help-36

[hybrid heath]

friend of mine got a great job out of college

[austere crystal]

where he work at

[hybrid heath]

sophomore year, start getting to know the college professors and faculty, ask about internships. Try to get into one by your sophomore or junior year. Get two good internship years at a company, and they'll hire you if you're good and they have an opening

[hybrid heath]

where I work

[austere crystal]

if u dont mind me asking

is it a top company

google, netflix, etc

[hybrid heath]

money is good. I'll say that

[austere crystal]

hahah ok

[hybrid heath]

anyway

[austere crystal]

alr imma headout its late af

[hybrid heath]

This is what you want

[austere crystal]

thx for help regardless even tho i am not fond of math

saved the image

laterrrr

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[elfin bough]

So I got given for reasons 1 and 2

And for 3 i got vertical angles are congruent

What is next for #4

They are congruent so you can tick those sides

[tranquil pine]

the triangles are the same right

[elfin bough]

Yeah

[tranquil pine]

doesn't that mean that they have all their

idk what to call it

identical

[elfin bough]

I think 4 is definition of midpoint

[tranquil pine]

I can't explain 4

I can help with 5 and 6 if you want

[elfin bough]

Sure

[tranquil pine]

since c is vertical angle that means that ACB and DCE are equal

[final saddle]

@elfin bough Has your question been resolved?

[elfin bough]

Uh ok

I thought the same too

What about number 6 though

Idk the reason

is it SAS, ASA, AAS

[tranquil pine]

you have 3 angles and one side

so AAS would be the most fitting one

@elfin bough

side is the given

[elfin bough]

Can you draw it

Look

Idk where the other side is

[tranquil pine]

those are the 3 angles that are equal

and one side

since you know all 3 angles just pick the ones next to the side you know

[elfin bough]

Hold on look

[tranquil pine]

also ac and ad aren't equal

[elfin bough]

What’s the third side

[tranquil pine]

ac and ce are equal

[elfin bough]

Whoops

I drew wrokg

[tranquil pine]

c is middle point of ae

[elfin bough]

So how would you mark it

Mark it on the photo

[elfin bough]

No don’t draw your own

Draw on the photo I sent

[elfin bough]

Yeah

So

Where is the second angle

[tranquil pine]

you know c and a and e

no?

@elfin bough

[elfin bough]

Yeh

You know it

[tranquil pine]

we know c1=c2

and a=e

right?

do you understand why

[elfin bough]

Idk

I gtg tho

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[north lily]

this is just a fun question, is base 3 better or base 12

[north lily]

because I was playing and found that base 3 seems to be the best

however everyone loves 12

[toxic tusk]

What does better mean? A base is just a base, sometimes some bases are useful and sometimes others are.

None of them are inherently better than any other

People like base 12 because 12 has a lot of divisors which can make it nice to work with, 3 is prime so that’s not the case

[north lily]

so

idk in general, because 12 has divisors, and 3 is efficient

and is 3 the most efficient

like write 100 in base 10: 100

[toxic tusk]

What do you mean by that? What is efficient about base 3?

This is also really more appropriate for like #math-discussion

[north lily]

100 in base 2 is 1100100

what is no access?

100 in base 3 is 1021

that quite neat as it just 4 digits and 3 possible numbers

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[thin mauve]

hi

idk how to do this

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[pure wharf]

Any good playlist while studying maths

[worldly spruce]

I mean, it's personal preference really.

Just what you enjoy listening to ...

[pure wharf]

i want something which isn’t too distracting

[verbal crypt]

Lo-fi, Jazz, or classical music it is well known that lyrics can be distracting

[worldly spruce]

¯_(ツ)_/¯

[pure wharf]

Thanks james

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[raven halo]

I had someone else jump on front of me on another channel so I’ll try this one. Can someone explain where I am supposed to start?

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<@&286206848099549185>

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[flat flame]

Total with tax in nova Scotia is 12.65

[autumn geode]

Set up una equation

Para hacer esta problem

[flat flame]

yes idk how tho

[autumn geode]

Por ejemplo la derecho direction de la equacion

es (1.13)x

[flat flame]

I can’t understand sorry

[autumn geode]

The right hand side of the equation

[flat flame]

ok

X is 11 tho?

[royal gust]

Okay so the total in Ontario also needs to be 12.65

[autumn geode]

Let x be the price you have to set in Ontario

[flat flame]

okk

[royal gust]

What's the price before tax, if the price after tax is 12.65? Using Ontario's tax

[autumn geode]

11(1.15) = x(1.13)

Remember that

To do tax you just add .15 of the total

So like you would get 11(1) + 11(.15)

[flat flame]

why is it 11(11)

[autumn geode]

I meant 11(1)

[flat flame]

Ok

[autumn geode]

Shuyan you need to get this right

[flat flame]

so 11?

@autumn geode

[flat flame]

So this one is an equation

I need to sue?

[autumn geode]

Yes

Now I will take my leave of absence from this channel@

[flat flame]

Ok how do I the other one

[autumn geode]

Remember my teachings

And don’t use it for evil

[autumn geode]

No you just solve for x

[flat flame]

Oh

[tranquil pine]

You got this already?

[tranquil pine]

Find the difference in sales tax rates between Nova Scotia and Ontario.

[flat flame]

Yes it’s 11.20

[tranquil pine]

Mmm different than mine but okay 🙂 Hope that works!

[flat flame]

11.19?

cuz I got that too but I just rounded it

[tranquil pine]

It's complicated but let me give you how I solve it

Original price in Nova Scotia = $11 / (1 + 0.15) = 9.57

Price in Ontario = Original price in Nova Scotia + (Original price in Nova Scotia * 0.13)
9.57 + (1.24) = 10.81

$10.81 is my answer 😄

[flat flame]

oh what

wheee did u get all those other numbers

[tranquil pine]

In Nova Scotia, the dreamcatchers are sold for $11, including a 15% sales tax, right?

[flat flame]

Yes

[tranquil pine]

So what I did, I calculated the original price before the sales tax, divide $11 by 1 plus the tax rate in decimal. 😄

hence, original price in Nova Scotia = $11 / (1 + 0.15)

[flat flame]

why isn’t it 11(1.15)

cuz we’re finding the total price?

[tranquil pine]

I was looking for the original price first for Nova Scotia

I divided the price including tax by 1 plus the tax rate as a decimal to get the original price before tax.

Once we have the original price for Nova Scotia, we can use it for the pricing in Ontario

And in Ontario, the sales tax is 13% right?

[final saddle]

@flat flame Has your question been resolved?

[flat flame]

Yes sorry

@tranquil pine

[tranquil pine]

So my take on this is that to ensure that customers in Ontario pay the same amount, we need to adjust for the difference in sales tax rates. 😄

[flat flame]

ok

[tranquil pine]

wait hahaha im trying to explain this much better

So in Nova Scotia, the dreamcatchers are sold for $11, including the 15% sales tax, right?

And so what I did to find the price in Ontario, I removed the sales tax from the Nova Scotia price and then added the Ontario sales tax.

[tranquil pine]

Subtract the sales tax from the Nova Scotia price: $11 / (1 + 0.15) = $9.57 (approximately).

[tranquil pine]

And then I added the Ontario sales tax: $9.57 * (1 + 0.13) = $10.82 (approximately).

Therefore, she should set the price of the dreamcatchers in Ontario at around $10.82 to ensure that customers there pay the same amount as customers in Nova Scotia. I really hope this makes sense as it does to me! 😄

[final saddle]

@flat flame Has your question been resolved?

[flat flame]

<@&286206848099549185> is the correct answer 10.82 or 11.20

because i’m confused

[flat flame]

i mean if u found the price in ontario why are we still solving ??

[tranquil pine]

haha what do you mean? I solved so I got the price for Ontario. It's not like it's given

[flat flame]

how did u solve for the price for ontario

im just confused because isn’t that what we’re looking for?

[tranquil pine]

I already explained step by step

[flat flame]

so that ontario customers pay the same as nova soctia customers

oh

[tranquil pine]

😄

[flat flame]

i’ll just put the answer i got and i’ll check it later

if it’s wrong then i learn smth new

[tranquil pine]

Okay, hope that works!

[flat flame]

😁

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[ancient thistle]

Hello

[ancient thistle]

$\lim _{n\to \infty }\left(\int _0^{2\pi }\frac{\left|sin\left(nx\right)\right|}{n^2+x^2}dx\right)$

[soft zealot]

LE SSERAFIM

[ancient thistle]

Not sure how to start

[vital crag]

Do you know dominated convergence theorme

Or limit of integral of uniformly continuous functions is the integral of the limit

[ancient thistle]

I haven't learned that

[vital crag]

Other one?

[ancient thistle]

That also..

[vital crag]

Then what did you learn

Theorems, lemmas, etc.

[tranquil pine]

hello Mr Riemann, just one question, is this exercise categorized as hard?

[ancient thistle]

Trig sub and improper integrals were the last I've learned

[vital crag]

You'll have to learn this first then

https://proofwiki.org/wiki/Definite_Integral_of_Limit_of_Uniformly_Convergent_Sequence_of_Integrable_Functions

[final saddle]

@ancient thistle Has your question been resolved?

[signal parrot]

i solved it using squeeze theorem and some manipulation, im not sure its correct though

[ancient thistle]

Can you share it please?

[signal parrot]

so you divide the denominator and numerator by n^2(this is the part im not so sure about and your left with 1/n^2 and integral |sin(nx)|dx

[ancient thistle]

I heard we have to first divide the integral into a piecewise function

Because of the abs

I really don't understand the Definite Integral of Limit of Uniformly Convergent Sequence

[signal parrot]

yeah i dont either...

ok so now you set up an inequality
0<= integral |sin nx|dx <= integral dx = 2pi
and if you divide by n^2 you can use the squeeze theorem and get the result

cuz max value of |sinx|=1

[ancient thistle]

Hmmm

I see

Thanks

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[midnight sparrow]

A function f has an inverse iff f is bijective, is it true for all injective functions too ? I mean for surjective the answer is no for sure but for injective I think it has an inverse ?

[tulip coyote]

Tl;dr “Well yes, but actually no”

Remember part of the definition of a function is that every element of its domain has an output (this is what might fail for injective functions, if they’re not surjective) that is unique

[midnight sparrow]

oh ok I see yes

[tulip coyote]

But for an injective function you can take its image and then on its image, define the inverse function to have that as its domain, and you’re fine

[midnight sparrow]

so I need to make another set when I take the inverse where all x has an image

a restriction of the previous set

and so it becomes a bijection and has an inverse

[tulip coyote]

Yep basically if you had an injective $f : X \to Y$ then replace $Y$ with $f(X)$ and you get surjectivity that you needed to invert $f$

[soft zealot]

@tulip coyote

[midnight sparrow]

oh yes I see 👍

ty a lot 🙂

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[rugged fox]

Translation: Replace the different loads with an equivalent resultant and effective torque acting at point A

[rugged fox]

How do I even begin with this excersise?

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[rugged fox]

<@&286206848099549185>

[rugged fox]

<@&286206848099549185>

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[dense garnet]

Consider a double integral where the region of integration is $0\leq x\leq y$ and $0\leq y\leq \infty$. Now I'm trying to find the new one given the change of variables $(x,y)\mapsto (x,y-x)=(x,z)$. I really struggle with this, especially grasping it visually.

[soft zealot]

Philip

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[dense garnet]

<@&286206848099549185>

[dense garnet]

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[ocean pebble]

I understand the concept but i got an answer of 138 days while my teacher got 28

[ocean pebble]

did my teacher make a mistake or did i?

[hard rampart]

cannot possibly be 28 days

if after 30 days there is 120 grams left

[ocean pebble]

yeah thats a logical way to think of it 😂

i just used the formula but the teacher probably plugged in the numbers incorrectly

[hard rampart]

probably

[ocean pebble]

thanks anyway ill email the teacher to notify him of his mistake

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[final saddle]

@amber sierra Has your question been resolved?

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@amber sierra Has your question been resolved?

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[oak arrow]

I just need to answer if it's true or false

So Fxx = x^2
Fyy = -y^2
Fxy = 3xy

and the derivative test is FxxFyy-Fxy, and if it equals 0 then the test is inconclusive. So I have (0)(0) - 0. So the test is inconclusive, and thus it must be false, right?

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[dreamy gull]

I've already determined whether each vector is linearly dependent/independent but i don't know how to do this, could someone help me and show me how to find the span of a set of vectors?

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[dreamy gull]

<@&286206848099549185>

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<@&286206848099549185>

[dreamy gull]

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[tame lake]

Did I set up the integrals wrong? After computing everything I didn't get it right

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[tame lake]

<@&286206848099549185>

[earnest gale]

Hmmmm

A good questio

[tame lake]

been trying this problem for 2 hours rip

[earnest gale]

Do you know the ans

[tame lake]

nope

wait I found a small mistake in my computation, there's hope

[earnest gale]

How are u proceeding

[tame lake]

nvm it's still wrong

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@tame lake Has your question been resolved?

[tranquil pine]

Why did you put 15/4 instead of 1?

[tame lake]

I solved it it's all good now

[tame lake]

I was supposed to put 5/12

It's not 1 bc the two equations in the bottom right don't intersect at x=1

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[final saddle]

Please don't occupy multiple help channels.

[tranquil pine]

for this one tell me if im on the right track
so just writing out the top part i got
((x+h)^2 - 9(x+h)+12) - (x^2+9x+12)

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[grand anchor]

13-Calculate the coordinates of the points that divide the end segment A(-2,3) and B(0,-1) into three equal parts.

[heavy loom]

find the vector between them and divide it by 3

[grand anchor]

AB=(2,-4)

then divide by 3?

[heavy loom]

yeah

then add AB/3 and 2AB/3 to A

[grand anchor]

i don't really understand, can you tell me how?

[heavy loom]

you get AB/3=(2/3,-4/3)

add that to A to get (-2+2/3,3-4/3)

[grand anchor]

we need find 3 points?

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[slow maple]

can someone please check if I did these right? (please ping on reply)

[celest crane]

@slow maple Reread what Problem 2 is asking you to find.

[slow maple]

"Find the dimensions that maximize the area"

[celest crane]

Find the dimensions that maximize the area"

[slow maple]

So is it 6 and -6?

[celest crane]

As you noted in your work, you only need the positive answer to determine the dimensions.

[slow maple]

So the dimension that maximizes the area is just x=6 and I don't have to show what the area is, so I can just erase that, right?

[celest crane]

What is the width of the rectangle? It's not just x.

[slow maple]

I'm not sure what you mean

[celest crane]

The rectangle spans the 1st and 2nd Quadrant.

[slow maple]

Yeah, I see

But the dimension can't be negative

[celest crane]

True, but you aren't calculating the dimensions with respect to the positive and negative sides of the x-axis.

[slow maple]

I'm confused now

Isn't the only dimension x=6?

[slow maple]

What do you mean determine the dimensions?

Wait

I think I get it

[celest crane]

Area is equal to length times width. What did you replace the width with in your Area equation?

[slow maple]

the equation 108-x^2

A=2(6) * (108-(6)^2?

[celest crane]

Yes, now break that apart into the respective width and lengths to get the dimension.

[slow maple]

What do you mean break it apart? Solving that would give you the area and the question isn't asking for the area, the equation has no variables so what do I do?

[slow maple]

I got 864

[celest crane]

The question is asking you for the dimesion of the rectangle, not the area. You need to find the length and the width of the rectangle, not the area, that fits in the boundary of the parabola. You determined the area of the rectangle can be calculated with the equation Area = 2xy where 2x is the width and y is the height.

You have found x so you can use the aforementioned substitution that you used to calculate the width.

You can also use x to calculate the height, y.

$\text{Area} = \underbrace{2x}{\text{Width}} \underbrace{y}{\text{Height}}$

[soft zealot]

Kookiemon

[slow maple]

Yeah, I understand this portion but I just don't get how to find the length

[celest crane]

You are given the equation for y.

y = 108 - x^2

[slow maple]

Yeah

[celest crane]

And you know x.

[slow maple]

X is 6

[celest crane]

So you can calculate the value of y, aka the height.

[slow maple]

72

[celest crane]

👍

[slow maple]

Are the dimensions 12 and 72?

[celest crane]

Yes.

[slow maple]

I didn't even think of it that way, I had the length and width but I just had to find them seperately

Just curious, are you familiar with electrical/computer engineering?

[celest crane]

Unfortunately no. That's outside my scope of knowledge.

[slow maple]

Ah, okay. Thank you for your help anyways!

@celest crane Can you check if I showed the work correctly, please?

[celest crane]

Looking

Looks good.

[slow maple]

Should I refer to y=108-x^2 as the width or as the height?

[celest crane]

I would call it the height.

[slow maple]

Great, and is the first question correct as well? If you don't mind

[celest crane]

Yes.

[slow maple]

Awesome, thank you!

[celest crane]

yw

[slow maple]

@celest crane Can you help me with this question?

[celest crane]

There are two geometric shapes in the problem. You will need to break the problem down into the relevant equations for each geometric shape.

[slow maple]

Is it a rectangle and a semicircle?

[celest crane]

Yes.

[slow maple]

I honestly have no idea how to start, I just know those are the shapes

[celest crane]

You are asked about the perimeter. What are the equations for the perimeter of the two shapes you mentioned?

[slow maple]

Rectangle= 2w+2l Semicircle: π(r)+2r

[celest crane]

Ok, one thing I want you to pay attention to is that you will need to ignore part of each of those dimensions.

The top of the rectangle and the diameter of the semicircle. Do you know why?

[slow maple]

Is it because there connected?

[celest crane]

Yes, they are not included the in the perimeter of the window itself.

[slow maple]

So what do you do with the formulas?

[celest crane]

Hmm, is there more to the question? It seems to be missing some information regarding the height of the window..

[slow maple]

No, that's the entire question

[celest crane]

Ahh.

[slow maple]

So, is this question unsolveable?

[celest crane]

No, it's solveable. Give me a moment.

[slow maple]

Alright

[celest crane]

So those are the two perimeters of the shapes that comprise the window.

You can ignore the diameter of the semicircle and the width of the top of the rectangle as they are not included in the perimeter of the window.

That leaves you with

Those two equations comprise the entire perimeter of the window whose total sum you are given as 24 feet.

You know the radius of the semicircle in terms of x so you can substitute that value in terms of x.

[final saddle]

@slow maple Has your question been resolved?

[slow maple]

What is it?

[celest crane]

Look at the image. What is the diameter of the semicircle?

[slow maple]

2π?

[celest crane]

The diameter is equal to x so the radius is half of that.

[slow maple]

Can you explain this?

[slow maple]

x/2

[celest crane]

So this is the perimeter of the window.

[slow maple]

What does the dotted line represent?

[celest crane]

That divides the window into two shapes; a semicircle and a rectangle.

[slow maple]

I see

[celest crane]

We ignore that dotted line when calculating the perimter of both the semicircle and the rectangle.

That leaves a perimeter for the semicircle as πr and the perimeter of the rectangle as 2x + y that when combined gives an equation for the perimeter of the window whose value we are given as 24 feet.

[slow maple]

I thought the perimeter was 2x+2y, how can you tell the 2's cancel out?

[celest crane]

2x are the top and bottom of the rectangles, however we remove the top value because it is "inside" of the window.

[slow maple]

What the the perimeter formula for the semicircle?

[celest crane]

πr + 2r, however we ignore the 2r because it is "inside" of the window.

[slow maple]

Okay, I see

[celest crane]

So you eventually have this

[slow maple]

The x/2 is just the radius of the semi circle, right?

[celest crane]

The total perimeter is **x + 2y + xπ/2.

Yes.

The 2y comes from adding the height of both sides of the window.

[slow maple]

What's next? Don't you need to have an equation in terms of y so you can plug it into the equation?

[celest crane]

So this is the "tricky" part. The question wants you to find the value of x that gives you the maximum area for the window. You now need to make an equation for the area of the window.

[slow maple]

How do you do that?

[celest crane]

What are the equations for the area of a semicircle and a rectangle?

[slow maple]

Rectangle is lw and semi cricle is πr^2/2

[celest crane]

So you "know" the values of the length, the width, and the radius. Substitute those values into an area equation of the window.

Those values are in terms of x and y.

[slow maple]

This question is so confusing

[celest crane]

Ok, let me first explain how these types of optimization problems are generally solved.

[slow maple]

Any tips would be appreciated, I know how to do the simple ones and the square ones, the cost ones but these I have no idea

[celest crane]

There are two components to area optimization problems, the perimeter and the area.

One value is often provided as a constraint to solve the other value.

You will either be given the value of the perimeter or the area.

[slow maple]

Yeah, I understand this part

[celest crane]

From the given information, it is up to you to make equations for the perimeter and the area.

[slow maple]

But questions like these where you have to break it up into multiple parts, and be able to eliminate stuff. That's where I struggle

[slow maple]

Why is x still in the equation for the rectangle? I thought you eliminate it

[celest crane]

The top of the rectangle is equal to x and the bottom of the rectangle is equal to x whose sum is 2x. Because we ignore the top of the rectangle, we remove an x value.

[slow maple]

I get it

Okay, I understand what you did in this picture. What do you do after this?

[celest crane]

Do the substitution for the radius and you have an equation for the perimeter of the window in terms of x and y. You are given the value of the perimeter of the window, 24 feet, which you can set equal to the equation of the perimeter.

24 = x + 2y + πx/2

[slow maple]

Okay, I'm following

What about making the equations?

[celest crane]

Well ... what are the formulas for the area of a semicircle and a rectangle?

[slow maple]

Rectangle is lw and semi cricle is πr^2/2

[celest crane]

And in terms of x and y?

[slow maple]

A=xy for rectangle, πx^2/2?

[celest crane]

The radius is x/2 so it would be (π(x/2)^2)/2.

[slow maple]

Why can't you x/2 as the radius?

[celest crane]

I did use it. You didn't.

[slow maple]

Oh I forgot to insert it lol

[celest crane]

So anyways ... you now have an equation for the area of the window.

[slow maple]

This is so relateable lol

[slow maple]

Yeah, at the end when we get to the solution. Can you put all the work for this problem on one page? So I can refer back to it later.

[slow maple]

Okay, I understand

Don't you need an equation for y?

[celest crane]

Now you know what the perimeter equals, it is 24 feet. This allows you to solve the perimeter equation in terms of x or y which you can substitute into the Area equation.

[slow maple]

Ohhhh

the alegbra here is going to be annoying

[celest crane]

Yeah, that's why engineers get paid the big bucks.

[slow maple]

Are you an engineer?

[celest crane]

CS retired.

[slow maple]

Nice

[slow maple]

Anyways, do I really have to do all of this algebra for this question? (my teacher doesn't let us use a calc)

[celest crane]

Yes.

[slow maple]

So find it in terms of y, plug it in for y then simplify, then take the derivative, set it to 0 and solve?

[celest crane]

Yes.

[final saddle]

@slow maple Has your question been resolved?

[final saddle]

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[storm turtle]

Hey

[storm turtle]

I need help with this work

[vivid walrus]

Is this for test?

[storm turtle]

No

[vivid walrus]

Okay

Do you know how to factor in general?

[storm turtle]

Yeah but I’m really confused on this

[vivid walrus]

Which part?

Are you confused on

[storm turtle]

Everything 💀

[vivid walrus]

Ok let's start with first one

Can you factor out 512?

To make it same as x^3

Think about it

@storm turtle

,, x^3+\square^3

[soft zealot]

Akira (fumo)

[vivid walrus]

Can you figure it

[vivid walrus]

^

[storm turtle]

Sorry just saw this

[vivid walrus]

No worries

[storm turtle]

8?

8^3

[vivid walrus]

Exactly

,, x^3+8^3

[soft zealot]

Akira (fumo)

[vivid walrus]

Can you factor it out

[storm turtle]

Wdym factor it out

[vivid walrus]

Uh

Like do you think you can able to factor that

Gimme sec I suck at latex

,, a^3+b^3=(a+b)(a^2-ab+b^2)

[storm turtle]

(x+8)(x^2-8x+64)?

[soft zealot]

Akira (fumo)

[vivid walrus]

Yes

That's correct

[storm turtle]

Now what?

[vivid walrus]

That's your first answer on your first question

Start the next one

[storm turtle]

That’s the solution?

[vivid walrus]

Yes

For x^3+512

[storm turtle]

Oh ok thanks bye now

[vivid walrus]

You're welcome

!done

[final saddle]

If you are done with this channel, please mark your problem as solved by typing .close

[vivid walrus]

@storm turtle

[storm turtle]

.close

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[naive axle]

e

[naive axle]

Hello

I need assistance with a few questions

[tiny gorge]

where are you stuck?

!status

[final saddle]

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

[naive axle]

1

step 1

[tiny gorge]

what happens if you multiply out the left hand side?

[naive axle]

ill try it out now

I got 5x^2+22x-2

I think i multiplied it correct

[tiny gorge]

5x^2 + 22x + ... is right

but the -2 is not right

[naive axle]

-48

[tiny gorge]

yea

[naive axle]

So 22= b

[tiny gorge]

yea

[naive axle]

damn that wasnt as challenging as I thought it was

do you mind helping me again?

[tiny gorge]

sure, depending on the question..

[naive axle]

?

[tiny gorge]

ok, any thoughts about how to approach this?

[naive axle]

(x+3) * (------) = (4x^3+14x^2-18)

I just dont know how I would find it

[tiny gorge]

try dividing both sides by (x+3)

notice that -3 is indeed a root of the right hand side, so it's divisible by x+3

[naive axle]

i got 4x^2+2x-16

so im assuming thats the width

[tiny gorge]

ha i'm too lazy to multiply it out by hand, let's check...

,w (4x^2 + 2x - 16)*(x + 3)

[soft zealot]

Results provided by WolframAlpha

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Requested by bungo.the.original

[tiny gorge]

really?

it's not gonna multiply it for me?

[naive axle]

,w (4x^2 + 2x - 16)*(x + 3)

[tiny gorge]

uh oh:

[naive axle]

that is what I got

when i multiplied 4x^2+2x-16*x+3

so im assuming I got it

If you arent pissed i keep asking questions I have one more

This is the one that we just learned

.close

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[slow maple]

Can someone please help me with this? (please ping me)

[warm ether]

any idea how you could write a function for this? (ping: @slow maple )

[slow maple]

Not really

Is (2.40x+20) right?

[warm ether]

not quite no

what would the function be between 0 and 20

[slow maple]

Im not sure

[warm ether]

it is 2.40 per can, lets say x is the number of cans

[slow maple]

Yeah

[warm ether]

then whats the price of x cans

[slow maple]

48

[slow maple]

How do you write the function between 20 and 70?

[warm ether]

oh write sorry
well
you have the cumulative cost from 0 to 20
2.4(20)
then every can after costs (2.4-0.02(x-20))
so you have a total
2.4(20)+(x-20)(2.4-0.02(x-20)) as the function between 20 and 70

[slow maple]

can you explain how you got the second equation

I meant the third one

I understand the second one

[warm ether]

2.4(20) is the cost up to 20 cans
the (x-20) are so that its only the x values after 20 that do anything
2.4-0.02(x-20) is the 0.02 discount for every x beyond 20

[slow maple]

Yeah, I understand

can you explain the one after

[warm ether]

the one after?

[slow maple]

last line

[warm ether]

i just did

i broke it down

[slow maple]

Can you explain why your adding 2.4(20) with (x-20) and why the (x-20) is being multiplid with the other part

[warm ether]

2.4(20) is the cumulative cost from the first 20 cans

(x-20) is every can after the 20th, when x=21 (x-20)=1, so we are counting anew

the multiplication is because (x-20) is the number of cans after 20
and (2.4-0.02(x-20)) is the cost of each can after the 20th

wait, i might be doing something silly

gimme a sec

[slow maple]

Ok

[warm ether]

nvm, its okay i think

just confused myself with the x boundaries for a moment

[slow maple]

So are you supposed to solve for x or do you plug 20 into it?

[warm ether]

neither,
youre finding when its maximal, so you find when the derivative is 0

[slow maple]

Oh right I forgot

I got 20

Is that right?

[warm ether]

impossible

what'd you do

[slow maple]

I took the derivative and then I set it=0 and I got 20

[warm ether]

show me

[slow maple]

I'm supposed to take the derivative of this right? 2.4(20)+(x-20)(2.4-0.02(x-20))

[warm ether]

yup

,w differentiate (2.4(20)+(x-20)(2.4-0.02(x-20)))

[soft zealot]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by aldrnari_

[warm ether]

,calc 3.2/0.04

[soft zealot]

Result:

80

[warm ether]

spoilers

but yeah you did something wrong

[slow maple]

The answer is 80?

[warm ether]

yeah, you should still try get it though

[slow maple]

It's supposed to be 72

[warm ether]

well damn, something has gone awry

[slow maple]

I mean 70

[warm ether]

,w differentiate x(2.3-0.02x)

[soft zealot]

Results provided by WolframAlpha

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

Requested by aldrnari_

[warm ether]

,calc 2.4/0.04

[soft zealot]

Result:

60

[warm ether]

phew at least its not that

[slow maple]

I hate optimization

Why is it 70?

[warm ether]

honestly, im not sure

ill have another look after i finish cooking

[slow maple]

Okay, please ping me if you figure it out

[final saddle]

@slow maple Has your question been resolved?

[final saddle]

@slow maple Has your question been resolved?

[final saddle]

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[swift oak]

I want to know what the percentages would add up to from 2014 to 2023

I'm not sure whether it's correct to add up all the numbers so I'm asking here for help

[deft ravine]

You need to multiply them like 1.011•1.033•...

[swift oak]

So i just multiply all percentages including negative ones and thats my answer

[deft ravine]

Like add 1 to each of them and multiply

[swift oak]

ooh

do i have to do anything special with negative

[deft ravine]

The reason why you need to multiply is that you need to account for the increases after each year. If you were adding them you would forget to consider that after each year the food price has already increased, so 10% of the prize actually becomes more money

[deft ravine]

*0.999 for this one

[swift oak]

for the negative ones I add 0.999 and then multiply

?

[deft ravine]

Always add 1 to each term => -0.001 +1 = 0.999, 0.011 + 1 = 1.1011 and then take the product out of all of those

[swift oak]

okay can you give me a minute to do it and check my answer please

[deft ravine]

I won't type it in

[swift oak]

thats fine can you just give me like a yes or no

im just doing this to put as evidence for my essay

i got 1.3479894165

would that be 134% ?

[final saddle]

@swift oak Has your question been resolved?

[swift oak]

My english essay is due in an hour please

<@&286206848099549185>

[rain breach]

101.1 × 103.3 × 100.8 × 99.9 × 101.6 × 101.6 × 101.8 × 103.9 × 106.3 × 110.4 × 103.3

Is this what you did?

Oh wait i messed up

Just divide all of the terms by 100

Yeah i think thats correct

Noooooo it's not 134%

You need to consider the original value so it's 34%

[swift oak]

okay thank you so much

Im literally so grateful for you rn i wish you the best in life 😭

[swift oak]

.close

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[fiery tusk]

undefined limit

[fiery tusk]

undefined (infinity / infinity)

in this case i usually divide by highest power

but here... what is highest power? x?

i prefier to use this

so i get

|x| = x since x goes to infinity

and then i can easily find highest power (x^1)

is there different way?

[formal trail]

when you have a power of x under a root, for the purpose of highest power counting it's always (power)/root, so e.g. an x⁵ under a cube root would have power x^(5/3)

[fiery tusk]

there is power added to some constant under root

which is harder

[manic flame]

$\frac{\sqrt{x^{2}+1}+1}{x-8}\to\frac{x\sqrt{1+\frac{1}{x^{2}}}+1}{x-8}$

[soft zealot]

Combustion

[manic flame]

*it should be |x| but x goes to positive infinity so |x| = x here

[fiery tusk]

or wait...

ah, ok

1 + 1/x^2 goes to 1 + 0 at x -> infinity

so it is just x

[manic flame]

yeah but just divide by x and evaluate it there $\frac{x\sqrt{1+\frac{1}{x^{2}}}+1}{x-8}\to\frac{\sqrt{1+\frac{1}{x^{2}}}+\frac{1}x}}{1-\frac{8}{x}}$

[soft zealot]

Combustion

[formal trail]

when we divide the entire root by x we get
$\frac{\sqrt{x^2+1}}{x}=\sqrt{\frac{x^2+1}{x^2}}$

[soft zealot]

cloud

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[queen flame]

so when doing first order differntial equations, this guy makes 3C = C coz C is basically a constant

[queen flame]

but when its being cuberooted, the C doesnt stay a C

why

like i cant do y = x + c

[zinc geyser]

you cant distribute cube root over addition

$\sqrt[3]{a+b} \neq \sqrt[3]{a} + \sqrt[3]{b}$

[soft zealot]

Bettim

[queen flame]

ah okay

thank you

.close

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[heavy laurel]

Can anyone help me with this problem?

[heavy laurel]

Specifically part A>

[final saddle]

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[grand meteor]

How to solve something like this? I don't understand how does this shows something. I know the three rules, like if its continuos on the domain then integrable, if it has finite number of discontinueitis and is bounded its integrable and monotinic and finite number of discontinues also integrable, but how to apply it?

[dense coyote]

🇱🇹

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[orchid surge]

what was the formula to work out inside angles

[raw fiber]

?

[orchid surge]

nvm i got it

.close

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[orchid surge]

@tranquil pine it didnt work for some reason

[tranquil pine]

you were supposed to find the interior angle of a regular pentagon

[orchid surge]

yes

[tranquil pine]

wait I got confused

[orchid surge]

i asked if i divided 450 by 5 u said yes and that was 72]

[tranquil pine]

okay so I'ma give you the long answer

[orchid surge]

ok

ill try understand

[tranquil pine]

[(n – 2) × 180°]/n

this is the general formula for interior angle

of any regular shape

with n being the number of angles

using the first part (omitting the /n) we get that a Pentagon has 540°, not 360°

[orchid surge]

why did we do 450 then

i just checked it and its correct

[tranquil pine]

we never did 450, we did 360

[orchid surge]

the 540

[tranquil pine]

540/5=108

did you put in 108?

[orchid surge]

yes

[orchid surge]

but 450/5 is 72 and thats what we got

[tranquil pine]

360/5=72.

,w 450/5

[soft zealot]

Results provided by WolframAlpha

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

Requested by n1h1l1sm

[orchid surge]

oh ye

ur right

thanks again

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[warm epoch]

This is the image I've drawn to help me visualise the problem. I've tried to consider the fact that the vectors representing the direction of the side lengths dotted together would be 0 and I've tried also using the cross product to find a relationship with no success so far. I've also tried a couple things that didn't use vectors and lead to overly complicated quadratics (i can't use a calculator for this). Any help would be greatly appreciated

[ashen creek]

it's geometry rihgt?

or?

[warm epoch]

as in the class or the field of maths?

[ashen creek]

class

[warm epoch]

no

[ashen creek]

field?

[warm epoch]

it is a geometry problem

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@warm epoch Has your question been resolved?

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@warm epoch Has your question been resolved?

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[tranquil pine]

i have a general question about proving if a function is surjective
assume u have a function f : A --> B for like x --> some expression
and y is a member of B
and i re arrange and do my stuff to get x = some expression in terms of y
so then i consider f(some expression in terms of y) = y
do i need to show that both the domain and range are still valid or just the domain
this might be a bit of a vague question so if u dont understand ill just provide an example lol

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[still vault]

So where im at, we have Math MAP (state testing pretty much) and I really need a 245, I have a 236 right now. It's tomorrow, I have been doing some studying but I need more tips, Any help?

[still vault]

Im in pre-algebra and starting to learn actual algebra via Khan Acadamy

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@still vault Has your question been resolved?

[still vault]

<@&286206848099549185>

[half salmon]

What kind of questions are you generally looking for?

[still vault]

Just how to study efficiently

pretty much

especially for state tests

[mortal trout]

do u guys have practice exams

i would do some practice exams and whatever questions u get wrong review those

also just do some general things

make sure u sleep, eat a good breakfast, etc.

that stuff is super important tbh

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[fringe kelp]

Question 2

Ik how to solve this but can anyone write it's solution in a proper way

[hearty zephyr]

how did you solve it?

[fringe kelp]

Ok let me tell

First I thought about the way to select different squares

And it formed a pattern

And then I thought that if we name first column c1 so relation between other columns c2 c3 ç4 were c1+1 , c1+2,c3+3 respectively etc

So I choose 8 random no.a1+a2+a3+a4 till a8

One From each column

And all the numbers should be any number from first column+1+ any number from first column+2+any number from first column+3 till 8th number

And as all the numbers are distinct the sum of those 8no with that propert will be( sum of all no from column)+ 1 +1+2+3+4+5+6+7

How do I write this solution in more mathematical form

<@&286206848099549185>

[hearty zephyr]

do you notices a pattern in the numbers as you go down each column?

[fringe kelp]

As I go to the next vertial column the pattern was it's just simply +1 of previous vertical column

Idk how to express the solution verbally clearly that's the main problem but I understand it mentally

[hearty zephyr]

look at the first column. Is there a pattern in the numbers 1, 9, 17, 25, 33, 41, 49, 57?

[fringe kelp]

Yes it's +8 but I am not talking about that I am talking about going horizontally from vertical column

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[fringe kelp]

No one's answering

.close

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[fierce yew]

Have I processed the left and right riemann sums wrong somehow?

[final saddle]

@fierce yew Has your question been resolved?

[manic flame]

you forgot to multiply by delta x

[fierce yew]

thanks so much

[manic flame]

[fierce yew]

is it possible if you could help me find this one out as well

I basically found the 0 at t=4

seperated negative and positive integrals

and used absolute value for the negative

so 46.5+2/3

=283/6

[manic flame]

the 0 isn't at t = 4

[fierce yew]

you factor v(t)

t=-5 or 4

[manic flame]

opposite

(t-5)(t+4)

t=5, t= -4

[fierce yew]

ohh

thanks lol

[manic flame]

[fierce yew]

what is my strategy for this one

in finding distance

how do I seperate it out

wait hold on i think i got it

nvm

Thanks

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[mighty knoll]

https://cdn.discordapp.com/attachments/1156686604866429081/1181636653287215214/image.png?ex=6581c7e3&is=656f52e3&hm=68c0aa55379b59c269eab5c981cd2f06b56ab710c7042c14da8a16c75b5cf7d5&

[mighty knoll]

Isn't this wrong?

Shouldn't it be sqrt(4-r^2)

Z is my function
The object will kind of look like a silo, a cylinder with a sphere hat
The volume is simply the double integral of the sphere hat (the function) over region R
I convert this to polar, shouldn't z be sqrt(4-r^2) ?

[final saddle]

@mighty knoll Has your question been resolved?

[lyric summit]

$\int_{0}^{2\pi}d\varphi\int_{0}^{1}\varrho\sqrt{4-\varrho^{2}}\text{ }d\varrho$

[soft zealot]

Joanna Angel

[mighty knoll]

Uhh, I don't understand

What's phi doing there

I guess that's the same thing as I said if I take phi to be r

So the answersheet is wrong then? It should be 4 not 1 under the square root

[lyric summit]

yoru mistake

was

not writng

number 4

Phi works liek theta

but in our institutes, we onyl use phi

[lyric summit]

$\int_{0}^{2\pi}d\varphi\int_{0}^{1}\varrho\sqrt{4-\varrho^{2}}\text{ }d\varrho=2\pi\int_{0}^{1}\varrho\sqrt{4-\varrho^{2}}\text{ }d\varrho=\\\text{Let }\text{ }t=\sqrt{4-\varrho^{2}}\text{ }\text{ }\text{then }\text{ }\varrho^{2}=4-t^{2}\\2\varrho\text{ }d\varrho=-2t\text{ }dt\text{ }\text{ hence }\\=2\pi\int_{2}^{\sqrt{3}}\left( -t^{2} \right)\text{ }dt=2\pi\int_{\sqrt{3}}^{2}t^{2}\text{ }dt=2\pi\cdot \left[ \frac{t^{3}}{3} \right]_{\sqrt{3}}^{2}=\\=2\pi\left( \frac{8}{3}-\sqrt{3} \right)=\frac{2\pi}{3}\left( 8-3\sqrt{3} \right)$

[soft zealot]

Joanna Angel

[mighty knoll]

Yes exactly, so the answersheet they gave us is completely wrong
Thanks

[lyric summit]

yvw:)

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[final saddle]

Please don't occupy multiple help channels.

[tranquil pine]

.close

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[warped bluff]

So basically the pentagon does not have the second blue triangle

But to calculate the area of that pentagon I need to get the area of the triangle

<@&286206848099549185>

[rich tide]

well im unable to understand your working

you may try to work with this

[wintry sigil]

how do u even know its a 3 dimensional shape

[rich tide]

#help-7｜zen1thxyz message

the idea would be to solve for y and z (pythag) and then solve for theta which would allow us to find area of the only non-right triangle

in the pentagon

[warped bluff]

It’s not 3 dimensional

[wintry sigil]

but u drew a 3d shape

[wintry sigil]

oh

[warped bluff]

That’s not 3d that’s just labeled by the sectors of the rectangle

[wintry sigil]

i get it

[warped bluff]

Yeah

So I want to find the blue triangle

[warped bluff]

1 vector folds to the other creating the pentagon

It’s just labeled

[wintry sigil]

so breadth will be same

and length will be half of the rectangles length

nvm its not regular

[warped bluff]

Yeah so do you see

My working

I just need to find the blue triangle

[final saddle]

@warped bluff Has your question been resolved?

[warped bluff]

<@&286206848099549185>

[raw pike]

You should try determining the angles. If you find the angle I highlighted in orange you can find the area of the triangle

[warped bluff]

OK trying right now

[raw pike]

Nvm that’s maybe not the angle you should try to find

[warped bluff]

Then which one

?

[raw pike]

Ok actually it works

[warped bluff]

OK

How do I even start with finding the angles

[raw pike]

Do you see how you could find the white angle?

[warped bluff]

No but the sum of them is 90

[raw pike]

The sum of the angles in a triangle is 180

[warped bluff]

Yeah but there is already one right angle

So the orange plus white is 90

[raw pike]

Yea indeed

So to find the white angle, you can use arctan

[warped bluff]

Oh no I am 14

[raw pike]

Oh! Have you learned about tan yet?

[warped bluff]

Yes

Tan is O/A

[raw pike]

Hmm hold up lemme think if there’s a simple solution

Ok I found a way! It uses only similar triangles

Have you learned about those yet?

[warped bluff]

Nvm I didn’t know that tan^-1 is arc tan

I know what arctan is

[raw pike]

Ahh alright

So there’s kind of two ways you can do this then

What we ultimately want to find is the base of the blue triangle. Because if you find that, you find the area

[raw pike]

The yellow and red triangles are similar. Can you use that

[warped bluff]

White angle is arctan 1/3

So orange angle is 90-arctan1/3