#

now could you solve the rest

abstract wolf
#

i cant see the third part :((

proud vortex
#

no its just dots

#

you have to calculate it

abstract wolf
#

sorry

#

uh

#

nonono

#

not that part

#

the

#

thing after volume of the material

proud vortex
abstract wolf
#

ok thanks!!

#

but why subtracting tho

#

i still dont get it

crimson sedge
crimson sedge
#

i suck at following along but

#

yh

#

ur subtracting the empty inside

#

from the full volume

#

to js find the iron leftover

#

u get it?

abstract wolf
abstract wolf
#

and thanks once again!

crimson sedge
#

ofc

abstract wolf
#

.close

cedar kilnBOT
#
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cedar kilnBOT
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green vault
#

Hi, is reverse matrix the same thing with inverse matrix?

green vault
#

And what does this phrase mean?
infinite reverse right-handed perspective projection matrix

#

.close

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#
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quick flume
#

Is this correct?

cedar kilnBOT
quick flume
#

It’s an exponential equation

mild sundial
#

the exponent rule says $a^{x+y} = a^x*a^y$

wraith daggerBOT
#

swerriee

quick flume
#

Like so?

mild sundial
mild sundial
quick flume
#

4*2^x-2

#

Idk

#

Tell me then what to do next

mild sundial
#

$x*a^x - a^x = a^x(x-1)$

wraith daggerBOT
#

swerriee

quick flume
mild sundial
mild sundial
#

The rest of it is correct

quick flume
mild sundial
quick flume
#

And what do I do next

mild sundial
#

simplify further

quick flume
#

How do I get 32 to exponential form

mild sundial
#

take lcm of 32

quick flume
#

2?

#

Alright doesnt matter

mild sundial
quick flume
#

And could you help me with this one aswell?

mild sundial
quick flume
#

Yeah I got it

mild sundial
# quick flume

bring sqroot to the other side and apply the quadratic formula

#

wait

mild sundial
quick flume
#

7^x^2

#

Is that possible to solve then?

quick flume
mild sundial
#

and root smh

quick flume
#

So how do I do it

#

.close

cedar kilnBOT
#
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pliant pine
#

this may seem like a silly question but

cedar kilnBOT
pliant pine
#

if u had a convergent sequence with limit L s. t. for all epsilon > 0, |an - L| < epislon for all n => N

#

why does it also follow that |an - L| < epsillon/2 for all n => N

#

or is there a way to prove it

azure horizon
#

it's true that |a_n - L| < e

#

so if you want |a_n - L| < f/2

#

then you can let e = f/2

#

and then that just works

pliant pine
#

but then wouldnt e just be restricted to the values of f/2

azure horizon
#

?

#

ok so: for all e > 0, there exists N st. n > N => |a_n - L| < e

pliant pine
#

yes

azure horizon
#

so suppose you want |a_n - L| < f/2

#

let e = f/2

pliant pine
#

ohh then u set e = f/2

#

and it still works

azure horizon
#

yeah it's like

#

a relabelling

pliant pine
#

how would this change for something like

#

2e tho

azure horizon
#

well it just works

#

i mean you could say the reverse thing

pliant pine
#

like does it follow that for all e > 0, there exists N st. n > N => |a_n - L| < e

azure horizon
#

ok so: for all f > 0, there exists N st. n > N => |a_n - L| < f

#

so if f = 2e

#

there exists N st. n > N => |a_n - L| < 2e

pliant pine
#

wait i perhaps asked the wrong qu

#

i want the converse of that statement

#

eg if < 2e then does it follow for all < e

azure horizon
#

yes

#

ok so: for all f > 0, there exists N st. n > N => |a_n - L| < 2f

#

you want |a_n - L| < e

#

so let e = f/2

#

then for all e > 0, there exists N st. n > N => |a_n - L| < 2f = e

#

like

#

the point is that if you can make this thing as small as you like

#

then you can just make it twice as small

#

sorta??

pliant pine
#

oh icic

#

one more qu

#

when u say for every e > 0, |a_n - L| < e for all n => N, it doesnt imply |an - L| = 0 for all n => N right?

azure horizon
#

for example just take like

pliant pine
#

then why do they do they do it in this proof

azure horizon
#

1, 1/2, 1/3, 1/4, 1/5

pliant pine
#

(last line)

#

unless im mis understandin

azure horizon
#

they're talking about the limits there

#

the limits are not the same as the sequence

#

ok so

#

take 1, 1/2, 1/3, 1/4, 1/5

pliant pine
#

yes

azure horizon
#

as one sequence

#

and then take -1, -1/2, -1/3, -1/4, -1/5 as another

#

basic

#

then the differences are

#

2, 1, 2/3, 2/4, 2/5,

#

none of these are ever 0

#

but the limits

#

the limit of the first one is 0

#

and the limit of the second one is 0

pliant pine
#

yes

azure horizon
#

and 0-0 = 0

#

the differences go to 0 but aren't 0

#

the limit of the differences is 0

pliant pine
#

waza

azure horizon
#

or something like that

pliant pine
#

but if the differences go to 0 isnt that the same thing as saying an becomes L...

#

ohh

azure horizon
#

no

pliant pine
#

go to

#

so it goes to L

#

but doesnt become L

azure horizon
#

gets arbitrarily close

#

like, as close as you like

#

but never touches

pliant pine
#

wait but then why do they conclude |M - L| = 0 tho

azure horizon
#

ok so

#

let the limit of the differences in my example be like D

#

so D is the limit of 2, 1, 2/3, 2/4, 2/5, ...

pliant pine
#

yes

azure horizon
#

then we can say

#

D < 2

#

D < 1

#

D < 2/3

#

D < 2/4

#

in fact

#

D < 2/n for all n

#

but a number that isn't negative that's smaller than 2/n for every n

#

has to be 0

#

because if D was positive then you could find 2/n smaller than D

#

but D < 2/n for all n

pliant pine
#

i am followin somewhat

#

i think this the type of thing which i need to let sit for a before it clicks

#

lol

azure horizon
#

yeah basically

pliant pine
#

also apologies if i ask a lot of qus

#

i tend to lol

pliant pine
#

the reason we say |an - L| is because if an tends to L, a_n will always get arbitrarily close to L but never actually approach it

#

hence the for all epsilon > 0, |a_n - L| < epsilon bla bla

#

however since L and M are fixed real numbers, if we say for all epsilon > 0, |L - M| < epsilon for all n => N, then this implies that |L - M| = 0 because unlike a_n which tends to the limit L, these are fixed real numbers

#

therefore the only way for them to be < epsilon for all epsilon > 0, is for |L - M| = 0

#

is that right @azure horizon ?

cedar kilnBOT
#

@pliant pine Has your question been resolved?

cedar kilnBOT
#
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open flame
#

hello , i have a question in my book that should be similar to this : but its a triangle that should be solved to find X

open flame
#

who can help?

subtle hinge
#

didnt u just get the vallue of x

open flame
#

no i meant its similar to this

#

question is :Question : find x that makes the triangle larger or equal to 20

subtle hinge
open flame
open flame
#

.close

cedar kilnBOT
#
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serene bison
#

shoudn't it be

$8(3-2x)^-4/7$

cedar kilnBOT
wraith daggerBOT
#

Daddy Goat

serene bison
#

how is it positive

dire geode
#

yup that's a typo

serene bison
#

he continued on solving it as it is lmao

open yew
#

typo

dire geode
#

can you share the video

serene bison
dire geode
#

thanks

serene bison
#

i put the time stamp read just play it

dire geode
#

rare organic chem L

serene bison
#

bro wants me to fail my math test 😂

#

good thing i noticed immediately tho!

dire geode
#

most of his videos are good

serene bison
#

so wait is the answer

#

$d/dx 52/7 ^7sqrt{3-2x ^11}$

wraith daggerBOT
#

Daddy Goat

serene bison
#

bruh

runic garnet
#

,rotate

wraith daggerBOT
runic garnet
#

try not to say d/dx = the original function

#

u wanna do

#

$\frac d{dx} [8(3-2x)^{-\frac 47}]$

#

anyways

serene bison
#

oh you mean the {}?

runic garnet
#

ok so look at ur application of the chain rule

#

when u took the derivative of the inner function

#

3-2x

#

whats the derivative of that

serene bison
#

i missed that

runic garnet
#

ye

serene bison
#

give me a sec

wraith daggerBOT
#

Stephen

runic garnet
#

also howd u get 52?

serene bison
#

,rotate

wraith daggerBOT
serene bison
runic garnet
#

but that 8 in front is being multiplied to the expression

#

its 8 * -4/7 * -2

serene bison
#

Oh yeh that should have been done first

runic garnet
#

ur final answer looks good now, just make sure u have parentheses around (3-2x) otherwise it looks like 3-2x^11

serene bison
runic garnet
#

why rationalize?

#

thats the simplest form ur gonna get

serene bison
runic garnet
#

then do it, but u wont be able to rationalize this

serene bison
#

.close

cedar kilnBOT
#
Channel closed

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runic garnet
#

dang

#

u deadlift 550 at 17

#

thats crazy

serene bison
cedar kilnBOT
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pulsar vault
#

part b, i worked out part a using cosine rule and have length ac but have no idea how to work out length dc

slow jewel
#

,rrcw

#

,rccw

wraith daggerBOT
slow jewel
#

Ig you can equate the power of the point(X) along AX and DX

pulsar vault
slow jewel
#

From the external point X, if a line is drawn to a circle intersecting at one or more points then product (BX)(AX) is a constant

#

Have you ever come across anything like that?

pulsar vault
#

im 14 bro 😭

raven shard
pulsar vault
#

is this not calculus stuff

pulsar vault
cedar kilnBOT
#

@pulsar vault Has your question been resolved?

cedar kilnBOT
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crimson sedge
cedar kilnBOT
crimson sedge
#

i dont understand how theres so many (x-6)^2

cedar kilnBOT
#

@crimson sedge Has your question been resolved?

cedar kilnBOT
#

@crimson sedge Has your question been resolved?

cedar kilnBOT
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hasty warren
#

could someone please help me? // check for convergence/divergence of series

cedar kilnBOT
#

@hasty warren Has your question been resolved?

dire geode
cedar kilnBOT
#

@hasty warren Has your question been resolved?

hasty warren
dire geode
hasty warren
#

yeah but i dont know how

#

can i just use cauchy

cedar kilnBOT
#

@hasty warren Has your question been resolved?

cedar kilnBOT
#

@hasty warren Has your question been resolved?

cedar kilnBOT
#
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uncut roost
#

hello can someone explain this

cedar kilnBOT
uncut roost
#

like how are they doing that

lost gyro
#

pretty sure that's just direct application of power rule

patent belfry
#

Yeah

uncut roost
#

it is but im not sure whats going on

lost gyro
#

d/dx(x^n) = nx^(n-1)

patent belfry
uncut roost
#

no i dont

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only if its not 0

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n =/= 0

patent belfry
#

So what do you not understand completely

uncut roost
#

what is happening in the first step

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they found the derivitive of x^4

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which is 3x^4

lost gyro
#

4x^3 but yes

uncut roost
#

oops

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i wrote it backwards

lost gyro
#

so what's confusing

uncut roost
#

then whats happening in the second step

patent belfry
#

Thats the other rule that i forgot the name of where you can take constants on a temporary vacation outside the derivative

#

So it can see the world

uncut roost
#

wow

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why is it on vacation

patent belfry
#

Its overstressed being in a function

#

Thats hard work for a poor constant

uncut roost
#

that is so sad

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i understand now

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he is a constant so he is worth nothing

lost gyro
#

do you have a textbook...reading it would probably help

uncut roost
#

he is USELESS!

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😢

#

but he only beileves hes useless

patent belfry
#

#constantslivesmatter

uncut roost
#

he is not actually useless

patent belfry
#

Yes

uncut roost
#

(what is the next step)

lost gyro
patent belfry
uncut roost
#

WOW!

#

how do you know if he has to go on vacation or not

lost gyro
#

I'm just going to leave cause I'm cringing at this conversation

uncut roost
#

LMAO

#

no wait

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DONT LEAVE!

#

@lost gyro how do you know if the constant has to go out

patent belfry
#

Sadly the fate of the addition constants in this case is death from overworking

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But multiplication constants can go outside the derivatice

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And it becomes easier to solve

uncut roost
#

so if it was

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so if it was 1/2 + 4x^3

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he cant leave?

patent belfry
#

Yep

uncut roost
#

wait where is the vacation place

patent belfry
#

He gets reduced to zero

uncut roost
#

where is he even going

patent belfry
#

Whether it be hawaii, or maybe a nice cruise ship in mexico

#

Whatever it desires

uncut roost
#

but where is the derivitve sign

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and why didnt they do that in that step

patent belfry
#

They just skipped a step

lost gyro
#

it's not implied... it's indicated by the f'(x)

uncut roost
#

does he have to leave?

patent belfry
patent belfry
uncut roost
#

always?

patent belfry
#

Yea

uncut roost
#

lets look at the second question

patent belfry
#

Same thing again basically

uncut roost
#

why cant you multipy the 4 with the 1/2

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for the first question

patent belfry
#

You can

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They do that

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To get 2x^3

uncut roost
#

cant they do that for the second step too

patent belfry
#

Thhe second question you mean

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They do do that

uncut roost
#

yes

patent belfry
#

They do 6*2/3

uncut roost
#

no

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multiply it from the top

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the little top part multiplied by the first number

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the exponent

patent belfry
#

Yea

#

They multiply those 2

uncut roost
#

no they didnt

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they f ' (x) it

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only the x^4

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🤬

#

WHY DID THEY MAKE THIS TECHNIQUE

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okay

#

i understand now

patent belfry
uncut roost
#

x^4 = 4x^3

patent belfry
#

Yes

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Then times 1/2

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And the second one

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x^2/3=2/3x^-1/3

uncut roost
#

its a different tecnique

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i understand now

patent belfry
#

Different application

uncut roost
#

okay

#

thank yo

#

you

#

:)

cedar kilnBOT
#

@uncut roost Has your question been resolved?

cedar kilnBOT
#
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uncut roost
#

hello i need help

cedar kilnBOT
uncut roost
#

with the first one

#

do i factor it?

spice kraken
#

You can expand it

uncut roost
#

okay

#

thank ypu

cedar kilnBOT
#

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cedar kilnBOT
#
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cedar kilnBOT
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crimson sedge
#

Can someone explain this to me?

cedar kilnBOT
crimson sedge
#

I dont understand any of it

cedar kilnBOT
#

@crimson sedge Has your question been resolved?

cedar kilnBOT
#

@crimson sedge Has your question been resolved?

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plush ferry
#

I have to factor by completing the square and I swear I did everything right but apparently the answer key says I’m wrong (second pic)

plush ferry
#

Nvm I used found a way to solve the process so I could see my mistake

#

.close

cedar kilnBOT
#
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cedar kilnBOT
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cedar kilnBOT
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azure marsh
cedar kilnBOT
azure marsh
#

Part b

#

Length of AB = AC = 2root(14)

hidden vapor
#

1)Apply herons
2) BC let be base
Write equation of BC and drop a perpendicular from A and find its length and 1/2 b * h

#

Kinda like this

cedar kilnBOT
#

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spice kraken
#

notice that n choose k is the number of subsets of S with k elements

cedar kilnBOT
#

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pseudo merlin
#

If a quadrilateral has 2 pairs of parallel sides then the opposite sides are congruent

pseudo merlin
#

The converse to this is If the opposite sides of a quadrilateral are congruent, then it has 2 pairs of parallel sides?

#

Is this false?

#

Maybe a counterexample could be a rhombus?