#help-38

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unborn estuary
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shell barn
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Find the smallest prime factor of 2^23 - 1

shell barn
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<@&286206848099549185>

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So we have that 2^23 = 1 mod p

zinc ginkgo
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shell barn
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So that means that the order of 2 mod p is 23

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And then since Zp is a cylic group under multiplication that means 23 has to divide the order of the group which is p-1

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Which is what my prof told me but I don't get that

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What does a cyclic group mean and why does 23 have to divide p-1

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@zinc ginkgo

zinc ginkgo
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???

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!noping

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shell barn
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Oh mb

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My prof went into something about cosets but I don't get that either

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iron swallow
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Suppose we draw a simple continuous curve bounded to the x-axis so that the curve starts at a point (x1, 0) with x1 < 0, and ends on (x2, 0) with x2 > 0, and the entire curve lies above the x-axis. I want to show that for any pair of points of intersection between this curve and y = |x|, that the curve can always be horizontally translated (can be translated both left and right) in such a way that the points of intersection will become (t,-t) and (t,t) for some real t > 0, if it is not already.

So far, I was thinking, for however you choose to draw the curve in that manner, we can consider the slope between the 2 points of intersection (which we will call m) and its sign, and we note if m = 0, then the points of intersection will be in the desired form ((t,-t) and (t,t)). If m > 0 on the chosen curve, we can horizontally translate it so eventually m < 0 and since this transformation is continuous, then we can assert that m = 0 at some point in between and likewise, if m < 0, horizontally translate until where m > 0, asserting m = 0 in between.

I am not sure how to further formalise this and/or if there are errors in this proof sketch, especially with the nature of how wildly one can draw such curves. Any tips on how to move on from here, or if there are any errors so far that I may have missed in this sketch?

tepid hamlet
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i assume you meant 2nd because abs value is positive but you are suggesting there's some point of intersection with a negative y

iron swallow
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oh yeah sorry i did mean (-t, t) since it is absolute value

tepid hamlet
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if your curve contains the points (x1, 0) and (x2, 0) then you cannot say that "the entire curve lives above the x-axis" because those two points are ON the x axis not above it and they are part of the curve

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so are you trying to say that all y values of points on the curve should be non-negative, but it is ok for them to be 0?

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anyway i think i kinda get what you're trying to say and i feel like it's just some kinda strange re-telling \consequence of Rolle's Theorem \ Mean-Value Theorem or something along those lines

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like basically, if one point is higher than the other, then we can move the curve horizontally and there must be some y value between 0 and that point's y value that is better suited, well that is just a consequence of continuity and the mean value theorem

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@iron swallow are you still here? 😛

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@iron swallow Has your question been resolved?

iron swallow
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But you got what i meant lol

iron swallow
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Like non function ones too?

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That part im not necessarily certain about

tepid hamlet
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if you could find some translation that guarantees a positive slope between the 2 points

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then some translation that guarantees a negative slope

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since the slope is also changing continuously as you translate

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mean value theorem guarantees there is some translation for every value in between (i.e. 0)

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it's kind of a classic mean value theorem set up but i'm not exactly sure on how to prove

iron swallow
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Ahh ok i see

iron swallow
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paper torrent
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so...this friday i have my annual exam of math, and i've done pretty less. But i'm kinda good at math but i'm still scared (like for eg on tests i get 25/30 and im in india so you can guess the educational system). They make like extra complex questions and some guides are just impossible to do. Many easy chapters are cut and this is the weightage

Number system-10
Polynomials-17
Linear equations in two variables- 7
Triangles-10
Heron's Formula-6
Surface area and volumes-9
Quadrilaterals-4
Circles-14
Statistics-3

(Its an 80 marks paper)

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paper torrent
wraith hinge
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these channels are meant for specific mathematics questions

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not to provide opinions or such

remote wave
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what kind of question is "can i do this or not"

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just try

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and you'll find out

paper torrent
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ohhk thanks

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so i'm confused in question number 8
i used the theorem angle subtended by the arc at the centre is double the angle subtended by it.
so <APB = reflex<AOB
2x50 = 100
so <AOB = 360-100 = 260 (but that cannot happen because according to ASP property of a triangle 260 cannot be an angle. Help?

tepid hamlet
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that has to do with an angle with its vertex at the center (i.e. angle POQ in this figure subtending the arc PQ) vs the angle PAQ where the vertex of the angle is on the CIRCUMFERENCE of the circle. in the case of problem 8, it doesn't involve a point on the circumference so it doesn't apply

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in this case angle POQ has double the measure of angle PAQ

paper torrent
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oh yes

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the circumference!

tepid hamlet
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the most obvious way to think of problem #8 is to use the idea that tangents to the circle will make right angles with a radius meeting at the same point and consider this quadrilateral:

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what is the sum of the angles of a quadrilateral (four sided shape)?

tepid hamlet
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yes, so then what would be the measure of angle AOB?

paper torrent
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OHH

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230?

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ohh

tepid hamlet
paper torrent
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oh shit

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yeah

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130

tepid hamlet
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and now triangle AOB is isosceles (the two radii are congruent) so you can find out the other angles in it with the obvious sum of angles in the triangle

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so final answer is? : )

paper torrent
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65?

tepid hamlet
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how are you getting that

paper torrent
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oh wait

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no

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NONONO

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25?

tepid hamlet
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yes

paper torrent
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lol

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i tried to do mental math but yeah it doesnt work for me ig

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btw one more thing

paper torrent
tepid hamlet
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because PA and PB are tangents

paper torrent
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tangents? 👀

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i'm just in 9th grade oml 😭

tepid hamlet
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the problem says: "in the figure PA and PB are tangents to the circle"

paper torrent
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oh....

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they didnt teach us that but wtv

tepid hamlet
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a tangent touches the circle at exactly that 1 point and is perpendicular to the radius to that point

paper torrent
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urea'
kl;

paper torrent
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okay!

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tysm!

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this was really helpful!

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and also

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what abt ques number 7?

tepid hamlet
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https://en.wikipedia.org/wiki/Tangent_lines_to_circles
read just the first paragraph of this

In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is perpendic...

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its a concept that comes up quite a bit

paper torrent
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ohh

tepid hamlet
paper torrent
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but in the 7th ques they say that tangent PR is of 50 degree, shouldnt it be 90?

tepid hamlet
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its 50 degrees to that chord, not to the radius

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its 90 degrees to the radius given there though

paper torrent
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so the radius <POQ is 90?

tepid hamlet
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what?

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the angle between the tangent and the radius is 90

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OP is the radius

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PR is the tangent

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so OPR is 90

paper torrent
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ohhk

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tangents are rlly confusing

tepid hamlet
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so that's actually what you need to use to solve the problem

paper torrent
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ohh okay

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then like radiis are equal and then isoceles tri property

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and then using ASP find the value of <POQ?

tepid hamlet
# paper torrent tangents are rlly confusing

its actually really simple, let me clarify just a moment...so the red is the tangent line right? and its intersecting the circle at a single point, im drawing a red circle around that one point yes?

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now draw the radius from that one single point to the center of the circle...

tepid hamlet
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and so you've drawn a right angle

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that's all there is to it

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you have the tangent line

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then you have the radius between the center and where the tangent hits the circle

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that's the right angle

tepid hamlet
paper torrent
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IT ALL MAKES

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so much more sense now

paper torrent
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so

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<POQ = 100 degree?

tepid hamlet
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yes and because isoscles as you say, you would also know the measure of which other angle?

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yeah, exactly, you got right to the conclusion

tepid hamlet
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yeah yeah you got it all

tepid hamlet
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consider a round ball resting on the ground, from the side it looks like a circle and the ground is touching it in a single point right? so you can think of the ground as tangent to the circle

paper torrent
tepid hamlet
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and if you draw the radius from that point to the center, the center is directly above that point of contact right? because it balances out, so that's kind of another way to see maybe how the radius is perpendicular to the tangent because the ground is horizontal and that line through the point of contact and the center is perfectly vertical

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or if you consider your position on a spherical earth...going along the surface of the earth is what you think of as the horizontal direction wherever you might be on the globe right? and straight down is the direction to the center of the earth, which is perpendicular to moving along it

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(anyway in case that helps)

paper torrent
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umm so hey

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i tried this ques

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ques 10...is the ans 40?

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and also question number 9 is so confusing...help?

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@tepid hamlet ?

tepid hamlet
paper torrent
tepid hamlet
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for 9 what have you tried? did you draw a figure?

paper torrent
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the figure 😭

tepid hamlet
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something like that

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just two tangents to a circle, they meet with a 60 degree angle and the radius of the circle is 3

paper torrent
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ohhh

tepid hamlet
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so if you draw a segment from the center of the circle to the vertex of that 60 degree angle, you split it in half

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then each side becomes a 30 / 60 / 90 triangle, you might know how to solve it from there

paper torrent
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what

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sorry i didnt get it 😭

tepid hamlet
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this segment bisects that 60 degree angle

paper torrent
tepid hamlet
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because everything is symmetric (even though my drawing is crap and it doesn't look like it)

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so each side is a 30 degree angle

paper torrent
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i could never draw that

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😭

paper torrent
tepid hamlet
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so you have right triangles and you can also get this angle

paper torrent
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oh yeah

tepid hamlet
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30 + 90 + ? = 180?

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i have no idea what ASP is

paper torrent
tepid hamlet
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ya that

paper torrent
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yee

paper torrent
tepid hamlet
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i assume you haven't learned trigonometry yet?

paper torrent
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its in 10th

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basically

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oh wait

tepid hamlet
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or at least properties of 30 / 60 / 90 triangles?

paper torrent
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im going to be in 10 this year

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😭

paper torrent
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which property??

tepid hamlet
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i'm actually not sure how to do this without that knowledge

paper torrent
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whats that property?

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oh wait

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they havent taught us that yet

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but i just googled it

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ig i can learn new stuff idm

tepid hamlet
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well just that the lengths of sides in a 30/60/90 triangle are always in a specific ratio and its a triangle that comes up so often that its worth memorizing basically the sides are in the ratio of 1 : sqrt(3) : 2

paper torrent
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so the length of the tangents are 3root3?

tepid hamlet
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so the large side (hypotenuse) is always twice the length of the smallest side and the middle one is square root of 3 times the smallest side. in this case the small side is the radius (3) and the problem is asking for the length of each tangent so i guess it would be $3\sqrt{3}$

solid kilnBOT
tepid hamlet
paper torrent
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it all makes soo much more sense now

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btw question

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did u do a PHD in maths or smthg?? ur maths is too good

tepid hamlet
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no, but i kinda minored in it in college

paper torrent
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our school teachers are weird

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they dont teach us this shit

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but they expect us to know all this fucking mess

tepid hamlet
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and i've tutored math a decent bit so i at least have some decent grasp of what comes up often in some high school and college classes

tepid hamlet
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well i'm lucky i knew these things at least : )

paper torrent
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u have a bright future in math 👍

tepid hamlet
# paper torrent but they expect us to know all this fucking mess

bad teachers is unfortunate, but glad you are finding ways to learn anyway; definitely try not to get behind in math especially because it all builds on itself and well if you get to something like calculus, there's a saying that "most people who fail calculus actually fail algebra in a calculus class" because they are basically lacking the foundation in the basics and it finally comes to bite them at that point

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it's actually pretty sad what a poor foundation in basic algebra most students in calculus have these days and they struggle like crazy because they cant do basic math

tepid hamlet
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-end rant about today's math education- lol

paper torrent
tepid hamlet
# paper torrent is calculus that hard?

actually i really believe it's very intuitive and beautiful \ fun but yeah it's hard for people who are also trying to learn the last 4 years of math they have been "getting by" in for the last 4 years

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that's pretty much always the case for the people who struggle with it

paper torrent
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ooh

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damn'

tepid hamlet
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the actual concepts intoduced in calculus can be explained more easily than how to do basic algebra and geometry in my opinion to anyone who is well versed in those things already

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anyway cheers, i've got to head off and best of luck : )

paper torrent
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lunar galleon
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how do i find the vertex of a quadratic function if i have two x intercepts and a y intercept

lunar galleon
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ping me if answer please

hot finch
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Use vertex formula

lunar galleon
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wha is that

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sharp topaz
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Determine the volume of silver needed to make the napkin ring, in the following figure, out of solid silver. Give your answer in cubic millimeters.

ocean gate
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progress ?

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where are you stuck

sharp topaz
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Do I have to convert it all to mm before starting? Or can I just convert, 22mm to cm? Do it "normally", so (pi-r^2xh)-(pi-r^2xh) and then convert that answer to mm^3? Also, I did try but according to my answer key they do pi(2.2)^2 but I really don't understand why 2.2 is the radius

sharp topaz
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no wait

ocean gate
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waiting

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take your time

sharp topaz
ocean gate
sharp topaz
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ye makes sense

ocean gate
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but here the question is asking about volume

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so do you how to calculate the volume of a cylinder ?

sharp topaz
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oh yeah I did times 2 as well

ocean gate
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then ig you are doing it correctly just subtract the smaller volume from the larger one and you should get your answer

sharp topaz
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pix2^2x2 - pi2^2x2.2 to clarify

sharp topaz
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then I guess I did something wrong along the way

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lemme recalcualte the same thing I set up

ocean gate
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sure

sharp topaz
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there is one thing, I do not udnerstand. In my answer key they say pi(2.2)^2xd2 - pi(2)^2x2

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pi(2.2)^2xd2 in that part, how is 2.2 the radaius that is supposed to be squared?

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thought 2 mm = 2.2 cm and that would be the height, not radius

ocean gate
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there is a circle which has radius = 2

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then from the edge of this circle, there lies another one which is 2mm far

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so the radius of the second circle comes out to be ?

sharp topaz
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omdddd

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Lmfao i'm so dumb ty

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I thought the line kept on going so that it was the height. No wonder, it would had been atrange if the heights were different anyway

ocean gate
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no worries (:

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wraith hinge
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wraith hinge
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Does the additivity of line integrals hold even if its a vector field?

dusty hound
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The integrand space doesn't matter

wraith hinge
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okay

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so ig define the parameterisations with something similar to
\begin{alignat*}{3}
C_1 &= \6{\vj r}t &&= t\vc\I -\vc\J &\q&-1\le t\le 1 \
C_2 &= \6{\vj r}t &&= \vc\I + t\vc\J &&-1\le t\le 1 \
C_3 &= \6{\vj r}t &&= -t\vc\I +\vc\J &&-1\le t\le 1 \
C_4 &= \6{\vj r}t &&= -\vc\I -t\vc\J &&-1\le t\le 1
\end{alignat*}

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ok there u go

dusty hound
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One copy paste later

wraith hinge
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i think that makes sense

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so yeah is that fine

dusty hound
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The 4th one is really poorly copy pasted

wraith hinge
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uh lemme check if that makes sense

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ok first is fine

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second is fine

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third is fine

solid kilnBOT
wraith hinge
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and now fourth is fine?

dusty hound
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Now yes

wraith hinge
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evil copypastes i tell ya

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so now uh its just integration

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ok thanks bezier

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ionic hull
#

When solving these types of questions... When I move the matrix to the right, must it be change to negative? Since the answer I compared to the text book is

-4 2
-6 0

uncut cove
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Hi, let me try to help you out!

ionic hull
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Sure

uncut cove
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When you moved the matrix from the LHS to the RHS you might have forgotton to add a minus sign?

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since you are subtracting it both on the LHS and RHS

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Does that make sense?

ionic hull
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So must put a minus sign?

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Here's the question...

uncut cove
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Okay let me rephrase. In your first step, for simplicity's sake let's call the written out matrix A. So the question is:
3M + 4A = M
then in the next step we should get
3M - M = -4A, where you got 3M - M = 4A

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since we are subtracting 4A from both sides of the equation

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Just like how you would do it if it were regular variables instead of matrices

ionic hull
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Ohhhh I see

ionic hull
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😊

uncut cove
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You're very welcome!

ionic hull
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dapper basin
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Need massive help with this one

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frail heron
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# dapper basin Need massive help with this one
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
dapper basin
frail heron
frail heron
dapper basin
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I guess that's how you do it?

frail heron
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No, I mean order the boxes lol

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I guess there is only one scenario that doesn’t violate the rule

dapper basin
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I hate probability so sorry if I'm dumb as hell lol I'm fine with algebra though

frail heron
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Nah, all good

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@dapper basin Has your question been resolved?

chilly bobcat
# dapper basin

yeah
if you see theres only one case for the condition to fulfil
CVCVCVC, with C for consonant and V for vowel

frail heron
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Exactly

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However, he has left

chilly bobcat
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sad

chilly bobcat
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No..

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4! Ways to arrange the consonants

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and 3! ways to arrange the vowels

frail heron
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Vowels are confined in certain locations, so are the consonants

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wraith hinge
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what is this find area inside the curves function and how to I approach and solve it

wraith hinge
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I think it's something my online teacher yesterday was doing

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xD he kinda rushed it so I still have no idea

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oh ye and at the start you don't know the function

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the problem is more like given this graph and how the area inside the graph shows every point that has an attribute that I forgot because I didn't understand

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maybe we could find the problem relating to that online

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uneven hatch
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uneven hatch
#

Du/dx = cosx

#

Dx= du/cosX

#

Integral(cosx*(sin(u-1))*u³)

uneven hatch
#

So I get rid of the cos

#

Cos the cos cancels out, heh

#

So I now have u³*sin(u-1)

#

So I integrate using the product rule

#

(U⁴/4) × sin(u-1) + ((sin²(u-1))/2) × ((u²/2)-1u+c)

#

?

#

Replace u with sinx + 1

#

Is that it?

digital bolt
#

it would be u^3 (u-1)

#

if u = sin(x) + 1, sin(x) = u - 1

uneven hatch
#

Oh yeah sorry

#

Lol I messed it up

#

(U⁴/4)×(u-1) + ((u²/u)/2)×(u³)?

trim joltBOT
#

@uneven hatch Has your question been resolved?

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marsh forum
marsh forum
#

Here's what I posted there

#

$\int \frac{x^7}{\sqrt{1+x^8}}dx$

solid kilnBOT
#

Why am. I here

marsh forum
#

maybe $x^4= tan(u)$

solid kilnBOT
#

Why am. I here

proven hound
#

1+x⁸=u?

wraith hinge
#

like 1 step only

marsh forum
#

.close

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#
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marsh forum
#

thanks though

proven hound
#

Lol mp

wraith hinge
#

bruh 2nd time xd

proven hound
#

Np

wraith hinge
#

💀 take a chill pill

#

just give the og question

marsh forum
#

.reopen

trim joltBOT
#

marsh forum
#

$\int \frac{x^5}{\sqrt{x^4+4}}dx$

solid kilnBOT
#

Why am. I here

marsh forum
#

is the OG question

#

I was trying to solve for cases with lower powers

#

wasn't able to

#

I'm considering x^2= 2 tan(u)

#

which is probably the best way to solve it

#

which will give

#

$\int 4\tan^2\left(u\right)\sec\left(u\right)du$

solid kilnBOT
#

Why am. I here

marsh forum
#

unless I've made a calculation mistake

#

.close

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#
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wraith hinge
#

would you get this ,i have bad handwriting

marsh forum
#

yeah, got it

#

tysm!

wraith hinge
#

:>

marsh forum
#

wait

wraith hinge
#

ik you wanna do it with your method only but still

wraith hinge
#

ig you can do that separately

marsh forum
#

Don't think That's easily integrable though

wraith hinge
#

gee! i suck

#

doesnt root over 2 tan(k) works ?

marsh forum
#

yeah, that should work

wraith hinge
#

oh lol i forgot one t

#

kekw nvm

#

its equally lenghty

#

i thought mine would be short but meh

wraith hinge
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split bluff
#

Hi, so for this problem I actually got an ans of 14,700N and wanted to verify the correctness of it
Ill explain I started with finding an equation which I did by multiplying 3 with 1000kg^3/L then multiplying it by 9.8
getting f(x) = 3000gx
then i applied trapezoidal rule
so b-a/n --> 1-0/2 --> 1/2
1/4[f(0) + 2f(0.5) + f(1)]
and that produces 14, 700N
not sure if it is correct so id like to hear someone else's reasoning, thanks!

#

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somber sable
#

danggg can someone guide me through this

somber sable
hallow cliff
somber sable
#

all of em

hallow cliff
#

Yep

#

So do it

#

Then see what you get

somber sable
#

then the 2^2 also factor out each other? leaving me with 2

hallow cliff
#

Check it again

#

Where did the - signs and + signs go?

somber sable
#

ahh danggg

#

so it becomes this right

hallow cliff
#

No, check the denominator once again

somber sable
#

the denominator is positive

hallow cliff
#

2^x(2^2) is not equal to 2^x+ 2^2 • 2^x

hallow cliff
somber sable
hallow cliff
#

What is the denominator originally?

#

2^x+2^2•2^x right?

somber sable
hallow cliff
#

Yes

#

Now you rewrote it as 2^x + 2^2•2^x

#

Which is also correct

somber sable
hallow cliff
#

Tell me what you get

somber sable
#

what you're pointing at

hallow cliff
#

Im pointing at the fact that your denominator is missing a +1

somber sable
#

ain't 1×2^2 the same as 2^2?

hallow cliff
hallow cliff
# somber sable

What exactly are you doing when you scratched out those 2^x ?

somber sable
hallow cliff
#

You are dividing the numerator and denominator by 2^x

hallow cliff
hallow cliff
#

Your numerator was 2^x•2^2 - 2^x•2 and when you divide it by 2^x, you get 2^2-2(the numerator you have written)

hallow cliff
#

Yes

#

So what do you get at the end?

#

After simplifying everything

somber sable
hallow cliff
#

You messed up the numerator again

somber sable
hallow cliff
#

Yeah

somber sable
#

I get 2/5 at the end

hallow cliff
#

Yes

#

It is 2/5

somber sable
hallow cliff
#

Yes but now you know

somber sable
#

thanks

hallow cliff
#

So just don't forget

somber sable
#

I wont🤞🏾

#

.close

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#
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honest sinew
#

How do I solve this?

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tepid cobalt
# honest sinew How do I solve this?

I believe the intention in "Step 1" is to tell what was done to go from this equation

$$40 = \frac{1}{2}mv^2$$

to this equation

$$\frac{40}{v^2} = \frac{1}{2}m$$.

solid kilnBOT
#

OneTrackPony

tepid cobalt
#

You can see the options in the drop-downs.

honest sinew
#

I figured it out

#

I'm good

dry viper
honest sinew
#

Thanks

dry viper
#

if both m and v are variables

honest sinew
#

.close

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#
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honest sinew
#

Unfortunately I have to do all these

#

How do I solve it?

dry viper
#

4c-11=5c+7
c=-18

#

now , check those options , how many of them don't give c=-18

#

first one does

#

second one does as well

#

the third one doesnt

honest sinew
#

Got it

#

Quick Question on something else

dry viper
#

ye

honest sinew
#

Imagine Math is something I struggle a lot with. How should I go about dealing with the questions?

dry viper
#

see , the way you perceive math might be different

#

if you perceive it as a burden , a boring thing

#

you'll never find maths interesting

#

let me tell you a cool thing

#

Maths is the language in which God has written this universe

honest sinew
#

Interesting

dry viper
#

see , whenever you get an equation with one variable

#

try to bring the variable to either side

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#
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dry viper
#

to an equation

trim joltBOT
dry viper
#

we can perform any operations on both sides

#

be it addition

#

subtraction

#

anything

honest sinew
#

What about equations with two variables?

dry viper
#

we need 2 equations for that

#

the no. of variables = no. of equations to solve it

#

and the lengthier the process

honest sinew
#

Ok

dry viper
#

want an example?

#

its pretty fascinating if you see

honest sinew
#

Sure

#

I'll share a problem I need help with if you don't mind

#

When you're done

dry viper
#

no issue

#

at

#

all

#

go for it

#

first lets solve your problem

#

I have to go in like 10 mins

honest sinew
#

Where am I even supposed to begin?

dry viper
#

how many variables do you see?

#

also , they are equations of kinematics

#

show me the question

#

the actual one

honest sinew
#

3 variables

dry viper
#

oh

#

see , you have to solve

#

for u

#

where do you see u?

honest sinew
#

In the middle. UT

dry viper
#

we can't separate t from u for the time being

#

lets try to make ut alone

#

from rest of the equation

#

would you mind if subtract x from both sides?

honest sinew
#

Go ahead

dry viper
#

5-x = 1/2 at^2 +ut

#

ut is getting lonlier

#

now how about I multiply both sides by 2? so that I can get rid of the 2 in the denominator of 1/2 at^2

#

should I?

honest sinew
#

I think so

dry viper
#

2(5-x) = at^2 +2ut

hallow cliff
#

you shouldn't be multiplying by 2 if you are solving for u

dry viper
#

10-2x = at^2 +2ut

hallow cliff
#

You will end up dividing by 2 at the end of the day to isolate the u

dry viper
#

now subtract at^2 from both sides

#

10-2x-at^2=2ut

honest sinew
dry viper
#

now divide by 2t , both sides

#

u = (10-2x-at^2)/2t

hallow cliff
dry viper
#

there you go

#

@honest sinew do as it seems easier , the 2 in the denominator won't help much if you're actually solving a kinematics problem

hallow cliff
#

Yep

#

The goal is to get the u on one side and the rest of the terms on the other side

honest sinew
#

I lost points trying to solve it, but I got it

#

.close

#

Oh wait he has to do it

trim joltBOT
#

@dry viper Has your question been resolved?

dry viper
#

.close

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eager mortar
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eager mortar
#

9.a

#

And all the roman numerals

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#

@eager mortar Has your question been resolved?

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#

@karmic spade Has your question been resolved?

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wraith hinge
#

,rotate

solid kilnBOT
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rapid dock
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rapid dock
#

i dont understand what the question is asking

dry viper
#

its asking the inverse of f(x)

rapid dock
#

but isnt it in the question

dry viper
#

no?

zinc ginkgo
rapid dock
#

oh okay

#

so x cant equal 4 is what its saying

#

so it can be any other number

#

?

wraith hinge
rapid dock
#

so can x = 1

dry viper
#

you need to find the inverse of the function , they specified the domain of f(x) that x=/=4

#

we just talked about finding inverse easily

#

replace x->y

#

and vice versa

rapid dock
#

yes but there is no y in the answers

dry viper
#

y=(x+3)/(x-4)

dry viper
rapid dock
#

so f^-1 x can be y too

#

i thought it was only f(x) = y

dry viper
#

we reversed domain and range by replacing x and y

rapid dock
#

mhm

dry viper
#

so inverse becomes y

lean prawn
lean prawn
rapid dock
#

so-

lean prawn
#

It's just really just an aesthetic choice

#

but now you have an equation where you can try to solve for x

#

and you'll notice that x depends on y

rapid dock
#

would it be d?

dry viper
#

didn't even replace yet lol

rapid dock
#

it would be c or d right

dry viper
#

its b

lean prawn
#

well I guess I don't really know where the confusion stems from

rapid dock
#

why b?

lean prawn
#

I feel like it might be a good idea to review how functions work in general and what inverse functions are

#

and solve inverse functions of simpler functions

#

like the inverse function for f(x)=2x+1

lean prawn
# rapid dock

and then try to apply that to this exercise, which is really the same thing but with a slightly harder equation to solve

wraith hinge
#

Write
y = f(x) {whatevr you are given in the questions}
Now make it so you get something which looks like
x = (something in y)
Now just write x instead of y and vice versa
You have your answer

rapid dock
#

but what does something in y mean

wraith hinge
#

y = 2x + 1
x = (y-1)/2

#

LHS should be x , RHS should not contain x

rapid dock
#

why is it y-1 tho

dry viper
#

and to make it a bit aesthetic , swap x and y

wraith hinge
dry viper
wraith hinge
#

Now as f(x) = 2x + 1
f^-1(x) = (x-1)/2

rapid dock
#

im confused on where you ger y-1 from

#

get*

dry viper
#

see how the domain for f is range for inverse?

#

and vice versa

wraith hinge
rapid dock
#

so why exactly in my problem would it be b

dry viper
#

the question says y=x+3/x-4

rapid dock
#

yes

dry viper
#

find its inverse

#

right?

#

y(x-4)=x+3

#

xy-4y=x+3

#

xy-x=4y+3

#

x(y-1)=4y+3

#

x=4y+3/(y-1)

#

to give it a "function" look

#

like a f(x)

#

replace x with y and y with x

#

y = 4x+3/(x-1)

rapid dock
#

ohhhhhhhh

#

okok

#

im sorry i was braindumb for a sec

dry viper
#

tip: use x and y instead of s and t to make it easy

rapid dock
#

alr

dry viper
#

personal choice

rapid dock
#

y for s right

#

t for x

#

for this problem you have to like work backwards right

dry viper
#

yes

#

kinda

rapid dock
#

so youd replace...

#

y for x?

dry viper
#

you know its the inverse

#

you have to find the original now

#

just solve for the opposite variable

#

make it x = something

dry viper
#

correct is b

#

i g2g

rapid dock
#

ok

rapid dock
dry viper
#

have a nice day

rapid dock
#

you too

#

.close

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#
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#
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regal hatch
#

what happened to the 20x here?

trim joltBOT
raw magnet
regal hatch
wraith hinge
#

what

#

its saying

#

r is equal to both of those

#

seperate

#

u make the 2 equations

frail heron
wraith hinge
#

equal to each other

raw magnet
#

r = $\sqrt{4x^2 + 20x + 25} = \sqrt{(2x+5)^2 } = 2x + 5$

wraith hinge
#

or wait no

#

tf

solid kilnBOT
#

nosqldb

wraith hinge
#

im not thinking this right

raw magnet
#

what my food friend @wraith hinge is trying to say

wraith hinge
#

ITS

#

THE SQUARE

raw magnet
#

is this

wraith hinge
#

yes

#

tyvm

#

i didnt realize that was it solved out

regal hatch
#

oh right

#

got it

#

thanks

#

.close

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#
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delicate lance
#

Why do i have to set the y value equal to the slope? What happens

#

I dont ge it

#

.close

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#
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real saddle
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real saddle
#

How can I solve for 9.?

#

I have a rough idea since 13pi/12 is 195 which is 15 degrees in quadrant 3

#

and I've solved for 15 degrees in 5. which was sqrt(6) - sqrt(2)/4 but I'm not sure what changes it being in quadrant 3 does when solving with addition/subtraction formulas

#

Would it just have the obvious effect of making them all negative or would it be different in otherways?

bright quarry
#

well you can use subtraction formula

#

using 225-30

real saddle
# bright quarry using 225-30

sin(225 - 30)
sin 225 cos 30 - cos 225 sin 30
-sqrt(2)/2 * sqrt(3)/2 - -sqrt(2)/2 * 1/2
-sqrt(6)/4 - -sqrt(2)/4
-sqrt(6) + sqrt(2)/4
?

#

i think the math checks out there

bright quarry
#

yea looks good

real saddle
#

ty!

#

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wraith hinge
#

i dont understand why this is true

trim joltBOT
wraith hinge
#

since it doesnt specify that F is R, F can be C, so can you not have a matrix with all diagonals being i for example

#

then RREF(A) wouldn't be the identity matrix or what am i missing

#

wait

#

that kind of matrix would still be reducable

#

deez

#

.close

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distant abyss
#

Hello! Still not on the clear with transcendentals, but taking baby steps

distant abyss
#

Is this correct?

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#

@distant abyss Has your question been resolved?

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zenith sinew
#

Hey

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zenith sinew
low gazelle
#

!status

trim joltBOT
#
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
zenith sinew
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3

low gazelle
#

What did you get

zenith sinew
#

for b 15 out of 20?

low gazelle
#

How did you answer a

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How you answered a could lead to different answers for the rest of the problems

zenith sinew
#

waittt

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i got it thanks

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.close

trim joltBOT
#
Channel closed

Closed by @zenith sinew

Use .reopen if this was a mistake.

trim joltBOT
#
Available help channel!

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Show your work, and if possible, explain where you are stuck.
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proven nymph
#

Hello

trim joltBOT
proven nymph
#

having troubles even understanding or starting this problem

marsh forum
#

Are you familiar with implicit differentiation ?

proven nymph
#

chain rule yes which i think implicit differentiation is based off of/almost the same

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but not exactly familir with implicit no

marsh forum
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Better learn that first

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I suggest you look up implicit diff on Khan academy

proven nymph
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i tried researching it but usually youre given two points which my teacher doesnt do

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so im not even sure anymore

marsh forum
#

try this

proven nymph
#

lemme take a look, thank you

proven nymph
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watched the video

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but now we have e^y on the other side, thats pretty confusing

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in khan academy it was just = 1

marsh forum
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try differentitaing $e^y$ using implicit diff

solid kilnBOT
#

Why am. I here

proven nymph
#

not really sure how to go about that

marsh forum
#

hint:_ $\frac{d\left(e^y\right)}{dx}=e^y\left(\frac{dy}{dx}\right)$

solid kilnBOT
#

Why am. I here
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

marsh forum
#

oops

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just a mo

proven nymph
#

np

marsh forum
#

$\frac{d\left(e^y\right)}{dx}=\ e^{y\ }\ \left(\frac{dy}{dx}\right)$

solid kilnBOT
#

Why am. I here

proven nymph
#

so it would just be e^y * (dy/dx)

marsh forum
#

that would be equal to teh differential of the LHS

proven nymph
#

is it always gonna be like that when doing implicit diff to e raised to a variable?

marsh forum
#

wdym?

proven nymph
#

i think

marsh forum
#

it seems to me you haven't fully understood implicit diff, please look at a few more videos to strengthen your concepts

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Hope this doesn't come off as rude

proven nymph
#

not at all, i def dont

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i dont understand how everything works but i tried solving it just now

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solved the problem to (5x^4) / (e^y - 4y)

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which is wrong lol lemme take another look at khan

marsh forum
#

Hmm, $5x^4 + 4y^3 \frac{dy}{dx} =e^y \frac{dy}{dx}$

solid kilnBOT
#

Why am. I here

marsh forum
#

Is what you should get

proven nymph
#

yea then i subtracted the second term over to the right

marsh forum
#

Yup

proven nymph
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ok then i did

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dy/dx (e^y - 4y^3)

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on the right side

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is that not right

marsh forum
#

Sounds right

proven nymph
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ok then

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i divided the e^y - 4y^3 to both sides

marsh forum
#

Yes

proven nymph
#

and was left with the answer

marsh forum
#

That should give you the right answer

proven nymph
#

i think i made a error when i was writing this on my notebook when i solved it a few minutes ago

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maybe wrote a number wrong

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so the answer then should be (5x^4) / (e^y - 4y^3)

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i believe

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yeaa i see the error i made, i forgot the y was cubed lol

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awesome thank you

#

.close

trim joltBOT
#
Channel closed

Closed by @proven nymph

Use .reopen if this was a mistake.

trim joltBOT
#
Available help channel!

Send your question here to claim the channel.

Remember:
Ask your math question in a clear, concise manner.
Show your work, and if possible, explain where you are stuck.
After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

young ice
#

Yoooo!

trim joltBOT
young ice
#

my question is

#

simplify the expression, write your answer using only positive exponents.

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125^3 divided by 125^8/3

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<@&286206848099549185>

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Can someone help me

#

Thank ya bb!

wraith hinge
#

its 3

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the answer is

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3

raw magnet
trim joltBOT
# wraith hinge its 3

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

sick onyx
#

u dont give the answer bro

young ice
#

dude really

#

!noans

trim joltBOT
#

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

raw magnet
#

But Fr

wraith hinge
#

😭

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ok look

young ice
#

way to be a helper dude

wraith hinge
#

dividing by a fraction

tepid hamlet
#

it's also not even the right answer 😄

wraith hinge
#

is multiplying the reciprocal

wraith hinge
#

oh

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its tot he 8th

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ok

sick onyx
#

yeah the answer is wrong-

wraith hinge
#

SEE SO IT DONT MATTER

young ice
#

yeah lol it’s wrong

raw magnet
young ice
#

don’t tell@me the answer also

#

that’s racist

raw magnet
#

Aight let’s move on

wraith hinge
#

....

raw magnet
#

Don’t clog this channel

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Anyway

young ice
#

u giving it cuz i’m white and fat?

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oh k

#

sry

wraith hinge
#

exactly

tepid hamlet
solid kilnBOT
raw magnet
sick onyx
#

125^3/125^8/3

raw magnet
#

Both of you guys

young ice
#

i’m offended

young ice
sick onyx
#

u just put the denominator to the numerator

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thus its exponent will become negative

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thats the initial

young ice
#

waiy i don’t get it

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how did u get that tool

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the twist

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tex it

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@solid kiln t

sick onyx
#

like

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what

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u talking abt

young ice
#

i don’t understand what u r trying to say

sick onyx
#

do u know that

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x^1

young ice
#

please demonstrate it

sick onyx
#

is also equal to

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1/x^-1

young ice
#

no

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i’m white

sick onyx
#

..

young ice
#

how am i supposed to know that

sick onyx
#

if u dont know that then its useless

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how u gona solve it

young ice
#

now just tesolain pls

#

explain Now

#

NOW

sick onyx
#

how

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u dont even know it

wraith hinge
#

ok

sick onyx
#

its a formula

wraith hinge
#

pause

scarlet cloud
#

hi

young ice
#

forget u

wraith hinge
#

listen

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stop

young ice
#

u suck at helping

young ice
#

pls help

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this helper can’t help

scarlet cloud
#

iam brazilian.-.

sick onyx
young ice
#

wait do u speak english

bright quarry
#

who sucks at helping?

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y r u being rude

sick onyx
bright quarry
wraith hinge
sick onyx
#

I already told him x^1 = 1/x^-1

wraith hinge
#

and understand

young ice
#

@bright quarry please help me

#

i’m failing

raw magnet
bright quarry
young ice
#

i’m just sad

kindred pier
bright quarry
#

he said hey bbg before

scarlet cloud
#

I'm using the translator.-.

young ice
#

OK ANYWAY

#

JUSG HELP ME

young ice
#

look every helper pls leave ok i’ve chosen @bright quarry as my helper

wraith hinge
#

i didnt even give the right answer

young ice
#

Thank you guys but no

wraith hinge
#

the right answer is 3/125^5

young ice
#

Leave

young ice
#

<@&268886789983436800>

wraith hinge
#

ooo bed time

#

bye all

#

lmao

sick onyx
wraith hinge
young ice