help-28

[torn jolt]

So what is your new integral then

[torn jolt]

Ok so integrate

[vestal verge]

How

They are products

[torn jolt]

Ok

So what can you do to make them not products

[vestal verge]

Distribute

But my brain hurts and that’s way too much

It’s gonna be really long

[torn jolt]

It really isn’t that long

If you think expanding a square binomial is too long then you shouldn’t be in calculus

[vestal verge]

It’s a 5th power binomial 😭

[torn jolt]

No it isn’t lmao

[vestal verge]

Nvm

I see I was looking at it backward

This?

[torn jolt]

Why’d you do it all at once 😭

Did you write any intermediate steps

It will make it easier for me to follow

[vestal verge]

I got it right according to my book

So I’ll just move forward

Thanks for the help though

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[brisk vortex]

Can someone advise if I've got the correct answer on this numerical reasoning question:
Food: 6 = 30%
Venue: 5 = 25%
Decorations: 5 = 25%
Marketing: 4 = 20%
As I'm confused on the part for marketing, I'm not sure that's correct?

[random compass]

is the question wrong or smth?

marketing should have 5 people right?

but then the total people would be 21

[brisk vortex]

I'm confused, yeah, because it's a group of 20

[random compass]

im not sure but it's most likely that the question has an error

[brisk vortex]

Okay, no problem

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[thick hedge]

is this a test?

[tiny flax]

coughs

[tender skiff]

No studying for my exam🤡

You think i would study for a measly test?

[grave elm]

hmm

Question is "How did you do?"

so i think its not a test

[tender skiff]

My issue is i have the answer but they do it in a different way to which i was taught so idk

[tender skiff]

Its save my exams

Yall better not dip

[tiny flax]

Wht method did they use ?

The coefficient one

?

[floral widget]

So , the method is pretty much for what value of m ^5 do u get -10x^3

[tender skiff]

Yes but i complete the square first they dont

[floral widget]

Elaborate with example

[tiny flax]

Actually x^3 can't be equal to -10

Since we are dealing with natural numbers

That's wht I think

[tender skiff]

Well its in the question🤡

[tiny flax]

It's the coefficient

[tender skiff]

Yeah

But why not

I solved for x^3 and it gave me the coefficient

Surelt u should equate them

[tiny flax]

If the coefficient is -10 then x would be -1

Coefficient of just x3

Do you know about this formula :
If (x+a)^n
Then

n
C x^(n-r) a^r
r

It's the formula for finding the term in the expansion

T (r+1)

That's wht they used in the first pic

[tender skiff]

The solution says equate it tho

[tender skiff]

Hr not looking cor x ur looking for m

[tiny flax]

Yes

My bad

But the above formula can be used to find m

And equate it by -10

Since we have -10 as the coefficient

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[hybrid nexus]

wolfram alpha cant solve it...

,w Integrate[Sqrt[Divide[Power[a,4],Power[b,4]]+Divide[Power[a,2]Power[x,2],Power[a,2]Power[b,2]-Power[x,2]]],{x,-a,a}]

,w Integrate[Sqrt[Divide[Power[3,4],Power[5,4]]+Divide[Power[3,2]Power[x,2],Power[3,2]Power[5,2]-Power[x,2]]],{x,-3,3}]

[glossy valve]

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[thick hedge]

lol

are you sure the problem is right

[hybrid nexus]

yea

i was trying to find out the perimeter of an ellipse

but its extremely messy

[thick hedge]

There's no standard closed form

,w perimeter of an ellipse

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[hybrid nexus]

no if u solve that integral u get the semi perimeter

,w perimeter of an ellipse

[thick hedge]

https://math.stackexchange.com/questions/191307/perimeter-of-an-ellipse

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[hybrid nexus]

oh okk thanks

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[round crypt]

need help understanding f sub xy

[round crypt]

i understand sub xx is just continuing in the x direction to see if it increases or decreases, but what is xy??

is it the concavity of y? or x?

both x and y??

[pearl trout]

move in the y direction, does the slope of the tangent line in the x direction increase or decrease

is what that's saying

[round crypt]

yes the tangent line at (1,2) for x is positive but what does the y mean

what do you mean by move in y direction

so i check for the tangent at y instead? do i multiply the signs of the tangent of x and y t osee if it' s + or -?

lik what am i supposed to do after finding f sub x

[pearl trout]

like if you move in the positive y direction then the x direction is becoming tastier than before for increasing the value of f

=> f_xy is positive (=move in the y direction and the rate of change in the x direction increases)

[round crypt]

so it's... diagonal?

checking the tangent line sign diagonally?

in the positive y direction for (1,2) is decreasing but x is increasing

[pearl trout]

you picture movement in the y direction and you compare two snapshots of the tangent line in the x direction and if the slope increased then f_xy > 0

[round crypt]

the slope doesn't increase though

wouldn't it be 0 then?

the rise from tangent of x direction cancels out with the fall of tangent of y direction

i cant see how it's increasing

[pearl trout]

there's only one tangent that you consider

but at different points in time

in the animation in your head

and I think the slope does increase

[round crypt]

???

like this?

x is increasing faster than y is decreasing?

[pearl trout]

like if your whole purpose in life is to climb the mountain in the x direction starting from (-1, 2), and after moving a little bit in the y direction you're like "fuck it's steeper now", then that means that f_xy > 0

[round crypt]

so im climbing both the x and y direction

[pearl trout]

shit I hope I'm not looking at the wrong point

[round crypt]

so diagonal

(1,2)

[pearl trout]

ohhhh okay good I was looking at the right one

[pearl trout]

naww don't think about it like that

To understand f_xy, you should first understand f_x, which is measuring how steep the mountain is in the x direction

[round crypt]

yes, see if the tangent is + or -

but im stuck on the y part

[pearl trout]

Then when you think about (f_x)_y, you can think about what would happen to the tangent if you moved a bit in the y direction

and in this case the mountain would become even steeper

in the x direction

so therefore f_xy > 0

[round crypt]

what do you mean a bit

like a very tiny amount??

[pearl trout]

yeah

[round crypt]

but then it would never change the sign if it moves by a tiny amount

[pearl trout]

which sign would never change?

[round crypt]

the first 2

i just reiterated those answers and got it right

because unless (1,2) has a slope of like 0.000001

and a tiny shift in y made it negative, thats the only time it will change the sign?

[pearl trout]

ah I see what you mean now

You need to remember that f_xy is not measuring the final slope

it's measuring the difference in the slopes

[round crypt]

oh

[pearl trout]

So (1, 2) could have a slope of 1 in the x direction, which could quickly become 0.9 when you move in the y direction, and that would correspond to f_xy < 0

And then maybe when you move some more in the y direction that slope would jump back to 1, in which case f_xy > 0

and somewhere in between f_xy changed sign

So, to understand f_xy, it's helpful to move in the direction of y

because at the end of the day, that function is telling you something about the change of f_x when you move in the direction of y

But, to understand the quantity that's changing, you need to look at the slope of the tangent line in the direction of x, because that's what f_x represents

[pearl trout]

Note that this is not what actually happens in your problem, this is just an example of something that could happen

[pearl trout]

In d I think it's maybe slightly easier to see, but tbh the chosen function maybe isn't the best possible choice for this exercise

If you start at (-1, 2) and move in the direction of y, a child who's wanting to slide down the mountain in the x direction will get happy because the slope is getting more negative, and thus f_xy < 0

Note that the slope is negative in the beginning, and after the child moves a bit in the y direction the slope will still be negative, and that has nothing to do with f_xy, what's important is that the slope decreases, that's what makes the child happier when they change their spot and that's what makes f_xy < 0

I mean really it's the same idea as in the first two problems except you're just picturing the movement in a different direction (of course I can't get inside your head to see how you solved the first two problems)

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[round crypt]

alright thanks

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[muted crypt]

hello

[muted crypt]

I am having trouble solving this

i know the circumference is 100 pi and the distance traveled by the cart is 160 ft

But im not sure where to go from here

[charred geode]

how much of the circumference did the car travel

[muted crypt]

160/100\pi

i assume the answer would be around 125

[muted crypt]

But im not sure how to actually solve this

[charred geode]

yup

[muted crypt]

like i know that its around there but im not sure what the exact answer is

[charred geode]

look

you can try this

[tulip oriole]

arc length and find sin of angle?

[muted crypt]

so if arc length = r theta and the length is 160 and r = 50, then theta = 16/5

16/5 radians

[muted crypt]

What does applying sin do? Am a little confused about this

[tulip oriole]

it gives you the height

[muted crypt]

how does sin apply when theres no triangle? or am i missing triangle? Sorry havent fully understood trig functions yet

[tulip oriole]

you can apply sin on the unit circle

and ur circle would be the loop

kinda

[muted crypt]

Ah

Let me try this

[tulip oriole]

but you have to consider that your starting point is not 0

since you start at the bottom

[muted crypt]

Starting is -90 right

[tulip oriole]

yeah

[muted crypt]

So convert 16/5 to degrees, subtract 90, find sin on unit circle?

[tulip oriole]

and add 25 feet

[muted crypt]

Ah yes

Thank you

[muted crypt]

It is incorrect

16/5 to degrees is 576/pi

sin(576/pi - 90) + 25 is approximately 26

When in actuality my answer should be about 125

<@&286206848099549185>

Are you sure that i should be doing sin?

[tulip oriole]

why should it be 125? do you have the answer

[muted crypt]

576\pi = ~180 degrees right

Which is the highest point of the circle

meaning

since radius = 50

Supposing the cart is at highest point, then the carts height is 125

Since the diameter is 100 and then add 25 since ride is 25 feet above ground

However, the cart isnt exactly at 180 degrees

meaning it would be 124.something

but im not sure how to find the exact answer

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[tulip oriole]

i got 124.915

you need to multiply sin(576/pi - 90) by 50 since the radius is not 1 but 50

forgot to say that

[muted crypt]

Ahhh

Thank you

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[muted crypt]

wait

[muted crypt]

like this ?

where is the 50 being multiplied exactly>

@tulip oriole

Sry this seems like a simple question but i cant find it-

[tulip oriole]

50 times the whole thing

also at the end it's + 25 + 50

since the sin only gives you the height above the center of the loop

well not the whole thing sorry

the whole sin()

[muted crypt]

as in this?

[tulip oriole]

50*sin()+75

[muted crypt]

Ah, thank you

I appreciate your efforts to help!

Thank you very much

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[brazen kernel]

Need help solving for phase shift

[brazen kernel]

This is my current work

I have been stuck for at least the past 40 mins now

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[split meadow]

When it comes to trygonometry equations, when should I use πk and when 2πk? for example, on sine equation sin((π/6)-2x)=1 the answer is (π/6)+2πk. Why isn't it (π/6)+πk?

[split meadow]

When it comes to trygonometry equations, when should I use πk and when 2πk? for example, on sine equation sin((π/6)-2x)=1 the answer is (π/6)+2πk. Why isn't it (π/6)+πk?

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@split meadow Has your question been resolved?

[thorn granite]

pi and 2pi are not the same values, it happens every 2pi, and so on.

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[coarse bronze]

Why would this be C instead of A

[hybrid nexus]

shud be A acc to me

altho i m8 be wrong

[coarse bronze]

the answer is C

i got A too

idk y

<@&286206848099549185>

[polar valve]

i would say that the average velocity is travelled distance per used time. travelled distance is s(8)-s(2), used time is 8-2, so the answer is (C).

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[coarse bronze]

i see, ty

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[low quartz]

I think i’ll need to use l’hopital but idk how

[violet loom]

does the numerator or denominator approach the same value as the limit approaches 0

let numerator = f(x)
denominaot = g(x)

so they both approach 0
now differentiate f(x) and g(x)

does the limit exist for f'(x) and g'(x)

[torn jolt]

or

factor out

(secx)^4

it will be easier that way

provided that you you know limit x tends to 0 sinx/x is 1

[torn jolt]

no i don't suggest using l'hopital

[low quartz]

Could you show me how if possible?🥺

[torn jolt]

uhh

how do i show

like

you know

factor out the sec term

you get it as (secx)^4(1-(cosx)^6)/x^4-x^2

do you agree with this

now use a^3 - b^3 = (a-b)(a^2 + b^2 + ab)

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[rain oar]

Can anyone help me figure out why I keep doing Gaussian elimination wrong?

[rain oar]

I dont know if there are any important rules I'm forgetting

Or I'm just doing the math wrong

But i keep getting different answers than the solution

[glacial pasture]

So you swapped rows, then you say you changed r2 but r2 didnt change at all, rather a 2 appeared in R1 for some reason

Unless im reading your process wrong

Also are you writing the changes a line before you apply them? Thats odd and a tad confusing to read if you are

Otherwise im not sure whats going on

[rain oar]

Yes, I swapped rows first. You're right that it's written in a confusing way, I should change that

But then

[glacial pasture]

You swapped rows wrong then, you miswrote R1

3rd entry is a 0 not a 2

[rain oar]

I guess this is where I'm probably forgetting something. I was thinking Im adding the new R1, what used to be R3, on to R2, so the -1 in the first column dissapears

This is where I think I've misunderstood something crucial

[glacial pasture]

If we assume your second matrix is right, which it isnt, then the third one is fine

[rain oar]

I guess I don't understand how you can swap rows wrong

I thought you could just

swap them

[glacial pasture]

You just wrote out the row incorrectly

As in you changed it

[rain oar]

oh

oh god

[glacial pasture]

1 -4 0 became 1 -4 2

[rain oar]

I see it now

Thank you so much hahaha, that was such a dumb mistake 🥲

[glacial pasture]

Happens to everyone

[rain oar]

well, I think I can figure the rest out myself then, thank you so much <3

[glacial pasture]

No worries

[rain oar]

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[plain fox]

Find the length of the chord cut off from the line 2x + 3y = 13 by the circle x^2 + y^2 = 26

[plain fox]

do i just find points of intersection and use distance formla to find the length?

oh ok ty

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[sage anchor]

I'm trying to solve this differential equation using power series, I think I'm doing good until now, I have been told that the constant - 2a_2 = 0 => a_2 = 0 but I can't figure out why.

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[sage anchor]

<@&286206848099549185>

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[sage anchor]

<@&286206848099549185>

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[raw ruin]

I need help

[mossy ibex]

What you need

[raw ruin]

About grouped data, wait lemme send the problem

[mossy ibex]

Ok

[raw ruin]

I'm trying to find Q1

Using this formula: LB + (K(N)/4 - cfp/f) 500

Since 60/4 = 15, how am I suppose to solve for Q1 if the lowest value of the cf is 39 and my K is 15?

@mossy ibex it's due an hour later pls helpp

<@&286206848099549185>

I just need to what number to subtract to 15

What cf to subtract 15 in

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[raw ruin]

No

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[true burrow]

Hi

[true burrow]

I'm not sure if I can ask this here

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[true burrow]

How can I find the probability of it??

[proven dirge]

Are you sure it was 11.11

That seems outrageously high

[true burrow]

Yeah

[hybrid nexus]

whats z-score

[proven dirge]

It's based upon standard deviation I believe

That is an insanely low std

11.1 though

I'm not sure that's possible

What scale is this for

[true burrow]

C.

[proven dirge]

Ah

I'm not exactly sure of the calculation

[true burrow]

What is it?

Maybe my prof got it wrong lmao

Thanks

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[sick needle]

Helppp

[sick needle]

I checked the marking scheme and it says that x and y are both 43

x with angle at centre is twice the angle at circumference

and y with alternate segment theorem

But i dont understand how the x is given that reason

shouldn't it be like angles in a semicircle

[ashen crescent]

The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle's circumference. In this case, PSR and POR are both subtended by the arc PR

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[crude phoenix]

Is it even possible for this gradient to have these critical points

[crude phoenix]

I only get (0,0,0)

Nvm mods

.close

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[crude phoenix]

.reopen

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✅

[crude phoenix]

Thing is how do you get all of the critical points out of this

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@crude phoenix Has your question been resolved?

[crude phoenix]

<@&286206848099549185>

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@crude phoenix Has your question been resolved?

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@crude phoenix Has your question been resolved?

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[rigid mauve]

Hey, I have this question in analytical geometry in circles,
A function of x+2y+1=0 is cutting a 120 degrees circle arc. It is known that the circle's middle point is located at (7,1). Find the circle's equation.

[rigid mauve]

I would like assistance, Thank you (:

[hallow walrus]

Try drawing a figure first

And send that figure here as well so we can guide you further

[hallow walrus]

Okay

Try drawing a perpendicular from the Center to the line

And mark some distances with variables

Remember that the perpendicular from the Center of a circle to its chord bisects that chord

[rigid mauve]

Alr

[hallow walrus]

Yes

If you know the formula for the distance of a point from a line, you can find that middle small distance

Of the point from the line

[rigid mauve]

How so? I dont have 2 points only one

[hallow walrus]

Yeah

But you have a line

x+2y+1=0

[rigid mauve]

So it means I have to find the m of the perpendicular from the red function's m right?

[hallow walrus]

Okay yeah sure

You can do that

There’s a direct formula for that distance but I suppose you don’t know it

The way you’re doing it is how we derive the formula in general

So it’s fine

[rigid mauve]

d = square root of ..?

this one/

?

[hallow walrus]

No

That’s for the distance between two points

[hallow walrus]

Go along these lines

[rigid mauve]

alr

[hallow walrus]

Find the equation of that black line, then find the intersection of the black and red lines and finally find the distance between that intersection point and the Center of the circle

[hallow walrus]

How did you get M_oc=1?

[rigid mauve]

When something is perpendicular the m is going to be like switched and the opposite

[hallow walrus]

Yeah, but you didn’t do it correctly

You divide by -1/2, not by -1

[rigid mauve]

wdym

the m of AB is -1 right?

-1 switched and opposite is 1

theres like a formula that I followed =
-1/mAB

[hallow walrus]

m of AB is -1/2, like you found out in the line just above that

[rigid mauve]

No hahaha its just that I had to divide it by 2 because it was 2y

[hallow walrus]

Yeah, which is what makes the slope -1/2 as opposed to -1…

[rigid mauve]

Ohhhh

correct

mb

let me just re calculate it rlq

ty

[hallow walrus]

Yes that’s correct

Now find point C

[rigid mauve]

by their intersection

one sec bro

[hallow walrus]

Correct

[hallow walrus]

Yeah that looks good

Now just find OC

[rigid mauve]

Ohh I think I have figured it out, its a 30, 60, 90 triangle, if I do a distance of oc, I can find the hypotenuse of the same triange as the rule says that oc is x and the hypotenuse is 2x

[hallow walrus]

Yeah something like that

Your r will be twice of OC

[rigid mauve]

And the hypotenuse is the radius which means that I just need to put the center dots to the circle equation and put the radius squared

yeah

ty bro

[hallow walrus]

Nw

If you don’t need any more help, just type .close

[rigid mauve]

.closre

.close

[full forum]

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Available help channel!

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[red finch]

hello frfr

[red finch]

If I forgor the way to solve it

like

$\sum^{27}_{k=1}\floor{\sqrt{109k}}$

[glossy valve]

Michael Jackson

[red finch]

is it not like $\sum^{27}_{k=1}\floor{\sqrt{109}\cdot\sqrt{k}}$

[glossy valve]

Michael Jackson

[red finch]

so evry time is it like for example for $\floor{\sqrt{109}\cdot\sqrt{2}}$

[glossy valve]

Michael Jackson

[red finch]

$\floor{\sqrt{109\cdot2}}$

[glossy valve]

Michael Jackson

[red finch]

so like

$\floor{\sqrt{218}}$

[glossy valve]

Michael Jackson

[red finch]

idk

where like

of 218

is like 14

and like $\floor{\sqrt{109\cdot3}}$

[glossy valve]

Michael Jackson

[red finch]

is

$\floor{\sqrt{327}}$

[glossy valve]

Michael Jackson

[red finch]

and like how do I know which is the closest square

fr

is it like 18

fr

oh can I look at like the tens

ye

and one would be 10

so it is like 10 14 18

so is like $\floor{\sqrt{109\cdot4}} 22$ fr

[glossy valve]

Michael Jackson

[red finch]

so is it like

idk fr

[civic storm]

where are u getting 22?

[red finch]

idk i haven't doneit yet

wait so it's like

of

436

so like

21

oh

no wait

20

[civic storm]

no

yes

floor basically chops off the decimal

ur rounding down 100 percent of the time

and only taking the integer component

[red finch]

what is a component fr

oh like from the square root

[civic storm]

no

[red finch]

so it's as many times as the number a hundred and as many times 9

so

[civic storm]

i meant part when i said component

a decimal is just a whole part with a fractional part

[red finch]

fr

[civic storm]

floor just gives you the largest integer less than or equal to your given input

[red finch]

so if the number times 9 makes the number needed to get to the next square then the number is more

[civic storm]

uh if you get to the next integer yes

[red finch]

ye I meant perfect square fr

and like at least that number

and for 5 it would be

wait what if I did all 27 fr

sisyphus time

it will be right

Ohh

so is like 5

$\floor{\sqrt{109\cdot5}}$

[glossy valve]

Michael Jackson

[red finch]

so like

$\floor{\sqrt{545}}$

[glossy valve]

Michael Jackson

[red finch]

and like

23

so it's like 10

14

18

20

23

every time we have the square root of something times 109

and like we gotta find the closest square root that isn't bigger than it

like of a perfect square

so like for 109 it would be 1 times 100

and 1 times 9

but like the closest next square after 100

but like the next closest square after 100

would be 121

like the pascal triangle fr

and we'd have more than or 121 if it was like

121*1

or over

and under 144

and for the second one

like

it would be 14

like the floor of (square root of 109 times square root of 2)

which would be

like the closest integer

that is not bigger than

that

fr

so we have of one times

then of 2 times

the floor

so the floor of the square root of 1 times the square root of that

and then of 2

and the floor is like

so how do I know where it rounds down

so first it's one times

so 10

then

does it like

increase gradually

[full forum]

@red finch Has your question been resolved?

[red finch]

how do you know what the numbers will be

so it would be like

10

14

18

20

[civic storm]

you just calculate

[red finch]

23

[civic storm]

not sure if there is a pattern

[red finch]

oh ok

google didn't say fr

[civic storm]

sometimes theres a pattern sometimes not

[red finch]

and I asked an ai and it said it wrong 12 times fr

or like something

idk

so like

we keep getting square root of 109 times something

so like of 25 it woukd be like

$\floor{\sqrt{25\cdot109}}$

[glossy valve]

Michael Jackson

[red finch]

so like $\floor{5\sqrt{109}}$

[glossy valve]

Michael Jackson

[red finch]

wait so now will like many people get pinged

if I ping helpers thing

fr

and many people will like see michael Jackson pinging them fr

<@&286206848099549185>

if I made it ghostping could they still see where it was from

<@&286206848099549185> can you read this message fr

[torn jolt]

Question ❓

[red finch]

yes

[red finch]

$\sum^{27}_{k=1}\floor{\sqrt{109k}}$

[glossy valve]

Michael Jackson

[red finch]

do you know how someone could know

what the others added could be

like the first are 10 14 18 20

and like

[torn jolt]

It's like from 1 to 23

Put in k

[red finch]

what do you mean

why not 27

[torn jolt]

Is that greatest integer function

[red finch]

idk

[torn jolt]

What is that brackets looking thing

[red finch]

oh

floor

[torn jolt]

So summation rt

[red finch]

what is rt

[torn jolt]

√109 +√109×2 +... √109×23

[red finch]

ye but like the floor of each

[torn jolt]

Right 🫡

[red finch]

but like the floor of each

[torn jolt]

Floor means less than or equal to integer

[red finch]

doesn't floor mean the biggest integer that is less than the number or equal to it

[torn jolt]

Like int - fractional part of int

[red finch]

yes

[torn jolt]

Ok

[red finch]

so do you know how someone could add the floors or like know which the numbers are

like

[torn jolt]

I think u need to use some trick or else this process will be very complex

Or u can use calculator

[red finch]

ye

the problem said no calculator

though

so evry time is it like for example for $\floor{\sqrt{109}\cdot\sqrt{2}}$

[glossy valve]

Michael Jackson

[red finch]

$\floor{\sqrt{109\cdot2}}$

[glossy valve]

Michael Jackson

[red finch]

$\floor{\sqrt{218}}$

[glossy valve]

Michael Jackson

[red finch]

and like $\floor{\sqrt{109\cdot3}}$

[glossy valve]

Michael Jackson

[red finch]

$\floor{\sqrt{327}}$

[glossy valve]

Michael Jackson

[red finch]

$\floor{\sqrt{109\cdot5}}$

[glossy valve]

Michael Jackson

[red finch]

$\floor{\sqrt{545}}$

[glossy valve]

Michael Jackson

[red finch]

and like for 4 like 20

[torn jolt]

I am figuring out if I can compile it in a graph

[red finch]

wait let's say ot was like up to 5

[torn jolt]

By using definite integral as a limit of sum

[red finch]

what do you mean

oh

[torn jolt]

It's basically just sum of square roots ×√109

[red finch]

ye

but like every time the floor

so like the closest integer not greater than the number

[torn jolt]

Yeah 😭

[red finch]

can someone like write it with hand in an image before sending it

like instead of using katex

latex

[torn jolt]

I thought it will form an ap

[red finch]

oh

[torn jolt]

But sadly it isn't

[red finch]

so I knew it was over 10 and under 11 because it was over 10² 109 and under 11²

fr

[torn jolt]

Is this University math btw

[red finch]

idk

[torn jolt]

Are u preparing for any exam

[red finch]

so how do we know between which numbers 218 or like 109×2 would be

[red finch]

no

wait does it matter how much above like 10² 109 is

cause for example

like square root of times 1

or like square root of 1

the 109

is like 10

so when it's floor of square root of 1 time it's ten

[torn jolt]

109 is a prime no. 🫠

[red finch]

yes

isn't it like

a super prime fr

and 27 a super prime too

[torn jolt]

I am not finding any method unless that calc thing

[red finch]

does it not matter how bigger than one hundred it is

cause like

[torn jolt]

That means u can't make it a constant in summation

[red finch]

what is a constant fr

like K

fr

[torn jolt]

It will get multiplied to further values and all other values added later

[red finch]

oh

[torn jolt]

From where u got this problem

[red finch]

so that I can't get another number from it and say like that it's always like 2 times something for example

idk someone sent it on a server

so like square root of 109 is square root of 100+9

but I can't seperate them

[torn jolt]

Yeah

[red finch]

Lx_|

so like Lx_|

would be like the closest not like bigger integer

and like floor of x times something

like Lyx_|

would not be Lx_|y

cause like

x could be 0.2

and for up to 4 times L_| would be the same

oh

[torn jolt]

What about subtract fractional part from integer

[red finch]

what does <> mean fr

oh

ye

[torn jolt]

It's the thing after decimal

[red finch]

how does someone find <>

though

and like would it be as easy to find of like $\sqrt{109\cdot x}$

[glossy valve]

Michael Jackson

[torn jolt]

√109 is also not an integer

[red finch]

ye

[torn jolt]

I think my brain died

[red finch]

idk but does it matter how much bigger than like 10² 109 is

cause liek

cause like

[torn jolt]

I don't think that matters

[red finch]

why though cause like

Lx_|

would be like the closest not like bigger integer

but

fr

like

[torn jolt]

Sandwitch theorem?

It will give an estimate but

[red finch]

Lyx_I would not be like yLx_I

oh

Can the estimate be wrong in the decimal part

integer part

part

can the estimate be wrong on the integer part

[red finch]

though

cause like for example

L0.2_I

could be 0

up to like L0.2×4_I

idk i think

right

but like

it would be 1 if it was L0.2×5_I

and up to 9 times

while 0.2 is like one fifth

and like 0.1

up to 1

it could go 9 times

[torn jolt]

The full answer is 967 enjoy

[red finch]

how do you know

[torn jolt]

I calculus

Calculated 🫠

[red finch]

with sandwich

oh

wait did you do all

no

oh with like calculator

how

[torn jolt]

Obviously calculator

[red finch]

so like the floor of 9,67 would be 9

is that related

[torn jolt]

Yup

Floor means the part before decimal

[red finch]

yes

[torn jolt]

The quotient only

I thought there would be some pattern, but there isn't any

[red finch]

what if there is a patter in how we find the sum

wait

the fifth number is 25

isn't it 23

idk

[torn jolt]

Yeah

So 967+23

Sorry for human error

🫡

I forgot the fifth one

[red finch]

fr sorry my device turn off

so like for example in 1.2 the decimal part is one fifth of 1

ye

fr

and the floor of (it times something)

is equal to the (floor of it) times something

untill 4

[torn jolt]

Remainder theorem

[red finch]

cause at 5 a number is made

[torn jolt]

Floor is just the quotient

[red finch]

what is the remainder theorem

fr

[torn jolt]

Q×Divisor + Remainder= Dividend

Basic division only

[red finch]

oh quotient is like the numbers Q

so like quotient is the integer part

ye

[torn jolt]

Like 1.2 = 12/10= 6/5=1+1/5

[red finch]

yes

[torn jolt]

Where 1 is your floor (before decimal)
And 1/5 is fractional part ( after decimal)

[red finch]

or like isn't it that 1.2=1+0.2 so like 1/(1/0.2)

+1

yes

[torn jolt]

1/5 is 0.2

[red finch]

yes

[torn jolt]

Same thing bro

[red finch]

ye that's what I said

[torn jolt]

Are u suspecting any pattern in this sequence?

[red finch]

so depending on the decimal part every something times the number there is a new number that gets created that gets added or like adds to the floor

so like when we do floor of (something times something)

[torn jolt]

Yup

But something should be whole number

[red finch]

so like since like $\sqrt{109k}$ could be like $\sqrt{109}\cdot\sqrt{k}$

[glossy valve]

Michael Jackson

[red finch]

oh ye

[torn jolt]

Yeah

[red finch]

or could it idk

wait but like in the start it's 10 14 18

so it's not like times an integer that is in every time

[torn jolt]

Bye bro , I am sleeping 😴

[red finch]

bye

[torn jolt]

U will be a mathematician someday🫡

[red finch]

no

[torn jolt]

Ok then

[red finch]

idk I will write the problem in the channel even though I won't find it

fr

oh

but could we know about where the decimal part in the number is

like does it matter if it's under something or over something

so like for example if it's bigger than one fifth and smaller than one sixth

idk idk anything

fr

so like if it was 1.1 it could be up to 9 times before it wasn't floor of 1 times the other

cause every some time another like one or fr like unit how it called gets to be from like the decimal part

[red finch]

@olive yoke

hello

fr

nickle nibbler

[olive yoke]

sup

[red finch]

oh the cieling is up

but wassdown

the floor

fr

[olive yoke]

alr resend the thing

[red finch]

$\sum^{x}_{a=1}\floor{\sqrt{y}\cdot\sqrt{a}}$

how

[olive yoke]

yeah cieling rounds up

[glossy valve]

Michael Jackson

[red finch]

ye but like floor rounds down

how

[olive yoke]

so like, 1.999 would round down to 1

[red finch]

what about 1.999...

[olive yoke]

yeah

that too

[red finch]

but if it was forever wouldn't it be 2

[olive yoke]

yea

[red finch]

but how do you do with product

[olive yoke]

every number less than 2 rounds down to 1

[red finch]

what about 0

[olive yoke]

idk about the product thing

[red finch]

0 is also less than 2

[olive yoke]

i dont think theres a formula for that sum

[red finch]

oh ok

[olive yoke]

u know what i mean

[red finch]

idk ye idk

do you know how someone could find

a formula

or how it called fr

$\mathbb{H}$

[glossy valve]

Michael Jackson

[red finch]

$\mathbb{Uwo}$

[glossy valve]

Michael Jackson

[red finch]

e

I mean

$\mathbb{W}$

[glossy valve]

Michael Jackson

[full forum]

@red finch Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

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• 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!

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[pearl oriole]

Hello, I need help with this question

[barren onyx]

which part do you need help with

[pearl oriole]

im kinda lost on every single one

i know how to find most but there is always 1 or 2 i get wrong but im not sure which

[barren onyx]

your answers are all correct except for that there is 1 horizontal asymptote (at y = 0)

for the function in question, the numerator is a constant 5, which is effectively a polynomial of degree 0

the denominator simplifies to -4x + 16, which is a polynomial of degree 1

[pearl oriole]

oh

[barren onyx]

if the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at y= 0

this is because as x approaches infinity, the denominator grows much faster than the numerator, making the value of the fraction approach zero

[pearl oriole]

i was confused because i wasnt sure if i had to use the degree of the number coefficient or the x value

thank you

can you help me with 1 more question please

[barren onyx]

sure

[pearl oriole]

i submtted this answer and it said it was incorrect

i put it into a graphing calculator but i cant find the x or y ints because of the asymptotes

[barren onyx]

i begin by simplifying the function:
$$f(x) = \frac{-4}{x + 1}$$

[glossy valve]

misha

[barren onyx]

vertical asymptotes occur where denominator of the simplified function is zero

here x + 1 = 0, so x = -1 is a vertical asymptote

you have it correct

next

the holes would be x = -4 and x = -3

you have that right too

[pearl oriole]

would the y coordinates of the holes be correct?

[barren onyx]

the degree of the numerator is 0, and the degree of the denominator is 1, therefore the horizontal asymptote is at y = 0

[barren onyx]

yes

and the y -intercept is at (0, -4)

you have the horizontal asymptote and y-intercept incorrect

[pearl oriole]

so there wouldn't be a x - intercept?

[barren onyx]

there wouldn't be x-intercepts because the simplified numerator is a constant (−4) and does not become zero at any point

[pearl oriole]

Thank you so much

I was stumped on those questions for a while

[full forum]

@pearl oriole Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

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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.

[torn jolt]

how do i do part d?

[torn jolt]

• the letters arent distinct, so its not a permutation
• the order matters (i think?) because different order of letters means different words

but now that i think about it, since letters arent distinct, there can be multiple instances of the same order of letters being counted more than once?

[full forum]

@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

.close

[full forum]

Channel closed

Closed by @abstract tendon

Use .reopen if this was a mistake.

[full forum]

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.

[dawn scaffold]

shouldnt the 1/3 be negative? since 1/3(-1^3)?

[lime jackal]

see -1 is in lower limit

so upperlimit - lower limit

hence -*- will become +

@dawn scaffold

[dawn scaffold]

so its like -[-1/3 -2]

[lime jackal]

yes

[dawn scaffold]

so then its just [1/3 +2]

ahh

i see

thanks!

.close

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[clever sequoia]

Suppose that the value:
σ = 1
μ = 0

How do I solve this definite integral

[analog raptor]

seems like an integral in the form of the gaussian integral

take the $\frac{1}{\sqrt{2\pi}}$ outside

[glossy valve]

math X meth ✓

[analog raptor]

simplifying the inside, it is $e^{\frac{-x^2}{2}}$

[glossy valve]

math X meth ✓

[analog raptor]

try a u sub maybe?

$u = \sqrt{2}x$

[glossy valve]

math X meth ✓

[analog raptor]

then simplify and solve