help-27

[restive river]

<@&286206848099549185>

[devout snow]

@restive river Has your question been resolved?

[soft umbra]

The rules remain the same

I guess you have misunderstood what your teacher said

[devout snow]

@restive river Has your question been resolved?

[restive river]

so the rules in the textbook are correct?

[devout snow]

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[sacred cloak]

imagine a rectangular prism with a square bottom

[sacred cloak]

and a square top

when the side length of the square changes, the height also changes, so that the combined area of all sides add up to 80 cm^2

decide a function V(s) on how the volume is affected by the side length

i am kinda stuck

like i don't know where to start

but i've drawn this piece of art

[restive river]

call the height h

express h in terms of s

using 80cm2

[mystic moth]

Hi let me try to help you out

[mystic moth]

To start out we should get an idea of how to use the given information that the combined area is 80 cm^2

Could you express this combined area in h and s?

[sacred cloak]

2s^2 + 4hs

combined area

[mystic moth]

So we have that 2s^2 + 4hs = 80

[sacred cloak]

yes

[mystic moth]

similarly, could we express the volume in h and s?

[sacred cloak]

s^2 x h

[mystic moth]

We thus have
V = s^2 * h
2s^2 + 4hs = 80

But we need to find V as a function purely of s

What we could try to do here is substitute the h in V by using the second equation

Does what I'm saying make sense?

[sacred cloak]

yes

[mystic moth]

So what you could try to do is rearrange the second equation in such a way that you get:
h = ...
and then substitute that value in the first equation to obtain a function for the volume purely in s

[sacred cloak]

okey wait

i need to do something

but i think ill try to do what you told me to do

[mystic moth]

good luck!

[devout snow]

@sacred cloak Has your question been resolved?

[sacred cloak]

V = s^2 * h
2s^2 + 4hs = 80

[mystic moth]

Hey, have you tried to rearrange the second equation?

[sacred cloak]

im at the supermarket right now

[mystic moth]

Ah okay, nevermind then :D

[sacred cloak]

2s^2 + 4hs = 80
80 - 4hs = 2s^2

and ill do the rest at home

[devout snow]

@sacred cloak Has your question been resolved?

[devout snow]

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[marsh creek]

Question 3) please

[devout snow]

@marsh creek Has your question been resolved?

[devout snow]

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[jagged loom]

X^2=5x hello i need help with this

[jagged loom]

its pretty basic

says i am suppose to get either x=5 or x=0

but i am not sure how i get there

i just put it in a calculator

[inland frost]

the best way is to write both of them on the same side.

[jagged loom]

so x^2-5x=0?

[inland frost]

then you will get x(x-5)=0

[jagged loom]

wait, how did you get x(x-5)=0

[inland frost]

it is the same thing, just do the multiplication

[jagged loom]

what do i multiplie? xD

[inland frost]

x(x-5)=x^2-5x

they are equal

x(x-5)=0. From this, you can see that there are 2 solutions of this eqn.

[jagged loom]

I am not following, we need to take a step back

I am still confused how we get the x(x-5)=0

x^2-5x=0 i do this first right?

move the 5x over the = and it changes to minus

[inland frost]

yes first step is ok

then x is common for x^2 and 5x

[jagged loom]

yes one is xx and the other is 5x

x times x

and 5 times x

[inland frost]

then you can write this -> x(x-5)=0

[jagged loom]

you remove the x in x^2 to get only 1 x?

but how does 5 x become x-5

maybe i am missing a basic rule

[inland frost]

ok, x(x-5) do this multiplication like 3*(4-2)

[jagged loom]

but dont all the Xs need to be the same nr?

in your example the x is both 3 and 4

[inland frost]

it doesn't matter, do this x(x-5)=?

[jagged loom]

then it be x^2-5X=?

[inland frost]

yes

[jagged loom]

Oh ok

[inland frost]

then your problem is this one x(x-5)=0.

[jagged loom]

yes

and then i can +5 on both sides?

x*x=5

divine by 2 on both side

x=2.5

hmm, thats not the answer

[inland frost]

either x is zero for the solution or x-5 is zero

if a*b=0 then a=0 or b=0

[devout snow]

@jagged loom Has your question been resolved?

[devout snow]

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[devout snow]

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[restive river]

There are 9 types of candy, a bag of candy has 19 pieces of candy.
If I want **atleast **one candy of each type, how many ways can such a bag of candy be arranged?

[urban jungle]

Say you are trying to make such a bag of candy. What is the first thing you do to ensure there’s at least one type of candy in the bag

[restive river]

The first step I took was that I concluded that the first 9 pieces can only be arranged one way.
So the question can be simplified to "How many ways can you sort 9 types of candy in a bag with 10 candy"

but after that it grinded to a halt

[urban jungle]

Alright so you’ve put in one of each candy

Now how many options do you have

For the next piece of candy

[restive river]

9?

[urban jungle]

Indeed

Now for the next piece of candy how many options do you have

[restive river]

Still 9.

[urban jungle]

And for the next choice…

[restive river]

But there can't be 9^10 ways, since the order the candies are placed doesn't matter, so it narrows the options down quite a bit.

Combinations not permutations if I understood the question right.

[urban jungle]

Hmm that is true

The problem could also be, how many ways can you distribute 10 identical objects into 9 containers

That would be equivalent

You could take the stars and bars approach https://brilliant.org/wiki/identical-objects-into-distinct-bins/

This website can likely explain it better

[restive river]

Oh thanks!

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[fierce scarab]

Consider the following data polot with points (-2, 2), (-1, 1), (0, -2), (1,0), and (2,-1)

a) Sketch a line of best fit for this data. Take your best guess without any computations.

b) Find the constant r corresponding to this data.

c) Find the least-squares line of best fit using linear algebra methods

[fierce scarab]

pretty sure I know how to find the constant r. it's the other stuff i'm not sure about. help would be appreciated

[soft umbra]

Do you know the standard function of linear regression?

[fierce scarab]

I don't think so, no

mind explaining?

[soft umbra]

Sure

[fierce scarab]

thanks

[soft umbra]

This is the so-called "best fit line"

[fierce scarab]

ok

what does mu y and mu x represent

[soft umbra]

mu x represents the average of x

Sorry, I wasn’t available

[fierce scarab]

no problem!

so once I find the average, I can solve for r using that formula?

[soft umbra]

yes

Do you know what sigma x represents?

[fierce scarab]

No

[soft umbra]

standard deviation

(y- the average value of y)=(r•standard deviation of x/ standard d of y)•(x-the average value of x)

[devout snow]

@fierce scarab Has your question been resolved?

[fierce scarab]

okay thanks, is this for b or c?

[soft umbra]

It solves every of them

a) make a guess
b)Find r
c)Use the prototype I provided

[devout snow]

@fierce scarab Has your question been resolved?

[devout snow]

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[devout snow]

Please don't occupy multiple help channels.

[night sundial]

.close

[devout snow]

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[devout snow]

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[digital jacinth]

$\int \frac{cos^2x}{sin^2x}dx:$

[woven radish]

putridplanet

[digital jacinth]

why cant this be turned into tan^2x

and then sec^4x

[young plover]

Well for starters it would be cot^2x

Since it’s cos over sine

[digital jacinth]

ok

[young plover]

And further the integral of tan^2x is not sec^4x

Maybe you should use a trig Pythagorean identity for this?

At least give it a try

Yeah that should help since if you turn cos^2x into 1-sin^2x you can split it up into two integrals of csc^2x and 1

[vast cedar]

I believe there's also a way to do u-sub here as well, but trig identities are probably the easiest way

[young plover]

Might be easier

[urban harbor]

my suggestion is to use the sin^2 and cos^2 to double angle identities and it should simplify pretty nicely

[young plover]

Yeah that may work too

There’s more than one way to skin a sheep as they say

It also applies to calculus

[vast cedar]

especially as you get to calc 2, problems start having a ton of viable solutions

[urban harbor]

theres also this less common idea

[young plover]

The thing about the Pythagorean approach that I suggest is it reduces to the antiderivative of 1 and csc^2x

But the derivative of cot is -csc^2x

So it’s basically no work

[devout snow]

@digital jacinth Has your question been resolved?

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[weak cove]

To apply this corollary

say I'm taking the limit of the top function as x->0

is it enough to say that, it is basically the same as inverting all of the 1/x terms and taking x-> infinity

so the corollary applies?

I'm not sure how to phrase it properly

[magic thicket]

What limit are you looking at

[magic thicket]

In general this is just a change of variables

[weak cove]

in black

p is just a polynomial

[magic thicket]

I thought you were trying to apply it to something

[weak cove]

yes the limit in black at the top

limit x->0 of p(1/x)e^(-1/x)

for p a polynomial

[magic thicket]

Well then yeah this formulation is begging for u = 1/x

[weak cove]

Gotcha

Okay thanks

.close

[devout snow]

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[magic thicket]

Though do worry about double sidedness maybe

[weak cove]

only taking the right hand limit

👍

[true plover]

Hello!
I am trying to solve an equation, but after an hour of long dividing and percentages mumbo jumbo I have arrived at answers that do not match the multiple choice options even remotely.

The problem
A bottle of cleaner has a label that reads "now 20% more." The bottle contains 28.8 ounces. How many ounces of cleaner are in a regular container?
The answer options are:
A. 20oz
B. 22oz
C. 23oz
D. 24oz

[What I did]
I googled how to get the percentage of a whole number, which brought me to this.
Part/Whole= (answer1) x 100 = (final answer)
I don't fully understand this. So I looked up how to divide a whole number by a percentage. I did not fully understand this either. So then I tried to use the answer options in the equation. I used 28.8 as the whole and 20(the first option) as the part. I figured 20 could be part of 28.8, it being an answer option and also smaller. I ended up even more confused with long division. I ended up with the answer of 70 (0.7 x 100), but that is not an answer option.
Do I apply some other layer of math? Am I completely missing what I am actually supposed to do?
Eventually, I gave up and just googled 20% of 28.8 and got 5.76. but 5.76 x 100 is 576. That is even further from the answer options. I tried making 20% be 0.2 and divide 28.8 by 0.2 instead, but that got me 144 even. That is also too big of a number.
Something is clearly wrong, but I cannot identify it. Even when I Google the answer, I cannot apply it.

I do not understand this at all. Please explain how I am supposed to solve this. I am terrible at math, so the simplest explanation please.

I would show my equations so far, but the page is very confusing to look at and likely would not help.

[magic thicket]

!help

[devout snow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[true plover]

Oh. I thought that it had closed so I could use it. My bad.

[magic thicket]

It's not open

Closed -> might become blocked

[true plover]

Ok

[devout snow]

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[solar goblet]

$\int_0^{\frac{\pi}4} f(\tan x)dx = 4$

[woven radish]

FungusDesu

[solar goblet]

$\int_0^1 \frac{x^2f(x)}{x^2+1}dx = 2$

[woven radish]

FungusDesu

[solar goblet]

Evaluate $\int_0^1 f(x)dx$

[woven radish]

FungusDesu

[solar goblet]

i let u be tanx

which turns the first integral to one that is kinda similar to the second

but its stuck with a x^2

dont know what to do bout that

[dense lynx]

imo this is more obvious if you try to turn the 2nd integral into one that looks like the 1st

[devout snow]

@solar goblet Has your question been resolved?

[solar goblet]

hmm

$\int_0^{\frac{\pi}4} \tan^2uf(\tan u)du$

this is what i got

i cant see why it would help

[dense lynx]

a few things...

first, you need to convert dx into du

[solar goblet]

my bad i did, but forgot to tex it

[dense lynx]

ah alright

that still seems incorrect though

[solar goblet]

oh youre damn right

[dense lynx]

👀

[woven radish]

FungusDesu

[dense lynx]

yep that seems pretty legit

think you know what to do from here?

[solar goblet]

IBP?

[dense lynx]

you achieved your goal of "making an integral that looks similar to the other one"

you already substituted x = tan(u), so ibp won't help you get closer to finding a value for the integral of f(x) here

[dense lynx]

@solar goblet any updates?

[devout snow]

@solar goblet Has your question been resolved?

[devout snow]

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[finite stream]

,rotate

[finite stream]

this is what i have for now, i don't know what to do next

[old wind]

Whats the question

[finite stream]

.

[old wind]

Ok sorry im rather dumb

[supple knot]

just use the taylor series for $2\log(x)$

[woven radish]

riemann

[finite stream]

i don't know it

oh wait hmm

i need help with it

i know denominator should be n!

and its alternating? so (-1)^n?

or is it (-1)^n+1

[supple knot]

what are you even reading

show the taylor series

[finite stream]

oh

wait im thinking of the general term sorry

,rotate

[supple knot]

this is what you should be doing

[finite stream]

oh

[supple knot]

you should just have the formula for taylor series for log written somewhere

or in your textbook

[finite stream]

i don't have it for log

[supple knot]

,w taylor series log(x) about x=1

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[supple knot]

yea use this

[finite stream]

but multiply everything by 2?

[supple knot]

yes 2 * log(x) = 2 * series expansion for log(x)

[finite stream]

so the coefficient is 2/50?

[supple knot]

what's the sign of the even terms in the expansion

[finite stream]

oh its negative for even terms

so -2/50

[supple knot]

yea looks right

[finite stream]

thank u sm!

.close

[devout snow]

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[devout snow]

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[restive river]

i need help

[restive river]

plz

[eager lodge]

translation plz

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[misty granite]

Okay I dont know where to start solving this problem. And i would like somebody to help explain this to me

[supple knot]

,tex .exp rules

[woven radish]

riemann

[misty granite]

so does it them become

what do i do with teh negative

7

[misty granite]

so what do i do from here do i just flip the x to get 1/x^7

am i doing this right

[devout snow]

@misty granite Has your question been resolved?

[devout snow]

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[obsidian junco]

Need help on how should I solve this empirical rule question

[obsidian junco]

Idk how should I go on this

[eager lodge]

First calculate the z scores

[obsidian junco]

Z scores? My instruction videos haven't taught that yet

[eager lodge]

It means how many standard deviations away from the mean

For example (55-67)/6=-2 so 55 has z score of -2 (2 standard deviations smaller thqn the mean)

[obsidian junco]

but then how do I caculate the percentage?

[eager lodge]

Use your graph here

I'll do part a for you

55 is two standard deviations smaller than the mean

79 is two standard deviations greater than the mean

So from the graph we add the corresponding probabilities

From the center we need two from the left and two from the right

[obsidian junco]

ah so 79 would be from the right

and 55 is to the left

[eager lodge]

Yes

[obsidian junco]

man I'm already starting to hate my professor already

[eager lodge]

Why

[obsidian junco]

oh its watch videos to learn and recognize other random BS that weren't in the videos on your own

[eager lodge]

They don't teach?

[obsidian junco]

yeah my professor is mostly, watch videos and teach on your own and I'll review some of the concepts at times we meet

I mostly go down to my math tutor in person to reinforce these concepts

and ones weren't mentioned in the video

apparently I'm not alone, my fellow classmates hate the videos and material as well

but anyway

thanks for the help

I think I could do the other parts of the question on my own

.close

[devout snow]

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[devout snow]

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[wary ruin]

How do I check if

$$\int_1^{\infty} \frac{e^{-x}}{x} d x$$

is divergent or convergent?

[woven radish]

dgh

[wary ruin]

From what I can tell, the function is the same as 1/(x*e^x)

How do I know what this improper integral evaluates to?

[eager lodge]

it's not hard to check convergence

[orchid shadow]

convergent

but i have no idea why

[eager lodge]

you can compare with e^-x

but it's hard to find the exact value

[wary ruin]

e⁻x

divided by x

is smaller than e⁻x

[eager lodge]

yes

e^-x >= (e^-x)/x for x>=1

integrate both sides

[wary ruin]

where

[eager lodge]

you get $\int_1^\infty e^{-x}dx \geq \int_1^\infty \frac{e^{-x}}{x}dx$

[woven radish]

WhereWolf(ping if needed)

[eager lodge]

the left is convergent thus so is the right

[wary ruin]

how did you reach this conclusion

[eager lodge]

which part

[wary ruin]

that if e^-x is a greater function

then the integral is greater

[eager lodge]

oh it's a well-known theorem

[wary ruin]

what is it called

[eager lodge]

I don't remember the name sry

I mean it's really intuitive tho

[wary ruin]

so if that left integral is greater then it means a divergence?

or i'm not following

[devout snow]

@wary ruin Has your question been resolved?

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[lime lintel]

nice one ibrahim

[crude meteor]

Can you please stick to your own channel?

<@&286206848099549185>

[eager lodge]

let s,m,l be number of small,medium,large cups sold respectively

you should be able to form 3 equations from the question

first one with "three times as many medium cups were sold as small cups"

second one with "number of large cups sold was 140 less than the number of medium cups"

third one wihth "total of the drink sales was $1360"

[crude meteor]

so then i subsititute the three equations into the last?

[eager lodge]

yeah that works

[crude meteor]

idk how to layout this statement

would it be 3m=s?

[eager lodge]

yes

[crude meteor]

so how would i subsititute a equation in a equation

[eager lodge]

umm

can you list all three equations out first

[crude meteor]

3m=s

l=140-m

l+m+s=1360

oh nvmd

[eager lodge]

?

[crude meteor]

so what would m be

[eager lodge]

both your second and third equations are wrong

[crude meteor]

140-m+3m+?=1360

[eager lodge]

l=140-m is wrong

should be l=m-140

for the third you forgot to consider the price

[crude meteor]

sorry got the wrong way

[eager lodge]

nah it's fine to make mistakes

[crude meteor]

so for the last one you would multiply by the price

[eager lodge]

yep

[crude meteor]

would i use this but just substitute the price for m where neeeded?

[eager lodge]

yes

[crude meteor]

so 2-140+3(2)=1360?

doesnt make sense

[eager lodge]

??

find out the third equation first

[crude meteor]

-142=1360?

[eager lodge]

no

[eager lodge]

total sales is 1360

so 1.5s+2m+2.5l=1360

price * number sold = total sales

[crude meteor]

so 1.5(3m)+2m+2.5(m-140)=1360?

[eager lodge]

yes

the rest should be easy

[crude meteor]

yes

thank you 🙏🏻

[devout snow]

@crude meteor Has your question been resolved?

[devout snow]

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[indigo charm]

how do I solve this question?

[indigo charm]

so far I know I can use multiplicity and end behaviour to roughly draw the graph of the equation but that is if it factorizes

f(x) factorizes to (x-1)(x squared - 7x - 7)

how do I proceed from there

and is there a better and easier approach?

[hasty saffron]

You can just equate the first derivative to 0

Those values of x will be turning points

[indigo charm]

x = 0 and x = 16/3

at those points, the graph has a slope equal to 0 therefore they are turning points?

[hasty saffron]

Yeah

[indigo charm]

if so then I have two turning points? also what does it mean to have them with a coordinate axis?

as in the options

and g(x) is just a flipped and stretched graph of f of x right so it too has only two turning points

[hasty saffron]

You've to check the y coordinate of the turning points

[indigo charm]

how

and what about them

[hasty saffron]

Just plug in the x values in the original function to find y coordinate
And because the options are asking us to check that

[hasty saffron]

Only the sign tho

[indigo charm]

aa yes gotcha

[indigo charm]

got it

[hasty saffron]

Nice

[indigo charm]

can I ask another question here related to the same concepts or do I have to

start a new help?

/close

[covert root]

What is your question

[devout snow]

@indigo charm Has your question been resolved?

[devout snow]

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[indigo charm]

this

[covert root]

I would graph the function on Desmos

[indigo charm]

is there no simpler way to do it on paper?

[devout snow]

@indigo charm Has your question been resolved?

[soft umbra]

Do you know any root of the cubi function?

This question requires observation

@indigo charm ping me when you’re up

[indigo charm]

hey

[indigo charm]

um no

[indigo charm]

yes that's how it's asked to be solved

[soft umbra]

Find it

[indigo charm]

using multiplicity, end points and all

[soft umbra]

Look it more carefully

You can rearrange the cubic function and place the redundant coefficients out side the function

[indigo charm]

ah I can't understand. Someone shared a solution can you have a look at it, share your insights on it and then explain your method as well

[soft umbra]

Do you have the answer? If do, I can directly share my progress with you

But if you don’t have the answer, due to the restriction of server rule, I can’t provide you with my complete progress

Based on the rules, the only thing I can do as a helper is to guide people 🥲

[indigo charm]

oh

dm?

[soft umbra]

Sure

[indigo charm]

Answer is 7

[soft umbra]

Oh, then we can discuss it here

Lemme rearrange my progress since they look messy atm

[frail crag]

Question been resolved?

[indigo charm]

.close

[devout snow]

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[devout snow]

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[still rune]

Can anyone verify that my answer to this problem is correct?

[still rune]

They say in part b) that I can check my formula but not sure how

[upper schooner]

,w [[0, 1, 2], [5, 0, 0], [0, 2, 4]]^2 * [[0], [4], [1]]

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by chartbit

[still rune]

Oh I see!

My solution is correct then

Ty!!

[upper schooner]

Believe so

[devout snow]

@still rune Has your question been resolved?

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[limpid tulip]

Using the Laplace transform, solve the system of differential equations.

x'(t)-4y(t)=-8cos(4t)
y'(t)+3x(t)=-9sin(4t)
x(0)=0,y(0)=3

After transforming to:

sX(s)-x(0)-4Y(s)=-8s/(s^2+4^2)
sY(s)-y(0)+3X(s)=-94/(s^2+4^2)

I cannot get X(s) and Y(s) that I can inverse Laplace transform. Thanks in advance!

[crisp niche]

note that the system you have after the transformation is a linear system

so oyu may even use cramer method or any other school method

to get X and Y

which are images of lapalces originals

when you get X and Y then you inverse transform with tables

that is all

[limpid tulip]

I am aware, and tried plenty of times to get an answer that can be inverse transformed using the taught formulas

[crisp niche]

so wh you worry ?

[limpid tulip]

Since I can't get an answer that is inverse transformable, I can't find the x(t) and y(t)

[crisp niche]

you got X(s) and Y(s) before inverse ? can you show it on paper or not ?

[crisp niche]

,rccw

[limpid tulip]

Any way I try to solve for X or Y, I cannot get anything that is transformable

I can, also, add the relevant formulas I have been given.

[crisp niche]

yes you can reach Y(s) from second

and plg in first equation

but better for your teache r to see

wud be if you use

cramer

method

unless you re really fluent in classical methods

of solvign systems

[limpid tulip]

There are the relevant formulas. I tried solving for either X or Y and plugging it in the other equation plenty of times but to no avail

While I wait for help, I'll look into the Cramer method

[crisp niche]

fidn cramer please

[limpid tulip]

This answer isn't Laplace inverse transformable with the given formulas 😖

[crisp niche]

it is not true

assumign you got correct answrs

then

you must take X(s) and Y(s)

and

apply partial fractiosn decomposition

and then you get X and Y in a way that you wull be able to use tables of L

partial fraction decompotions

[crisp niche]

your system of diff equaitons is not difficut, it is onyl time consuming little bit you must be aptient

patient*

i help you here, i take

your X(s) answer

and i show you :

but i assume, you got it right

2 minutes plz

[limpid tulip]

I am getting somewhere. With partial decomposition I think I am getting proper results

You've been a ton of help already! 😁

After completing calculations of partial decomposition and using the inverse Laplace transform formulas, I got

x(t)=144-38sin(4t)
y(t)=36-36cos(4t)

This sounds quite reasonable. I think it's correct. thanks!

.close

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[round saddle]

why does the square root of x * square root of x = x?

[round saddle]

just never seen it before and it got me a little confused

[polar flower]

$sqroot(a)* sqroot(a) = a$

[near trout]

?

[woven radish]

swerriee

[near trout]

that's what the square root is

sqrt(2) * sqrt(2) = 2

sqrt(4) * sqrt(4) = 4

[round saddle]

ohh

[near trout]

that's just how the square root works

[polar flower]

the root gets cancelled out

[near trout]

you're squaring the square root

[polar flower]

suppose sqroot6*sq root 6

[near trout]

(sqrt(a))^2 = a

square of the square root

[polar flower]

it would be sqroot 36 which is basically 6

that's where it's derived from

[round saddle]

ok i get it now

sorry if that sounded stupid, its 11pm and im burnt out lol

ty guys

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[lament schooner]

why did i get wrong here

i did my calculations so many times

[worldly field]

Hey. So they ask for the velocity at time t. Did you find the velocity function v(t)?

[lament schooner]

yes i have found it

i can show my work if you want

[worldly field]

Sure. And also I'm thinking, when they ask for the velocity at time t, you get just a number. Did you use some specific value for t?

[lament schooner]

values?

[worldly field]

Yeah, how do you get -95? I would expect something that depends on t.

[lament schooner]

C is -5

cuz v(0) = -

5

[worldly field]

So the velocity at t = 10 is -95.

In other words, v(10) = -95.

[lament schooner]

yes

[worldly field]

But they ask for the velocity at a general time t, not at t = 10.

Can you enter -t^2/2-4t-5?

[lament schooner]

they did mention Find the velocity (in m/s) of the particle at time t
.

tho

so like number tho?

[worldly field]

Yeah, but they never said what t is.

From my point of view, it could be any point between 0 and 10.

This is why I am thinking that they are just asking for the general expression for the velocity. So like put in

-0.5t^2-4t-5

in that field might work.

This is the velocity at time t.

[lament schooner]

ah

ill tyr that

[worldly field]

By the way, it must be a mistake that they write "meters" here.
It should be meters per second.

[devout snow]

@lament schooner Has your question been resolved?

[devout snow]

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[restive river]

solve for x

x=2pi/7

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[formal bronze]

Bro the question is really good whoever replies to your solution just ping me once please

jee?

[devout snow]

@restive river Has your question been resolved?

[restive river]

oof,yeah

[restive river]

isnt it

honestly i dont think many cannot do this question
although i had one guy do it but he used some Real Analysis book, bruh
ig few can do it

[devout snow]

@restive river Has your question been resolved?

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[restive river]

hi

[restive river]

I suck at solid figures and nets

Lile

Like

Its not my thing

help pls

[topaz peak]

I think its A

[restive river]

how tho

Cus it can form one

[topaz peak]

idk guessed

oh

idk then

[topaz beacon]

honestly its just a matter of being able to visualize it

but also you cant have a U shape of connected pieces like the one in D

[restive river]

Yup i cant

so D?

tysm

[topaz beacon]

yes

[restive river]

.close

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[copper dagger]

Apologies for the silly question but

[copper dagger]

Q should be (-b,-a) right?

I thought it would be the reflection in the line y = -x

[winter patrol]

not a relfection,

show your graph

[copper dagger]

The red is xy = 1 and blue is x^2 - y^2 = 2

Apologies for the pink that was for a different part of the question

The green is meant to represent the lines y = x and y = -x

[winter patrol]

under your assumption of reflection over y=-x, you're actually getting the black point

[copper dagger]

oh?

[winter patrol]

what's going on here is actually rotational symmetry around the origin

[copper dagger]

ah

So (-a, -b)?

Or is that still incorrect

[strong cargo]

Yes

[copper dagger]

oh right, thank you

.close

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[cunning roost]

how do i solve ?

wait

shouldnt i plug in 1 to the derivative?

[small raptor]

Yep

[cunning roost]

Ohh ok ty

.close

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[cunning roost]

how am i supposed to solve dis

[misty crest]

horizontal tangent means derivative is zero

because the slope is zero

[cunning roost]

0

Ik dat

So do i set the derivative to equal 0 ?

[misty crest]

so find the derivative function

yes

[cunning roost]

Wait why does that make sense tho

Setting the slope of the horizontal x point to equal 0

[misty crest]

i can’t tell ur tone

the derivative is a function that models the slope

[cunning roost]

Yes

[misty crest]

the same way for y=mx+b we say the slope is m for all x because y’=m

for functions that aren’t linear the slope changes so it’s a function of x

[cunning roost]

ok so im just making slope = 0 and that tells me the point where the slope is 0

[misty crest]

yes

[cunning roost]

ohh ok that makes sense now

[flat wren]

A hiking trail is 20 kilometers long. Park organizers want to build 5 rest stops for hikers with one on each end of the trail and the other 3 spaces evenly between. How much distance will separate successful rest stops?

[misty crest]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[misty crest]

did u get x=-1/3 and x=1

[cunning roost]

for me?

Im still doing it

yes i got tha

@misty crest

so to find the y value

do i plug it into the derivative or original funciton

?

[misty crest]

the original function

[cunning roost]

why tho

[misty crest]

the original function models the y value

[cunning roost]

ohh

OHHH

UR RIGHT

[misty crest]

the derivative function models the slope

which was useful for finding the x coordinates of the max/min

but we know the function of x to find the y value

so we can use that x value to find the y value

[cunning roost]

yes ok ur right

Atp ur my tutor

[misty crest]

lol💀

[cunning roost]

Ill pay u in pennies

[misty crest]

nono this is complimentary

volunteer work

i get bored

[cunning roost]

so nice

[misty crest]

my life is so fun right

[cunning roost]

evrytime i help someone w math i end up getting humbled

[misty crest]

😹😹😹

[misty crest]

y

[cunning roost]

maybe u could be a teacher which is actual fun

[misty crest]

no that sounds awful

[cunning roost]

😭 ?

[misty crest]

i help other students

in my study halls

and classes in general

but i’d never want to have to teach a whole class

[cunning roost]

are u math major?

[cunning roost]

Why not

[misty crest]

i’m in high school

senior

gonna be a math major tho

[cunning roost]

wtf so am i

[misty crest]

math and physics

[cunning roost]

why are you so much smarter

do you study math in your free time

[misty crest]

i read math books yea

i read a bunch of books

don’t compare urself to me

[cunning roost]

wth

Im getting muted

[misty crest]

ur message got deleted

hmm

[cunning roost]

For talking about intelligence points

[misty crest]

strange

[cunning roost]

Intelligence quotient

[misty crest]

yea everyone has their strengths

[cunning roost]

Thats so true

[misty crest]

i cant draw

🤷🏼‍♂️

[cunning roost]

I can draw really good

[misty crest]

see

[cunning roost]

Ig that makes up for it

[misty crest]

you’d be considered a genius relative to me

[cunning roost]

not rly its not like i can be an art major in this economy

😭

good thing u studied something that will acc make money

[misty crest]

no one can be an art major in this economy lol

[misty crest]

yup🤌🏻🤌🏻

[cunning roost]

Its ok im doing stem

[misty crest]

i’ve always loved it tho

ever since i was a kid

doing mental math for fun

shower math

[cunning roost]

every time i do mental math i get humbled so fast

[misty crest]

was that kid that refused to count on my fingers

[cunning roost]

i did 39 - 48

[misty crest]

goat at those multiplication tables those worksheets in a minute

[cunning roost]

and i confidently thought it was 7

[misty crest]

close enough

[cunning roost]

I have a test tomorrow

[misty crest]

calc?

[cunning roost]

Yes wanna see my topics

[misty crest]

sure

ur not in ap

[cunning roost]

Idk what ap is tbh

Im canadian

[misty crest]

maybe ur not

yea

not american

trenches lol using black board

[cunning roost]

Ik and my teacher is 6'7 not kidding

[misty crest]

teacher gave the whole test

[cunning roost]

right and i still fuck it up

bro

[misty crest]

guy cares about class average huh

[cunning roost]

but ive had him for 3 semesters

he adds shit on the test that was never on the homework

💔

[misty crest]

like what does it say?

the equation of the tangent line

just use point slope

y-y1=m(x-x1)

[cunning roost]

another derivative question using the power rule? find a point with a particular slope, find the equation of a tangent line, questions like those parabola questions, maybe something else

[misty crest]

where m=f’(a)

[misty crest]

yea ik

[cunning roost]

Or can i just do y = mx + b and plug in the points

[misty crest]

i thoiyht u were asking

[misty crest]

no

[cunning roost]

wait fr?

[misty crest]

because the slope is found using the derivative

you’ll only have one point because the tangent line is always changing

you’ll have the tangent line to the curve at some point (x1,y1)

and have to find the slope

then use point slope form

[cunning roost]

ohh ok

[misty crest]

to find the general equation

[misty crest]

using f’

to get a numerical value

[misty crest]

no basketball in canada

waste of potential

[cunning roost]

💀

[misty crest]

6’7 and not a pro athlete is criminal

[cunning roost]

bro he played hockey infront of us and he fell twice

I told him beforehand i would cheer for him

that shit is so embarrassin

😭

[misty crest]

typical math teacher

parents must’ve been crying when he didn’t come out a d1 athlete

[cunning roost]

embarrassing how instead of cheering i screamed

[cunning roost]

LMAO

[misty crest]

he might as well donate

no one needs to be 6’7

[cunning roost]

Ik

Do u think hes insecure about it

[river tapir]

yo

[cunning roost]

I want to make jokes ab it

[misty crest]

insecure?!?

batman

[river tapir]

can you guys help me rq

[misty crest]

jason todd

[river tapir]

lolll

[misty crest]

with

[river tapir]

it like a min booklet need to get it done by tom 12

this one

lol

[cunning roost]

no one is opening that ip stealer

lmao JK

[river tapir]

loll

i just need help on it

[misty crest]

just got doxxed

[river tapir]

broooo

[cunning roost]

Nathan Drake 21

[river tapir]

i didnt even do anyhting

[misty crest]

y send a link?

[cunning roost]

Send it in screenshot form instead

[river tapir]

cuz its a booklet

trust me

ong

[misty crest]

bro just send a picture

[cunning roost]

Bro wtf get your own channel im struggling over here too

[misty crest]

yea lol

right

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[cunning roost]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[cunning roost]

Im gonna try these questions

Do they require the slope equation formula

[misty crest]

they require the derivative

and evaluating it at the point

[cunning roost]

Oh wait this is easy

[misty crest]

yea

u can find the equation of the tangent line

[cunning roost]

Ill find a harder

This is the same thing isnt it

[misty crest]

essentially

[cunning roost]

Ok tbh this is confusing now

Its still the same right

[misty crest]

try this y=arctan(sin(e^x)) at x=pi/3

[cunning roost]

absolutely not

he wont add anything trig on the test

[misty crest]

boring

try this

y=x^x

at x=3

[cunning roost]

ok

lets speedrun who finishes it first

[misty crest]

u sure?

[cunning roost]

Nvm

I dont even know how to find the derivative of x^x

[misty crest]

i got it

[cunning roost]

wtf

[misty crest]

e^1+ln3

[cunning roost]

Oh ok yea im not that far into the unit

[misty crest]

or wait

no

ok it’s

1/(1+ln3)

[cunning roost]

lets speedrun this question

[misty crest]

i’m doing this in my head btw

[cunning roost]

WTF

STOP

[misty crest]

(-1/16)^-3/4

1/8?

maybe

[cunning roost]

this is my teachers answer

[misty crest]

ahh i was close

i forgot to take the reciprocal

when doing ^-3/4

i just did to the 3/4

[cunning roost]

wtf

this is how far i got

[misty crest]

lol

get good

[cunning roost]

V_V

I have to in 5 hurs

[misty crest]

plenty of time

i have break

february break

i have no school for 5 days

[cunning roost]

why the hell did he do y = mx + b here

[cunning roost]

lucky

[misty crest]

parallel means same slope

so the slope was -1/16

just subtract over x

and divide by 16

then doing the derivative u notice the 3 cancels

[cunning roost]

OHH UR RIGHT

[misty crest]

-x^-4/3=-1/16

damn i can’t believe i forgot to do the reciprocal

i raise both sides in my head to the 3/4

those damn negatives

[cunning roost]

ur doing it in ur head bro

u get a pass

[misty crest]

nah i’m usually better

brain rot

[cunning roost]

ds,r

same*

[misty crest]

fun practice is integrating in ur head

[cunning roost]

fuck no

i can alr tell how hard that must be

[misty crest]

not at all

if u have a good memory

[cunning roost]

yep nope

[misty crest]

it’s real useful

i don’t like to write

[cunning roost]

Me neither

I do anything to avoid it

what the fuck

he set the derivative to the slope

[misty crest]

yes

[cunning roost]

OH

[misty crest]

because the derivative is the slope

but the linear function they gave

was some random one

totally unrelated

[cunning roost]

ohh

[misty crest]

just something parallel

to the slope at the point they gave

[cunning roost]

im confused

if x^-4/3

becomes a reciprocal

dont u get rid of the - ?

bruh

nvm

[misty crest]

x^-4/3

[cunning roost]

they did

[misty crest]

is 1/x^4/3

that’s what i forgot to do

robins back

[cunning roost]

excuse my mental math but how is x^4/3 = 16

haha i get it batmin

[misty crest]

x^-4/3=1/16

so take the reciprocal

because ^-4/3 is just 1/x^4/3

or cross multiply if u see it better that way

[cunning roost]

ohh

[misty crest]

1/x^4/3=1/16

16=x^4/3

[cunning roost]

i dont understand the cross multiplication

tbh forget ab it prob not gonna be on the test anyways right 😓

[misty crest]

it’s basic algebra

multiply the by the denominators

[misty crest]

yea

wait wtf

y would he do 1/1/16