math-help

[mint vortex]

that leads to

Sqrt(2x)Sqrt(3/2 - x) and the derivative of sqrt(2x) is the derivative of (2x)^1/2

[prime minnow]

Sqrt(2x) can get cancelled out by dx = 2sqrt(x) du from u = sqrt(x)

[mint vortex]

But since 3/2 is an integer, then itd a square of sqrt(3/2) soooooo cant you just put that in sin^-1(u/a)

sqrt(3)/sqrt(2) = sqrt(3)sqrt(2)/2

Multiply by sqrt(2) on both sides

This simplifies further into sqrt(6)/2

[prime minnow]

I'm not sure about putting it into the sine part, that part's supposed to be the answer cuz I'm trying to get time from velocity and displacement using v=dx/dt

[gleaming kindle]

Hi

My name is Aryan, I very grateful to be a part of this community.

[ember garnet]

your final answer in the 3rd line is the same as the solution in the 1st line, so you did it correctly

[prime minnow]

I got someone else to explain to me 2/√2 = √2 :'I thank you anyway

[wanton crag]

Thank youuuu!! I figured it out that any nth root of x^n +- y^n works out, so the euclidean distance is a particular case

[vapid spruce]

can anyone help with this question?

I tried taking x^2 common from inside but it wasn't doing much help, so i just took x^4+1 = t^2 but it was getting to complicated. What do i do here?

I dont think multiplying by x inside will do much help either

[ember garnet]

if you need help with integrals try this https://www.integral-calculator.com/
it also has steps

[mint vortex]

either try u = x^2 and then substitute again for tan(x) , because 1 + tan^2 = sec^2 , or substitute u = x^2 and THEN sub again but this time for sinh

because sqrt(sinh^2(u) + 1) = sqrt(cosh^2(u)) = |cosh(u)|

where sinh is hyperbolic sin

[timid delta]

good ol days

integrals

[wanton crag]

Is anyone able to supply me a proof?

I actually don't know if it is or not a subspace, but I conjecture it is

[mint vortex]

That sounds kinda trivial tho

If you have that V is a vector space

Then proving that V is a subspace of the other sounds kinda trivial

A sum of real numbers is... real

[mint vortex]

a_n = a_(n + p) doesn't seem to change that fact in anyway

If a_n is real then it's sum with another real sequence will be a real sequence

[foggy torrent]

1< x<5; if X/r3 +Xr3 is an integer number, how many real numbers fit Х?

[gray veldt]

9?

[vapid spruce]

thanks dude

i realised it today

[plucky gale]

hehehe no problemm

[foggy torrent]

yeaaa !! how?

spent like 40 mins on this

[gray veldt]

they gave range right?

1<x<5

first multiply it with root 3

you will get another range

then again divide with root 3 u will get another

add them

[foggy torrent]

wow im dumb

damn

tysm!!!

[nocturne zodiac]

😭

[gray veldt]

Trolling?

If not then, send 4 to rhs after that divide the rhs with 3

[weak lotus]

I hope so xp

[nocturne zodiac]

yes

[mint vortex]

How to find/what's your way of finding a formula for a determinant on a general commutative ring F^(nxn) ?

[gray veldt]

....

[undone ledge]

Hi can I get some help with this question, I’m doing logarithms

[weak lotus]

I was thinking, if 2 limits are not the same then we say it's not riemann integrable. What method do we use then? Or just nothing?

[left knoll]

sin(220) = sin(180 + 40) = -sin40
sin(150) = sin(180 - 30) = sin30
cos(220) = sin(180 + 40) = -cos40
cos(-40) = cos40

(sin(220) + sin(150) + sin(40))/(cos(220) + cos(30) + cos(-40)) = (-sin(40) + sin(30) + sin(40))/(-cos40 + cos30 + cos40) = tan30 = 1/√3

[mint vortex]

What two limits are you talking about?

Generally a function is riemann integrable on a closed and bounded interval [a,b] whenever there exists an integral on it for that function, the integral exists if |S(f) - L| < e for any e > 0, where S(f) is a riemann sum of f

[weak lotus]

I know. Well what do we do if that is not the case. That's the question

[mint vortex]

What do you mean?

What is not the case?

[weak lotus]

If there is an e where fore |S(f) -L| <e is not true

What we do in that situation

[mint vortex]

If there is such an e , then L is not an integral of f on [a,b]

Also i simplified here, but the riemann sum S(f) is taken over a tagged partiton on [a,b] that satisfies the condition that it's norm is less than delta (just saying)

[mint vortex]

If there doesn't exist any L in R that would satisfy that condition then the integral of f , doesn't exist on [a,b] , thus the function is not riemann integrable

[mint vortex]

Eventually you could try checking different integrals

Maybe the one that uses darboux sums

I think its called riemann-stjeltjes integral

[undone ledge]

Thank you! :))

[foggy torrent]

thanks!

what should I do with cos795 here? I thought about finding diff between 795 and 720, but it's equal to 75. Idk if I can find cos75 (w/o calculator) or at least express it in other way

[spark vault]

810-15 maybe

[mild sluice]

how will you calculate cos810 and cos15???
I was thinking something along the idea of cos(720+75)
cos(720) = cos(2pi), and cos(2pi) = 1

[weak lotus]

That's what I needed. Ty so much for your time!

810 is 90 + 4pi and 15 is 45 -30 @mild sluice

[spark vault]

Like this

[left knoll]

cos(75) = cos(45 + 30) = cos45cos30 - sin45sin30

[foggy torrent]

yeaa makes sense thank yall !

[acoustic forge]

Gsce 2020, pls help, i'm going crazy over this one😵‍💫

[weak lotus]

B = E

So 100

That's about it I'm sure you can go from there

That's the only thing you need to see

[candid rivet]

Tangential angle in a circle gives you the angle FBC (40°)
In a cocylclical quadrilateral, opposites angles sum up to 180°, so DBF + DEF =180 (ie DBF=80)
Then you only need to use the fact that ABD+DBF+FBC=180

[fluid saffron]

Hi guys can i please get help with this

[acoustic forge]

Thank you so much!!

[vivid void]

Hi! I'm learning about measures of location and spread and i dont quite understand these equations... does anyone know what these mean or if you can give me a link to look at?

[solemn vessel]

It’s a little unclear to me what y and x bar are in these slides, but the concepts are simple. If you want to understand what these are saying, it can be very beneficial for you to use a calculator. Pick a function y(x) and then some constants c and graph them in your calculator as is shown

so say y(x) = x^2, for a nice simple example

test cases such as
Translated Sample: y(x) = x^2 + 5
Rescaled Sample: y(x) = 5x^2
… etc

once you play around with enough tests, you should gain the intuition needed to understand what’s going on

[candid rivet]

I guess x bar is the mean value of x1, x2, ..., xn. So equation 2.1 is just :
if yi=xi+c for i=1,...,n then : y bar = 1/n * sum yi = 1/n sum of (xi + c) = 1/n *sum of xi + 1/n sum of c = 1/n sum of xi + c = x bar + c

[summer kestrel]

https://forms.gle/rYAf8r76cmiH9WwaA

please answer the survey with 1 number

need 80 responses

1 question bruh

77 to go

[civic saddle]

This ain't opening

[summer kestrel]

how bruh

[civic saddle]

I keep getting back on discord

[summer kestrel]

wdym

[civic saddle]

When I open the link then the browser opens and then I get on discord 😕

[summer kestrel]

dam

idk man

[civic saddle]

I will try that on pc

[summer kestrel]

yea prolly works better their

there

[civic saddle]

Hmm

[vivid void]

@solemn vessel @candid rivet thank you both!

[hollow trail]

I need to memorize a bunch of equations by next Tuesday so are there any techniques for that

To memorize them

And also to memorize strategies related to the equations

[foggy torrent]

i got stuck

[ornate ocean]

well, you need to repeat as many times possible the equation and strategies

You can also write them many times until you memorize them

It is effective in a few days only

[steady vale]

Is it Turkish?

[hollow trail]

Alr thx man I’ll try that fs

[foggy torrent]

Yes

[vale wyvern]

I don't see another step

Is this the final answer?
Or is it rationalised somehow

[foggy torrent]

they gave ³R2 as an answer

im gonna ask my professor the other day, i think theres a mistale

[vale wyvern]

What does ³R2 means exactly?? 😅

[foggy torrent]

i meant this!

[vale wyvern]

There seems to be some mistake in the ques then

I calculated your expression with calc and it comes out to be 2.14........
Where as 2⅓ = 1.2599.........

[vale wyvern]

Isn't this too long?
Something this simple should be good for this ques

[vale wyvern]

@opal hare @somber yarrow

[opal hare]

Yeah, I just overcomplicate the solution🙇‍♂️

[somber yarrow]

@opal hare@vale wyvern thank you guys

[vale wyvern]

your welcome :)

[obtuse citrus]

hi i got a statistic question ://

"the following results were found in an experiment with a small sample size from a symmetric population:
136, 138, 138, 142, 144, 145, 145
Can we conclude that at 5% significance, the median is equal to 144? Give the p-value."

I calculated the mean and the stdev and got enough information to calculate the confidence interval at 95% and got [137.92;144.36]. With this I could conclude that yes, the median is equal to 144 at 5% significance. This is deemed correct by my answer key. To find the p-value, I calculated the t-test statistic and got -2.01. Looking at the distribution table, I thought the p-value would be little over 0.05, but apparently it's 0.156? I don't get how they calculated that..

[somber yarrow]

which book are you using

iam craving for these sums

[tawny kelp]

are the last two problems correct?

[vale wyvern]

you understand that Y output is giving out the price for x numbers of bracelets in the first one right
Y = 10X
This means the constant that should be added to this equation is the money she has already made,
In other words if Y is the total money made
And she has sold X number of bracelets after the mentioned 5 in the ques, total number of bracelets sold are (X + 5)
Therefore total money made, Y = 10 × (X + 5)
Y = 10X + 50

Same goes for the second question
You should write it as y = 3x + 42

So y = 3×(x + 14)
In other words, x + 14 number of goods sold for 3 / each price

[dire aurora]

How to evaluate this integral algebraically?

[loud kiln]

Try with the change of variables x = 2*sin z. It's trigonometric substitution

[candid rivet]

You can also see it geometrically

[dire aurora]

e^(1.5)-e^(-0.5)+e^(-1.5)-e^(0.5) Can someone please simplify this into one fraction?

[vestal wolf]

ı want to learn abıut calculus so before ı start to learn calculus where should ı begin

should ı start from algebra or just from functions?

and am ı have to know all about algebra to understand better calculus ?

[tiny spade]

I have a potentially dumb stoichiometry question

Starting with miles per gallon and calculating miles, you'd do the t chart like the one above

But, to calculate the opposite, how many gallons to go X miles, it's easiest to flip the chart essentially, right?

[timid delta]

30 mile = 1 gallon, 1 mile=1/30 gallon

60 mile = 60/3 gallon

2

[tiny spade]

Ya, I'm trying to figure out a simple way of explaining it to a younger sibling

[timid delta]

oh

[tiny spade]

But like, I'm making sure the way I explain is feels intuitive or flows right

[timid delta]

hmmm

a physical demonstration will be better

i feel like

just fill up a water bottle and compare it with the time it takes to get empty

and then you can compare with this?

[dawn blaze]

i don't know if it will help but a cross product is really simple to explain

im not sure if it work but it really easy to understand

[tiny spade]

It's been a little while since I used terms like that. Can you give an example of what you mean? 😅

I know how to do the math, but explaining it is a bit rough

[dawn blaze]

im not sure to understand the problem with gallon because im not english but like is it to run 30 mile you need 1 galon how much do you need for 60 miles

to run 30 miles you need 1 gallons how much gallon do you need to run a mile. its just a simple formula that we learn an then you apply it

you make a table where you put your value and then you make the cross

ping me if you didn't understand

i use this technique with my younger sister and they understand it

[tiny spade]

Ahhhh ok. That makes sense

I just wasn't sure if it was weird since I was thinking of the notation as 1/1gallon and that felt weird

Oh wait

I understand now why it goes the way it does

[tiny spade]

Wait. How would the miles measurement cancel out? I thought it would have to be somewhere below to cancel out

Wouldn't this lead to Miles^2/gallon?

[dawn blaze]

i don't understand what you mean

im pretty sure the awnser is correct

[tiny spade]

Oh, I didn't realize you were cross multiplying

Was on mobile and didn't see the full pic without opening

[dawn blaze]

ok no problem

[ember garnet]

For question 8, I think there is a typo. It would make more sense to solve it if the denominator was (pi -2x)³, otherwise the limit would be just zero.

so in that case, you need to apply L'Hopital's Rule three times, and final answer should be 1/16.

[potent rivet]

yea that's what I was thinking cause I was getting 0/-pi^3 which is 0

[potent rivet]

thank you 🙂

[ember garnet]

you're welcome :)

[delicate brook]

characterstic equation for this matrix

[potent rivet]

square matrix ?

[delicate brook]

yes

[proven salmon]

can someone help me with this problem? why is the answer 10 and not 20? if 2 of the classes can be picked out of the 5 then that means that the chance of the first course being picked is 1/5 then theres 4 left to be chosen from so 1/5 * 1/4 = 1/20

[ember garnet]

1/20 is the chance for the ordered pair

since the order in which they're chosen doesn't matter, you also need to add the chance for the other ordering (second course being chosen first, and first course being chosen second, which is also 1/20)

more simply, the number of different pairs of courses you can choose out of 5 would be 5 choose 2, which is 5!/(2!3!) = 10. So the chance of any pair being chosen is 1/10.

[proven salmon]

thank you for the explanation, my professor did not go over this during lexture so i dont exactly undersatnd but i get the gist of it

[ember garnet]

no problem :)

[urban narwhal]

could you please explain the step that i marked and also how they did the first 2 steps in case 2 please ? thank u

[cyan acorn]

can someone help me with this?

[urban narwhal]

Could u tell me why they did it ?

[pine mortar]

to isolate x

[candid rivet]

@cyan acorn

u_n is the number of seats of the (n-1)th row (and that's why I have to do minus 1 at the end)

You might prefer to do it with the sequence v_n defined by :
(i) v_1 = 145
(ii) v_(n+1) = v_n + 3
and then v_n is exactly the number of seats of the nth row, but you'll have to be careful when summing the terms of the sequence since v_0 is not defined

[candid rivet]

if a²> 1 then you only know that |a| > 1 (you can see it on the graph of the square function) which is the same as -1 < a < 1.
Remember that x²>c where c is a positive constant, does not imply x > sqrt(c) but implies |x| > sqrt(c).
The square root function is only defined for positive numbers ! Hence, a² > 1 => sqrt(a²) > sqrt(1)=1 and sqrt(a²) is positive and thus equal to ±a according to the sign of a

[candid rivet]

for case 2 i'm sorry i don't really understand what they are trying to do. Furthermore the use of "=>" implication arrow seems not really rigorous :/

[urban narwhal]

Oh ok , thank u 😄

[urban narwhal]

Cute cat btw

[candid rivet]

Cute guinea pig too ^^

[urban narwhal]

thx ^^

[olive glade]

If anyone is interested in helping

Please help 🙏

[vale wyvern]

What's the question?

Or should I say which one

[olive glade]

(3, -4)

Is it f(-4) = 3?

[ember garnet]

no, it's f(3) = -4

[cyan acorn]

thanks!

[torpid ember]

Can someone solve it and explain it to me pls

Answer is 64

Sorry for the bad pic

[vale wyvern]

Aakash? Hmmmm

So here you wanna make a 2×3 Matrix which means it will has a total of 6 number of places to fill
Now for each place you can either place 1 or -1 (which means 2 possibility)

So for 6 number of places
Total number of possibility are 2×2×2×2×2×2 = 64

[torpid ember]

@vale wyvern yes Aakash

Thank you master

[vale wyvern]

master?? You can call me bro :)
Your welcome

[solemn vessel]

refer to the “counting principle” for further explanation if needed, since i see it was already solved.

[sturdy rock]

summation of : 1 + i + i^2 + i^3 + ... + i^202 = ?
I got 3 different answers lol 😭 it's 4 am I spent soo long in this

[brisk hound]

Try 202/4

Follow the standard

[sturdy rock]

I did, i got i as the result

but I'm not sure

[brisk hound]

I think it’s correct

cus u get 1 + i - 1

[sturdy rock]

yup, chatgpt showed 1-i and -1 so I got really confused when I wanted to confirm the answer. Thank you!

[brisk hound]

that’s weird

U’re welcome!

[brisk hound]

did u write like this on chatgpt? cus so, it read like “ 1 + i + i^2 +i^3 + i^202”

that’s why it answered -1

[sturdy rock]

No i wrote ... before i^202, it just regenerated different responses

[weak lotus]

You can find an algorithm it's always something like that

Try mod

[torpid ember]

Thanks mate

[subtle sluice]

hi i need help with letter e. i have to add 50 beds to each public value and calculate for the measures of the public sample alone right? or is it for both private and public as one sample?

[brisk hound]

the last one u had to combining it, so I think it’s both private and public 🤔 but it’s really confusing

[tacit vine]

I’m very confused

[subtle sluice]

Yeah i just did both combined and public alone in case lmao

[undone ledge]

Could I get some help on question 13

I feel like it’s simple but im overthinking it ahhh

[crystal patio]

So it's asking for the length it covers in one sweep.
If you contextualise that (e.g redraw), the dusty area under the red dot is essentially a pie (sector), so its asking you for the arc length.
So you need to figure out the radius of the circle which the pie belongs to, and then apply the arc length formula.

Is all that sounding familiar?

[undone ledge]

L = angle times arduous?

Radius*

Hold on I’ll try again thank you @crystal patio

[crystal patio]

that's if the angle is given in radians. if they give it in degrees it is another formula

[delicate brook]

can someone help me find the characteristic equation of these two matrices

[sinful kernel]

|A-xI|=0
I is identity matrix
After getting a equation in x, substitute A as x
You'll get the eqn

[paper mortar]

can anyone help me understand the disk washer and shell methods? Calculus II.

[vale wyvern]

What do you mean by "getting a equation in x"
Can you explain a little

[tacit vine]

fake

[left knoll]

do i just use math tutorials till ik how to do it

[untold comet]

Send a problem that you struggle with

[left knoll]

im not in school yet i just dont know shit

im to smart bro i dont need this

[untold comet]

oh okay

[pulsar turret]

When we have a negative exponent, we must make the base a fraction (so if you have a^-1 then you should make it 1/a^n).

Why can’t we just leave it to a negative exponent?

[solemn vessel]

you can write it however is most useful for you. it is not wrong to write it either way

[vale wyvern]

Bro can you remove this @unreal plaza

[undone ledge]

Could I get some help for question 13?and 14 and 15.. is it to do with ambiguous triangles?

[stable oracle]

hey can anyone help with finding the solution to the nth term of this sequence? Im having trouble with the alternating zeroes

[delicate brook]

can someone solve this and send

[delicate brook]

thanks

[candid rivet]

i'm thinking of |cos(npi/2)| to get a 0 when n is even, and 1 when n is odd
Hence:
a_n = |cos(npi/2)|((n+4)/2) / ((n+6)/2)) = |cos(npi/2)|*(n+4)/(n+6)

[candid rivet]

15. if cos(x)=A then since cos²(x)+sin²(x)=1=A²+sin²(x) it implies that sin²(x)=1-A². Furthermore, the cos function is 2pi-periodic, so cos(2pi+x)=cos(x). Hence the value is A+1-A², where A is sqrt(3)/2

[candid rivet]

14. If sin(a)=sin(b) then a=b (mod 2pi) or a=pi-b (mod 2pi) ie a=b +2kpi or a=pi-b + 2kpi for all integers k.
    Here we have sin(x)=-sqrt(3)/2=sin(-pi/3), so x=-pi/3 +2kpi or x=pi - (-pi/3) +2kpi. Now since we want the solutions x to be between 0 and 2pi, we get x=-pi/3+21pi=5pi/6 (only k=1 works) or x=4pi/3 +20pi = 4pi/3 (only k=0 works)

[candid rivet]

13. Here the best thing is to see it on a drawing. Draw the trigonometric circle, with one angle (small preferably so it will be easier to see the formulas) (if you dont know what is the trigonometric circle go look a video on what it is). Ok now let's go one by one :
    A. sin(pi-x) isnt equal to -sin(x) (because it is equal to sin(x) ), so False
    B. cos works, True
    C. tan(pi-x)=sin(pi-x)/cos(pi-x)=sin(x)/-cos(x)=-tan(x). Moreover, we know tan is odd so -tan(-x)=tan(x) =-(-tan(x)) = - cos(pi-x) so the second property isnt verified by the tan function. False
    D. sin( (pi-x)/2) = sin(pi/2 - x/2) = cos(x/2) which obviously is different than -sin(x/2) so fist property isnt verified. False
    E. tan(2(pi-x))=tan(2pi - 2x) = tan(-2x) because tan is pi-periodic. And tan is an odd function so tan(-2x)=-tan(2x) so the first property is verified. However -tan(2x) isnt equal to -tan(-2x)=tan(2x) so the second property isnt verified. False

the alpha angle is a bit too large here, it's better to have it really small (it will make it easier to distinguish between if a value is equal to sin(alpha) (very small then) or cos(alpha) (value close to the radius of the circle)

Hope i didn't get anything wrong guys 🙂

[candid rivet]

Al Kashi theoreme in the ADC triangle gives you AC which is also equal to AB. Then Al Kashi again in triangle ABD gives you x. Tell me if you want me to explain it more in details (:

[sharp cradle]

Calc

[sharp cradle]

i got it

[dense wigeon]

why is one degree in Italy not the same as one degree in Scotland? The centrifugal force of the earth which causes it to be shaped like a mandarin orange.

[true drum]

translate in english

[true drum]

@left knoll

Factorize it and over

Was bored. Take another method too

[true drum]

No thanks for this I see

I wouldn't even thank myself lol

[outer kettle]

C mi?

[true drum]

the answer of this is 0 right?

[whole bluff]

Can some one help me out with a)? I've been at this for way too long

[candid rivet]

you have u_0=1m =1 and u_(n+1)=e×u_n (geometric sequence) hence u_n=e^n
then you have to do the infinite sum of the u_n which equals to 1/(1-e) since 0<e<1

[whole bluff]

Yes I've gotten this far, but I thought you needed a certain figure? Or is 1/(1-e) the answer to this question?

[sonic trench]

It's so joever man

[candid rivet]

yep i think its just 1/(1-e)

[whole bluff]

That's a bit silly

But anyways thank you, I was really doubting myself

[true drum]

it's (1,infinite)

[vocal hull]

Anyone help with c?

[true drum]

take lcm, power 6 meaning ((----)^3)^2
Do the cube part first, you are left with 4 terms now.
(..+..+..+..)^2
do it by
((..+..)+(..+..))^2
again factorize it and you will get the answer

[lilac vigil]

pls someone help, how can absoluteValue(x) = -x (These are my teachers notes)

[pulsar turret]

I solved this equation by writing the radicals as rational exponents but for the second last step — don’t we need the bases to be the same in order to add the powers?

[solemn vessel]

in both terms, the base is x

[pulsar turret]

God, I should get some sleep

Thanks though 🍻

[solemn vessel]

No problem, have a good night. Cool handwriting, by the way

[left knoll]

Help! I think one of my formulas is wrong can someone correct me plz !

[vale wyvern]

In 24th,
2 sinA cosB = sin(A + B) + sin(A - B)

[vale wyvern]

What the power of n in the numerator?

[weak lotus]

What i would do is work out the integral and look for trigonometric identitys

Some integrals are just trail and error

[true drum]

What sorcery is this

[undone ledge]

Hi can I get some help with question 13 a)
What does it mean by double it? I know how to show it being reflected but idk what it means when it says it’s doubled…

Thanks to whoever helps 🙂

[vale wyvern]

So here it says the period of a function y = 2sinx -1 gets doubled

First,
Period means after minimum of x the graph repeats itself
For example in y = sin x, value of y are same for these values of x (0, 2π) (2π, 4π) (4π, 6π) and so on...

Here the period of eqn
y = 2 sinx - 1 is 2π (theres a method to find it, not writing here as it has many points)
You can check it on desmos

So doubling the periodicity means modifing something in the previous eqn so it's periodicity becomes 4π,

I already know what you should do for it so.. eqn comes out to be,
y = 2sin(x/2) - 1
Be sure to check it out on desmos to understand

This is the periodicity part
Then you have to modify the eqn to get a mirror image along y axis, since you asked about periodicity here it is, If you want further answer just MSG here

[tranquil adder]

Hey guys I got this equation that I’m just not understanding in the point the says (2-1) square root 2 so we subtract 2 and 1 so we have 1 left square root it by 2 you will have 2 but then the 2 is gone that’s my teacher explanation that I haven’t mange to understand

[surreal cypress]

The original question should be the following. Find the equation of a parabola that has a vertex (1,3) and goes through point (2,5).

Equation of a parabola in vertext form is
y = a(x-x₀)²+y₀, where
(x₀,y₀) - coordinates of the vertex
a - coefficient…(x₀, y₀) = (1,3)
x₀ = 1
y₀=3

y = a(x-1)²+3
if x=2, then y=5
5 = a(2-1)²+3
5 = a + 3
a = 2
the equation of the parabola is
y = 2(x-1)²+3

[tranquil adder]

Than you so much @surreal cypress for helping me I really appreciate it god please you.

[undone ledge]

Ohhhhhhhhh okay ahahahah thank you 🙏🏽

[left knoll]

Can someone help .
I'm stuck and don't know how to solve

This one also

LDE means linear differential equation

[vale wyvern]

Your welcome :)

You basically multiply the integrating factor to whole equation
So you left out to multiply in RHS, so the eqn becomes

(x + 1)y/e^x = integral[(x+1)^(x+1) dx + c ]

[left knoll]

It's hard to understand can you write it on a paper

[vale wyvern]

Basically final eqn comes out to be

[frozen tundra]

Can anyone please help me solve these 🙏🏽🙏🏽🙏🏽

[vale wyvern]

Not sure why denominator becomes zero at last, so it becomes un defined
But basically you get a value of c (from the given y(1) = -1) and put it into the last equation to find a eqn of x and y

Can you check once more if the condition given is correct or not
talking about y(1) = -1

For 17 ↑

[vale wyvern]

For 18th

Just lemme know if you want how I did the integral part
I mean how I did from marked equation 1 to next step

[cunning oasis]

can someone help me on why non-linear operator does not have inverse?

[dawn flower]

Hey guys i need a book or whatever to understand probability theory , i can't understand it at all . Thank you in advance

[proper venture]

Is limit infinity or what

[ember perch]

Could anyone help me with these? Ignore the answers I already circled, they’re probably wrong 😭

[vale wyvern]

10.D Correct
11. E
You wrote the correct equation,
5x + 5a = 5x + xa
5a = xa
x = 5

12. E correct

13. E
    Just substracte both the equation,
    (3x + 2y + 2z) - (3x + y + z) = 19 - 14
    y + z = 5

14. A
    You formed correct values for price of boat for each group, ques is just asking it's difference,
    x/3 - x/4 = x/12

15. A correct

16. B
    Here the graph is just moved up in y axis so you add 1 to f(x)

[vale wyvern]

17. B
    So the shaded quadrilateral angles will have a sum of 360 and the other 2 angles other than x and y will be same as it's a regular polygon so (let it be m)
    2m + x + y = 360
    2m + 80 = 360
    2m = 280
    x = 140

Angle and no of polygon formula
140 = (n-2)180/n

Solving for n,
n = 9

18. D Correct (a hint, in these type of questions it's better to calculate each option and then compare, it's easier)

19. C
    So here it says it's 1 foot for each unit in vertical axis
    And difference in 3 pm and 4pm is 2 y units which means 2 foot,

Now let at 3 pm the water was at x foot, it decreased by 10% which means
10% of x = 2 foot
x/10 = 2
x = 20

Which means 20 foot water at 3 pm and as it decreases by 2 foot in 4 pm it becomes 18

20. D Correct

[ember perch]

Thank you 😍

[brisk hound]

Can someone please explain how the (x^2 + y^2) + x(x^2 *- y^2) turned into (x^2 + y^2 + x)?

[ember garnet]

It didn't. Look at the whole expression. They took out (x² - y²) as a common factor.

[brisk hound]

Thank you!

[turbid spire]

can anybody help me with this problem?

[river tree]

Can somebody help me with this. I can't get to the answer. I tried many times still not able to.

Please help!!!

=tex if a+b+c =0 then the value of {a^2(b+c)+b^2(c+a)+c^2(a+b)} / abc is?

[river tree]

Ooh thank you!
Here's the one that my friend helped me with...

[ancient prawn]

is this a typo

[ember garnet]

no

[ancient prawn]

Nvm I figured it out

Factor 🥰

[mental widget]

lol anyone wanna tutor me from the basics

im 20 with math at like a 3rd grade level😭 if anyone wants to be a teacher i would be a good practice student LOL

[untold comet]

Can someone help me with alegbra 2

[weary arrow]

Post your questions here and you're more likely to get help

[hexed stump]

Post your questions here

hi everyone, i’m looking for the boundaries of this integral. I think 1 to 4-x would be correct but i’m not sure. Anyone can help me? thanks

I’m trying to integrate the red triangle

[vale wyvern]

Is it necessary to solve it this way?

Can't you just write the equation for the red line, then integret it for 0 to 3 and subtract the integral of yellow line from 0 to 3

Or the other way
Integrat the equation from y axis from 1 to 4

[hexed stump]

I dont think so, it's a multi-variable integrate

[hexed stump]

yes it is necessary

[ember garnet]

yes, it's 1 to 4-x

[hexed stump]

well thanks!

[vale wyvern]

Oh okay
that's some high level s

[woven mirage]

help me evaluate this please

[limpid crane]

1/2 ?

[woven mirage]

the answer is -1

But i dont know how to do it

[ember garnet]

I find it is -1/2

[woven mirage]

Can you show how to do it?

[ember garnet]

you have to take 2x-y as a common factor in the numerator

so it cancels out with the denominator

[woven mirage]

I can’t find a common factor from the denominator, what did i do wrong

I mean in the numerator

[ember garnet]

you can force it by dividing each term by it

but you can also make it appear

leave the denominator as is and multiply the parentheses by y/y and x/x which are 1 so it doesn't change anything and pass the numerators inside the parentheses

[mental widget]

i will! i will start preparing for my placement test soon and its all algebra 1 stuff lol so when i post pls dont make fun of me lol

[ornate monolith]

everyone has to start somewhere 🙂

[mental widget]

yeah im doing sociology and compsci i dont know how you guys do all this math stuff my brain always feels like its going to explode

[hexed stump]

well definitely i feel the same

[swift lark]

i love all 3 of these subjects, feel free to @ if u want help w/ anything

[weak lotus]

That writing 🥰😍

[stark dune]

ayee multivariable calculus

[bright pecan]

Hi guys!! Can anyone here help how to do this? Thank youuu

[shy rapids]

make circles for all categories

and then you will see

did you try that ?

[shy rapids]

....

[bright pecan]

I see thank you so much!

[clever plinth]

Does anyone know why this data set Q1 is not 64 and Q3 is not 73.5?

[solemn vessel]

this is incorrect

all cats are furry

your picture shows SOME cats are furry

[shy rapids]

This sais not all cats

[solemn vessel]

The first statement is "All cats are furry"

[shy rapids]

Hmm wait

All cats are furry but not all furry are cats

So there can be a category of furry and spotty

Right

Furry could mean and does mea something other than cats

Sorry misread the original qn in a hurry

How is this

[shy rapids]

Am I right ?

Furryneed not mean cats it's just a category

[solemn vessel]

cats must be furry. some cats are spotty. a cat that is spotty is also furry, by definition of cat. ie, there are cats that are spotty and furry which means that some furry are spotty

[atomic ravine]

What happened here

[true drum]

sum of AP is given by
n/2*(a+l)
a is the first number, l is the last number.
There is a proof of this theorem too, If you wanna watch.

[atomic ravine]

Damn it bruv thanks man

I just forgot it

Ur a real G

[agile whale]

Hi

Could someone explain this one thing to me

I have to prove that all m = Z values in
(m + 7)^4 - (m-9)^4 can be divided by 16

[true drum]

Can be done using factorization.
Use the formula for (m+7)^2*(m+7)^2 and same with (m-9)^4 too,factorize it, the m^4 from both side will cut each other.
Take 16 common from there, if all have integer coefficient, proved

[median sail]

BRO
FRЕЕ GIFТ DISСОRD NIТRO - https://cutt.us/w6v38

[amber vapor]

consider convergence:

please help me im depressed with this :((

[dire mason]

please help me to find the limit

[dreamy grove]

anyone have tips on how to solve integrals ?
i have all the formulas and theorems down but really confused on how to approach problems

[left knoll]

Help me

The ans is r=b(1-cos theta )

[wise phoenix]

a=?
b=?
c=?

[jade creek]

what class is this

[left knoll]

Uni 1 year

[jade creek]

calc 2?

[left knoll]

DE&C

[jade creek]

sorry what course

oh differential equations

i’m taking ODE right now

is that the same thing

[left knoll]

Can you tell me where I messed up?

[jade creek]

maybe

i’ll try

did u differentiate wrong?

here you can just multiply by d theta

and then it’s separable

[left knoll]

?

[jade creek]

multiply by d theta on both sides

dØ

from where I circled

[left knoll]

Oh shit you are right , I have spent more than 30 min trying to figure out where I went wrong
Thanks buddy ❤️

[coral scarab]

Could anyone help me prove that T-I is not invertable?

[true drum]

a=10(total numbers), b=5, c= 275(Sum)

[wise phoenix]

Thank you

[left knoll]

How he got a= 2

[dreamy grove]

he added the 2 eq
-a + b = -5
and 3a+b = 3

[left knoll]

💀lol sorry thanks

[hazy moth]

Given the radius of a circle, calculate the area of the triangle that circumscribes the circle (triangle outside).

help me plsssssss

:c

[vestal peak]

what is this asking me to find

this is gr 12 btw

like i use remainder theorem and the b values are diff

[vestal peak]

what does it want me to do****

[ember garnet]

divide the equilateral triangle into six equal right triangles. Each one of them is a 30°-60°-90° right triangle and if you know one side you can find the rest by trigonometry. This image shows the side lengths in a 30°-60°-90° triangle. x would be the radius.

[vestal peak]

how can i find the remainder using remainder theorem if i dont know b

[ember garnet]

you will find the two remainders in terms of b and set them equal

[hazy moth]

I don't understand it very well :CC

[vestal peak]

im dumb i just found the remainders now lol

how do i find a value that can be used by both x-2 and x+1?

[ember garnet]

you can't, for x-2 it's x=2 and for x+1 it's x=-1, find the two remainders using these values as per the remainder theorem

[vestal peak]

just looked at the solution i was just supposed to do f(2)=f(-1) and evaluate that way

[hazy moth]

THANK UUUUUUU

:3333

[ember garnet]

yeah that's what I meant by set them equal

[hazy moth]

And last little question, how do I find the height?

D:

[ember garnet]

for each of the right triangles the height can be either one of the two perpendicular sides, one of them is R and the other is R*sqrt(3)

[hazy moth]

do you mean the small triangle or the one that circumscribes the circle?

[ember garnet]

the small

the big one will be 6 times the small in area

[hazy moth]

thank uu

❤️

[ember garnet]

no problem :)

[left knoll]

if Set A and B are independent and Set B and C are independent, does that make A and C independent?]

[weak lotus]

💀

Fr?

[old thunder]

I solved it

[hexed stump]

No

[atomic ravine]

Why does multiply the selection of girls with boys it is not related like

[gray veldt]

you are taking cases here so you should multiply as they mentioned consisting of 2 girls

[shadow kite]

Some help please in French

[ember garnet]

If n is even (pair), then A = 4. If n is odd (impair) then A = 0.

[shadow kite]

Tnx

[old thunder]

Could someone write the Σ of this one?

[vale wyvern]

you already wrote it yourself,
the last term

[muted grail]

^

[vale wyvern]

so it's
Σ n×2^(n)

[muted grail]

nx 2^(n) * @vale wyvern

[vale wyvern]

um yea I just wrote the same thing? no?

better?

[muted grail]

nono, its using the variable x

[vale wyvern]

it's multiplication bro

[muted grail]

its addition homie

[vale wyvern]

lol

[muted grail]

(1x 2^1) + (2x 2^2) + ...

[vale wyvern]

exactly and that in the middle is × not x

I mean multiplication not x

[muted grail]

honestly it looks like its using the variable x and then it addition, so not multiplication to me

[old thunder]

yee that's what I did so S1= Σ 1×2=2

[vale wyvern]

na bro, it's multiplication see ↑

[vale wyvern]

yep

[left knoll]

For the first two, it is asking to determine whether the given number is a solution to the equation

It has been a bit, so I am struggling a little bit with remember how to do these properlt

properly

[weary arrow]

Since they are not asking for the solution, just asking if the given number is correct, you don't have to solve it. Just set x = 26 (for the first one), and then see if both sides become the same number

For 127 we need more information, how does age correlate with heart rate? I'm assuming that info is given somewhere

[ivory dust]

helloooo i need help defining a sequence explicitly

i did it but i'm not sure if it is correct, so i just want to see if my answer works

[left knoll]

@weary arrow sorry for the confusion, but there is no use of specific age, they just want a formula model with the specifics in the problem, they dont need a answer but how it would look trying to solve it I believe?

[weary arrow]

So there is a correlation between age and maximum heart rate - its strange its not mentioned in the problem. But its something like 200 - age IIRC.
So the formula would be something like:
H(a)= 9/10 * (200-a)
Very odd there's no mention of the correlation?

It might be 200- how much older than 16 you are or something, I'd Google the specifics of that

[left knoll]

yeah for some reason not at all it is a very strange problem and sounds good thank you : )

[warm raptor]

After solving this equation, I plugged it into the calculator and got 36. I thought I must have expanded the logarithms wrong but then I realized that my biggest problem was the last step when I multiplied and added everything together getting 6.3. Apparently if I did (.3+.3+3) * (10), I would have gotten 36. What did I do wrong and how can I avoid this mistake from happening? This happens to me a lot in math, that last step I would end up adding and multiplying in the wrong order.

[weary arrow]

Is it that you're struggling to remember the order of operations?

[warm raptor]

yeah but if I do follow order of operations wouldn't it be (10*.3) + (.3+3)?

That would equal 6.6

if I followed the order of operations, I should be multiplying first rather than adding and then multiplying later

[weary arrow]

Nah you forgot to add parentheses

Since it's 10 * log(4) + 3, when you expand the log It becomes 10*(log(2) + log(2)) + 3

I'm not sure how you got 36 though

My calculator gets 9

[ember garnet]

@warm raptor and you made the same mistake earlier when you broke 4 and 10^3 apart, fix these two and you'll get ~36

[weary arrow]

Where do you see 10^3?

[ember garnet]

step 4 and 5

[weary arrow]

Oh I thought that was from a different assignment

I was only looking at step 6 I thought the numbers were exercise numbers lol

[warm raptor]

@weary arrow I put the parentheses around +3 as well. My logic hear is that I have to represent log (410^3) at its exact form so log(10^3) which is equal to 3 must be included in order to express the proper value of log(410^3) .

4*10

[weary arrow]

I didn't read the whole question so you can ignore what I said

[warm raptor]

Alright, thanks for the help

Another question lol. I know I messed up at step 4 where i subtracted 10^6-1. I know I can expand 10^6 as 110^6/210^1 but where would I go from there? I thought it could be 1/2 * 10^5 but that isn't equivalent to 5,000,000, what exponent rule am i missing here? Most of my old equations always canceled out because they had the same coefficient.

110 is really 1*10^6

and 210 is 2*10^1

nvm, i guess i should have but parentheses over the numerator and denominator

[untold comet]

can someone help me understand what this asking for

[ember garnet]

I guess it means to write a linear equation in the form y = Ax + B where y represents the amount of water in the pool in gallons and x represents the minutes that the pump has been working.

[untold comet]

I checked the answer key and it said the Linear Model was (y = -50x + 1000) which doesn't make sense to me

[ember garnet]

yeah that's right, -50 is rate of change of water in the pool in gallons per minute and 1000 is the initial amount of water in the pool in gallons

[untold comet]

Ohh I see, thank you !

[left knoll]

yo anyone here who got AP CALCULUS BC? i need to ask some questions

[left knoll]

im struggling on my last hw problem a little bit

[ember garnet]

what exactly are you struggling with?

[left knoll]

would it be 3/100 ? 4/5 + 1/2

the question mark is where im confused I feel like im having brain fog and I know its simple but what do I do between the 3/100 and 4/5

@ember garnet

[ember garnet]

You have to use the formula. What do you think x should be in the first part of the exercise?

[left knoll]

8/10?

[ember garnet]

x is the number of years after 2000. So for 2010 x would be 10.

[left knoll]

ohh I see, so 3/100 10, + 1/2

[ember garnet]

yes and the answer from the model would indeed be 8/10

[left knoll]

ohhhh I see now thank you : )

[ember garnet]

you're welcome :)

[worldly dome]

can someone explain why:

(p->q ) ^ (q ->p) == notp iff notq (idk how to type it)

[gray veldt]

try using a truth table

[left knoll]

Can anyone check the calculations

[candid rivet]

looks good to me

however (i might be wrong) i feel like to calculate the average velocity you have to calculate the integral

[sly sandal]

I cant figure this out, can someone help please?

ive tried all of these

isnt it just when f(x) is decreasing

[ember garnet]

did you try [4,12]?

[left knoll]

Average velocity is the the quotient of total distance travelled ÷ in how many seconds

[left knoll]

Thanks

[worldly dome]

i got (p -> (r -> q)) ^ (p ^ notr) -> q
can someone double check

[candid rivet]

i got the same

exercice 2 you forgot to divide epsilon by 8 "since n>N> epsilon"

except that this is really good well done !

[vale wyvern]

bro Idk why I saw this
but you might have to rename the file name before submitting
cuz I thought you sending something..... uhm.....
I mean I thought you trolling or something

then I read "real analysis"
and was like ooh okay

someone else might get the wrong idea ykyk

might as well rename the file before hand

[ember garnet]

it's a non-constant periodic function, the limit at infinity doesn't exist

[sharp thicket]

Change the variable x with 1/x ->0 but the same problem

[ember garnet]

change the variable everywhere? that's equivalent to the original problem but with x -> 0. Then the limit is 1.

[sharp thicket]

But 1/sinx --> infinity

[ember garnet]

yes and the parenthesis is 1 so 1^inf = 1

[sharp thicket]

Thanks

[ember garnet]

no problem

[sharp thicket]

It's not 1

Cause if x->infinity
X=1/x so X ->0
x=1/X
Same problem

[ember garnet]

wasn't sure how exactly you wanted to change variable but if it's the same problem then again the limit doesn't exist

[bold atlas]

can we add subtract the same value in limits of integrations? considering the range we add/sub the func is continous and differentiable?

[left knoll]

Are they correct?

[ember garnet]

how did you do c?

[left knoll]

At max height velocity is 0

So it's basically 0.5gt²

The initial velocity determines how long it goes up for

[ember garnet]

but your answer seems to be independent of the initial velocity.

[left knoll]

It's -16t²

And initial velocity determines t

[ember garnet]

you should plug it in then and write the answer in terms of v0

Also you should keep v0*t in the equation for the height, v0 is a constant, not zero

[left knoll]

V is only constant if its horizontal velocity

But is vertical

And V has to be 0 otherwise its not max height

And t can't be 0 as max height is reached after a certain amount of time

I don't get why Vo is constant

[ember garnet]

because it's the initial velocity

also how can the max height be negative?

[left knoll]

Why initial velocity is constant

[left knoll]

Because max height is a displacement

And displacement is a vector quantity

It can either negative or positive value depending on which way is positive

If upwards is positive downwards is negative

Vice versa

[ember garnet]

because it is the initial velocity, it's the velocity it had at time = 0, it cannot change, it is a given data

[left knoll]

Do you know the formulas?

S= ut+ 1/2at²
V = u+at

When calculating displacement

U is 0

At max height

If U didn't change then the ball would continue going upwards for eternity

Okay so

I think I was incorrect

You were right

But bro your reasoning was stupid that's why i had trouble believing what you were saying

[ember garnet]

these are the formulas

[left knoll]

I have to use v² = u²+2as

[left knoll]

Same stuff

Different notation

[ember garnet]

you just plug in t=Vo/32 in equation 3, or in equation 4, but a is negative here, so either case you will get a positive max height, as you should

you can also use eq. 5 with a being negative again

[left knoll]

The sign doesn't really matter

It just indicates direction

Anyways thanks!

[ember garnet]

well when it says upwards it usually means positive, so it also implies that Vo is positive

and anyways your answer for max height has to be in terms of the given data, which is Vo, not in terms of time which is a variable

[left knoll]

well it didnt specify that it has to be in terms of Vo

[ember garnet]

max height is Vo^2/64

[left knoll]

but okay

[left knoll]

yep

[ember garnet]

it has to be a constant answer, not one that depends on time, that's all

[left knoll]

Okay

[sharp thicket]

but m not sure if this limit exist or no

[ember garnet]

@sharp thicket

[fringe hare]

hi guys im new here, i might have an idea for this problem

we studied it just last week

its called the comparison solution

we simply try to do the limitaion for every cos(x) and sin(x)

to make the final form

we start with this: -1 <= sin(x) <= 1

[fading glade]

Anyone can solve it???

[fading glade]

If it ….. find …..Words in Arabic

[fading glade]

@fringe hare @ember garnet
@left knoll

???

I want a solution quickly...please 🥹

[left knoll]

im literally too tired and irritated

[vale wyvern]

trying..

[white venture]

please transtlate to english

i could help

[fading glade]

Arabic words are not important …if …find

[vale wyvern]

Google translate literally translates it to "for god"

[fading glade]

Forget the translation 😂

[vale wyvern]

I think we gotta find dy/dx for the eqn given

[fading glade]

There is a question and a want dy/dx

[vale wyvern]

mhm

[fading glade]

Yes

[white venture]

change it to (2x/y)^1/2 or st like that

[fading glade]

Oh
It's hard on my keyboard

Is there something unclear?

[vale wyvern]

answer d option

[fading glade]

Can you solve it on paper? 🥹🥹🥹🙏🙏🙏

[vale wyvern]

telling sorry beforehand cuz of my crappy handwriting

[vale wyvern]

wait

fk

missed squaring the 2 on the RHS

[fading glade]

Where is dy/dx

?

I want to know how you arrived at the final answer

[vale wyvern]

wait, I did a Lil mistake

[fading glade]

Ok

[vale wyvern]

@fading glade
first step is just taking common √2 from every term
then...

[white venture]

damn i forgot that arabic read from right to left :)))

[fading glade]

@white venture @vale wyvern
The answer d or c ??

[vale wyvern]

d

you can't understand my solution?

is it too badly written?

[fading glade]

No haha

It's not mine it's my brother's 😂

I will show it to him

[white venture]

neither do i

[vale wyvern]

oh okay

[vale wyvern]

my handwriting or what have I done?

[white venture]

this part

[vale wyvern]

btw in the last step you can just show

x= y
diff wrt to x,
1 = dy/dx

[vale wyvern]

this is called the chain rule in differentiation,
basically to write differentiation in one go, don't have to assume or take stuff and substitute and do all those thing

[vale wyvern]

@white venture you can do it this way too

[white venture]

=)))) i do this in the different way

[vale wyvern]

yep I already sent the exact thing here ↑

[white venture]

i confused about what dy/dx is

then i realize that i've studied this before

[vale wyvern]

mhm
its basically differentiation of y with respect to x

[white venture]

yeah

in vietnamese we call it Đạo Hàm

[vale wyvern]

Hàm like a hamburger?

oh my jokes it's right at lowest

[white venture]

yup

hàm mean function

[white venture]

this is the math we leart at 2nd year in college

a must-do thing to get a D

[vale wyvern]

hmm,
double intergration

its so much time I have last studied it damn

[white venture]

and triple intergration

me too

i passed and i forgot all about it

[vale wyvern]

happens to everyone ig hahah lol

[white venture]

[thin hamlet]

any help in the first question

[clever haven]

The angle DCB is half of DAB, because they see the same circular sector in the circumference. But it is half, because the angle DCB is an inscribed angle, and DAB is the angle of the center.
So the answer to fist question is 58º.

[thin hamlet]

big thanks my friend

[leaden token]

Hi everybody, is there a website where i can find math exercices for 12th grade

[left knoll]

hi, need math help

[clever haven]

You're welcome

[clever haven]

What's the question?

[autumn crown]

where's the physics's help channel?😭

[supple flint]

when is james ever going to stream again...

[dim pawn]

=tex \int_{a}^{b} x^2 dx

where to use maths bot////

=tex \a

[left knoll]

Can anyone help with this one?

[dim pawn]

aayo do u know how to use the bot///

[left knoll]

Naa dude

Is there a bot for these stuff?

[scenic falcon]

@left knoll

sub L back into initial equation to find h at the original state where the ladder is up the wall

[clever haven]

I did in this way:

And the result approximately to the ladder is: 17,76
And to the height is: 12.07

Using the equation system with tg.
And Pythagorean theorem at end

[eager palm]

Can someone tell me how you get that? (the app wants me to pay money for an explanation) I don't get where the 1/3 comes from...
When I do the linear factorization I get 1/(x-2) + 1/(x-5) and nothing more

[vale wyvern]

here

[eager palm]

Thanks, I get what you did but now I don’t get why one has to do it this way. Is there a rule for this kind of linear factorization?

[vale wyvern]

basically, we want to make a term which is actually integration allowed, we know the formula for integral of 1/x
so we try to turn the equation from 1/x² to 1/x basically

here you cant integrate 1/x² is cuz you have got a constant and x term with it too

[eager palm]

I get it now:) 🙏 thank you for the help

[vale wyvern]

You're welcome

[crude river]

this might sound dumb, but if a number with the power of 2 is always positive, then why is the graphic function look like this? (fx=-x^2)

isnt it suppose to be like the other way around?

[ember garnet]

x^2 is positive, but -x^2 is negative

[crude river]

how.
if lets say there -2^2. its 4 right?

since it cancelled each other

[ember garnet]

in this function, it is only x that has the exponent

[ember garnet]

it's a good idea to put parentheses to be sure. (-2)^2 is 4 but -2^2 is -4 in a calculator

[crude river]

ahh...intresting

[crude river]

just checked it, shieee ur right. thanks man

[ember garnet]

no problem

[broken ermine]

Hi, does anyone know what 'M' means here? I understand that 'inf' stands for infimum, but I don't get what's the question asked

[ember garnet]

M is a point on the graph C. The question asks what is the minimum distance between the graph and the point O.

[broken ermine]

oh i see, thank you.

[undone ledge]

Hi can I get some help with graphing y=4X^3-12x^2+12x
I factorised it to help get x intercepts
0=4x(x^2-3x+3)
So one x intercept would be 0
But what do I do about the (x^2-3x+3)?

[terse adder]

Hi! Who can help with the task? He decided on K based on mathematical formulas, then for some reason he does not accept it.
Let 𝑋 be a random variable such that 𝐸(𝑋)=3, 𝑠𝑑(𝑋)=4 , and let 𝑌be a r.v. such that 𝐸(𝑌)=1, 𝑠𝑑(𝑌)=2.
𝑋 and 𝑌are not linearly independent, and 𝑐𝑜𝑟𝑟(𝑋,𝑌)=0.5.
a)What is 𝑠𝑑(4𝑋+2𝑌+2)? Round your answer to two decimal places
b)What is 𝑠𝑑(3𝑋−3𝑌−5)? Round your answer to two decimal places.
can send my code

[candid rivet]

This polynomial is always strictly positive hence the only real solution is 0
Maybe try to have a look at the derivative, try to search if there are local minimum/maximum (f'(x)=0), try to see if the function is odd/even, the limits at ±infinity

[atomic ravine]

This two are different identities in vector rt

They why does Sir breaks modulus of |a+2b|^2 like as if it's (a+2b)^2

[atomic ravine]

Yo boys

Why is it

Theta cos inverse one by root three
Instead of cos inverse one by root 26

[limpid tiger]

anyone good with linear optimization and tryna help me with my hw xd

[graceful oracle]

If𝑓(𝑥−3)=𝑥2 +2𝑥+3,find𝑓(1).

@everyone @here please what’s the answer to this question

[ember shoal]

27

[fringe hare]

19

?

f(4-3)=f(1)

[vale wyvern]

It's f(x-3) = x² + 2x + 3

27 is the correct answer

[abstract cipher]

in that case yeah

[sinful copper]

anyone valo rn need one for 5 stalk

[calm quartz]

a

how did they rewrite and simplify this?

[vale wyvern]

the just took the LCM,
to note here in last second equation, the first term has only (√s +7) in denominator whereas in second term it has (√s + 7)²

[rancid olive]

Can someone help me with this? It's confusing me.

[wanton crag]

Does someone have some sort of textbook or any kind of stuff about asymptotic analysis?

Not on the Computer Science side, but more towards math and Real Analysis

Like to study the convergence of series or sequences by using big-O and little-o notation

[vale wyvern]

what is your doubt in this?

[vital oar]

hi can anyone help me with this?

[ember garnet]

Yes, the volume is V = pi r^2 h and the area of the can is the curved surface area plus two times the base so A = 2 pi rh + 2 pi r^2.
Now, you want the volume to be constant, so you can write h in terms of r and it will be h = V/(pi r^2).
Then you can plug that in the formula for area so we have A = 2V/r + 2 pi r^2.
So you need to find the value of r for which A will be minimum, so calculate the derivative dA/dr and by setting it equal to zero, so dA/dr = 0, you will find the value of r for which A will have a minimum (you will substitute V = 355 at this point). You can then calculate h from that and you're done.

[undone ledge]

Ohhhhhh right thank you 🙂

[crude acorn]

Yo can someone explain how the answer isn't 23317 for the weighted answer? I should be using the corect formula and everything

[vast prawn]

hey guys does this logic make sense?

f: B -> C and g: A -> B are one-to-one

To show (f o g) is one-to-one, choose any z∈C and find some x1, x2 ∈ A such that (f o g)(x1) (= z) = (f o g)(x2) and x1=x2, or there does not exist an x ∈ A which satisfies (f o g)(x) = z.

Assume that there are x1,x2 ∈ A. g(x1) = g(x2)
=> f(g(x1)) = f(g(x2)) (one-to-one)
=> (f o g)(x1) (= z) = (f o g)(x2)
=> x1 = x2

Suppose there exists no x ∈ A which satisfies (f o g)(x) = z
=> there is no g(x) ∈ B so that f(g(x)) = z
=> there is no x ∈ A so that g(x) = y

if not, is this version better?

f: B -> C and g: A -> B are one-to-one

To show (f o g) is one-to-one, choose any z∈C and find some x1, x2 ∈ A such that (f o g)(x1) (= z) = (f o g)(x2) and x1=x2, or there does not exist an x ∈ A which satisfies (f o g)(x) = z.

Suppose there exists no x ∈ A which satisfies (f o g)(x) = z
=> there is no g(x) ∈ B so that f(g(x)) = z
=> there is no x ∈ A so that g(x) = y

Given z, assume there are inverse images g(x1),g(x2) ∈ B so that f(g(x1)) = z and f(g(x2)) = z
=> g(x1) = g(x2) as f is injective

For any y ∈ B, there is x1,x2 ∈ A so that g(x1) = y and g(x2) = y
=> x1 = x2 as g is injective

Take (f o g)(x1) = (f o g)(x2) => f(g(x1)) = f(g(x2)) => x1 = x2

[vital oar]

Thank u sm!!

[candid rivet]

2nd version is good, yet i don't see the point of working on the case if there exists no x in A which satisfies f(g(x))=z i think it is not needed

[vast prawn]

oh I see. I was hoping to include the point that injective functions don't always have a inverse image. is that not necessary?

also tysm for looking at it!

[candid rivet]

f is injective if and only if f(x)=f(y) => x=y
Have a good day !

[vast prawn]

ah gotcha thx!

[cloud edge]

Help, I don't know how to solve it

It equals:
A. 1
B. 4
C. 3
D. 2

[candid rivet]

Basically you use the properties of the log function, and recognise that it is of the forme x²+y²+2xy which equals (x+y)². For these kind of problems try to always rewrite the terms with the smaller integers (which are the prime numbers) possible inside the log

[cloud edge]

Thank you!!!

[sour sandal]

does someone wanna help me with these pls

[split orchid]

can someone help me

[undone ledge]

Hi does anyone know how do to question 1 🙂

[gentle trellis]

take e^x as some variable t , then find roots of that quadratic t(t-9)=0 , its clear that roots are 0 and 9 , and then equate e^x=0,9 , we'd neglect the 0 case , cuz it would give -inf as answer , which is not considered a root

[gentle trellis]

try applying l'hopital rule , most of them can be done through that

[brisk scroll]

Just take e^x-9=0 ,e^x=9 and apply natural log on both sides therefore the equation now will be ln(e^x)=ln9 which is equal to x=ln 3^2 which is indeed x=2*ln(3)

[supple island]

e^x=0 is just impossible, you can't say it's true for x=-inf because x=-inf doesn't mean anything
you can say that the limit for x->-inf of e^x is 0

[gentle trellis]

yea ofc we'd take limit here 😐 , its obvious

[supple island]

it's not and that's not what you said

[gentle trellis]

😭 man wtf , aight you win lmao

[supple island]

not trying to win anything, just try to be as precise as you can when giving an explanation, i know you get the gist on how it works, but the people you're explaining to might not

[brisk scroll]

Demn

[leaden token]

can anyone help pls

[flat magnet]

HEEEEEEEEEEEEEEEEELP!!!!!!!!!!!!!!

@here

does it become "n+2" or what?

[mental lodge]

idk

[warped adder]

Pls help

[fresh oxide]

wish i could help, just started studying the subject

[coral kite]

(n + 1)! * (n+1)

[warped adder]

It’s ok guys I gave up

Prof lets us choose other ones

[flat magnet]

I ain't sure if this helps

@warped adder

[gentle trellis]

what exactly do we have to do here?

[gentle trellis]

what do we even need to find here? - just that the question isn't clear to me

just curious

like do we have to convert this into some telescopic series? and find an's last - simplified expression ?

and if you do have solution , then please share

[fresh oxide]

Just uses sums, and you have to solve it. Been 1 year since I’ve really studied it. But I’m touching base on it again and I would have a proper answer by the end of this year

[gentle trellis]

okay man ! , thanks a lot

[left knoll]

Anyone??

Got this in ig

[warped adder]

That’s the thing I think I’m suppose to find the general solution but I don’t really even understand what that means but I’m just dropping this for now I spent way too much time on that one question

[ember garnet]

8 m

[fresh oxide]

He is correct, but I'd rather help you understand than just get the answer. So first we know with the green cube that the ratio of the shadow is 2/3 and we know that the red one has a 6m shadow on the ground and another shadow that is parallel. So we can calculate the first part by using the previous ratio to get the unknown x in x/6. Idk if you know that you can place them side by side and do as follows:

Which gives you 4. Then we know that the other parallel shadow is 4m and since it is parallel, we do not need to apply any calculations. We add the two lengths and we get 4+4=8

[candid rivet]

can someone help me with this integral.
I've checked that it is equal to pi/2^(p+1)
I tried to find a recurrence relation by doing twice an integration by parts but it seems to not work and it is werid to do it twice since i'd like to show that J_p = J_(p-1) / 2

[gentle trellis]

did you find the relation through by-parts?

i did find it through that but i first tried to find the indefinite integral of the whole term , which i tried by applying by-parts twice - but i got a weird expression , from which the final answer would arrive to be 0 , can't attach my solution rn but i took cos(px) as second function first and did byparts again in the second integral formed , keeping sinpx as first function , and final integral came out to be (cos^(p)x.sin(px))/p

and for proving the reccurance relation , just expand cos(p-1)x term in Jp-1 and take byparts of the second term (sin one)

[gentle trellis]

ik i am most probably doing some silly ass mistake in my solution

[candid rivet]

No, I haven't

[gentle trellis]

wait lemme just attach the solution , gimme a min

i hope the handwriting in understandable 💀

[candid rivet]

ohh thank you so much that is smart !

[candid rivet]

Totally fine don't worry haha

[vivid void]

Hi! To anyone who knows some stats, I'm currently learning sampling distribution. It's mentioned that for a large enough n, the sampling distribution is approximately normal. How does the distribution exactly get normal? Does anyone know a video i can check or something for this?

[left knoll]

Yea dude i missed the height part.... thanks🫂

[fresh oxide]

welcome, i hope you understood

[left knoll]

Yup

[tepid umbra]

Help please!

We want to measure a tower in front of which a stream runs (and we don't want to get wet). From a certain distance we see the highest point of the tower at an angle of 43 degrees. Moving 12 meters away the angle is reduced to 35 degrees. Find the height of the tower

[vale wyvern]

@tepid umbra this might the first time I am helping someone using maths in real life lol

[weak lotus]

using equivalent triangles is also a good option

or the triangle inequality

[stark raven]

hey any one there pass the discrete mathematics for cs student?
i have some qs in logical p q r and subtrees

[peak field]

hello

i need help with a maths proof question please

if x is rational and y is rational; and square root(y) is irrational and square root(x) is irrational. prove that square root(x) + square root(y) is irrational

[fringe hare]

this is chatgpt's answer here

[undone ledge]

a particle has a constant acceleration of 12m/s/s. if the particle has a velocity of 2m/s and is 3 meters from the origin after 5 seconds, find its displacement after 10 seconds

could i get some help with the question above.. i have been stuck on it for a while now..

[supple island]

use the equation of motion for constant acceleration
x=x0+vt+1/2at^2
subsitute the first time (5seconds) to find x0 and then you can substitute the 2nd to find the final displacement

[worldly copper]

Hi, can someone help me solve this for x= 2m pi

[quasi bridge]

if x = 2mπ (m * (2π)) then cos(x) = 1 as cos(2π) = 1.

on opening the summation,
1/2 + (cos(2mπ) + cos(4mπ) + ... n times)
1/2 + (1 + 1 + ... n times)
1/2 + n = (2n + 1)/2

[worldly copper]

Oh my god yes!!! I see it now

Thank you so so much

[quasi bridge]

you're welcome!

[worldly copper]

[ebon osprey]

Hello i need help with this problem please

[undone ledge]

Thank you 🙏🏽

Could I get some guidance on question 4, do I use the normal volume formula for this shape? Or.. I’m a bit confused..

[quasi bridge]

for the first part,
TSA of cylinder = 2πr(h + r) = 8π
r(h + r) = 4
h = (4/r) - r

for the second part,
V = πr²h
V = πr²((4/r) - r) = 4πr - πr³

for the third part,
differentiate V = 4πr - πr³ with respect to r

for the fourth part,
after finding dV/dr, equate it to 0 and find the values of r (you'll get two values of r). the sign of double derivate at that points can be used to tell whether those points are maxima or minima

[wanton sierra]

Can anybody tell me how to improve in math
I lack in every corner
Like ratio and proportion question,algebra,surds and exponents
My basic is not clear

[supple island]

using the angle and the radius of the big circle, calculate the radius of the disk. now you can get both circumferences and the answer becomes easy

[long belfry]

same here

[long belfry]

yep got i t

[long belfry]

no other way but to actually start with basics

[wanton sierra]

which basics

i dont know where to start also

[long belfry]

Start from where u dont know

Prolly go to khan academy math

[undone ledge]

Thank you so much that cleared up a lot 🙏🏽

[worldly dome]

Problem: Determine those integers n for which (7n-4)/6 and (5n + 1)/4 are also integers

so i understand that for the two expressions to have integer quotients, their remainders need to be 0
but idk where to go from there

[vale wyvern]

hello, do you still need any help?

if you still do here.....

a little rare answer, but the answer is no integer 'n' can make both the expression an integer at the same time

lemme know if I did any mistakes

[worldly dome]

Ah i see thanks for the help

[frosty tinsel]

can someone explain how the answer is 0 please?

[solemn vessel]

Use a calculator, and keep multiplying 2/3 by itself, youll see that the numbers get smaller and smaller

you can also think of (2/3)^x as 2^x/3^x... looking at it this way, the denominator will get larger than the numerator faster, and so the whole thing goes to 0

[sharp thicket]

help

[gentle trellis]

-1?

just divide numerator and denominator by root x

num will give -1 and rest terms would become 0 , and in denominator , it will give 1 and rest will become zero

[silk cedar]

can someone explain what's happening in here?

[worldly copper]

Hello can someone help me analyse this depending on alpha

[quasi bridge]

they've used the following identity

cos2x = 1 - 2sin²(x)
so, 2sin²(x) = 1 - cos2x

so, 4sin²((π/4) - (a/2)) = 2 * [2sin((π - 2a)/4)]² = 2 * (1 - cos((π/2) - a)

cos((π/2) - a) = sin(a)

[quasi bridge]

can you elaborate what do you mean by "analyse"?

[silk cedar]

thank you so much!!! :))

[worldly copper]

Depending on alpha what happens with the sequence. I have to solve it with mathematical induction in intervals for alpha

I must determine if the sequence is convergent in the interval for alpha and if there is a limit

[floral valve]

Hi, can anyone explain the term Recurrence relations for me ?

Im learning Discrete Mathematics and cant even know what it is after searching and reading it definition.

Or u can just solve this one for me, so i can understand from that.

[candid rivet]

@floral valve
if you call p_n the number of permutations of a set with ne elements, you want to find a relation of the form p_(n+1)= f( p_n ) where f is a certain function.
(Actually it can be harder sometimes where the relations is of the form g( p_(n+1) )=f( p_n ) but that's a bit rare). Hence if you know the value of p_0, then you can calculate the value of p_1 (p_1= f( p_0) and then you can calculate p_2 , then p_3 etc... so you kind of know the value of every p_n

1. a) if you know p_n, you want to calculate p_(n+1), meaning you add a (n+1)th element to the set. Let's now build the permutation of this new set of n+1 elements.
   •the first element : you choose its image ie n+1 choices
   •the n other elements : it just becomes a permutation of n th elements ie p_n choices
   Thus, we have : p_(n+1)= (n+1) × p_n

2. b) Now to be able to calculate every p_n , we just need to know the first valu of the sequence ( which is p_0) . If you have zero element, there's only one permutation possible
   (or you can start the sequence with the term p_1 if p_0 doesn't make too much sense) (the number of permutations of 1 element is obviously 1) so p_1=1. Or we know that for every integer n p_(n+1)=p_n. Frome there you have to guess the value of p_n and prove your guess by induction
   (here you calculate the first 4 terms maybe and guess that p_n = n!, then prove this by induction)
   Tell me if you still need explanation !

[echo thunder]

anyone good with Euclidean geometry?

[wheat laurel]

Hi are anyone here can give me some references about "weighted homogeneous polynomial "

[worldly copper]

Hello, can someone please help me with this: Depending on a, investigate the convergence and find the limit of the recurrent series.

[candid rivet]

have you already found some things or nothing ?

we know that if (a_n) converges then its limit has to be one of the roots of the polynomial 4X²-5X+1 which are 1 and 1/4

then we should graph the function f(x)=(4x²+1)/5 (and y=x) to guess for what alpha does the sequence converges

sorry i'm not really good with this

maybe for alpha in a certain interval you can show that the sequence is monotone and bounded , thus convergent ie its limit exist and is 1 or 1/4

[strong stump]

can somebody help me lol. Im not really sure how to do part c.

physics btw

[stable hull]

anyone knows how to change floating point numbers to binary ones

i know how to do it befor comma cuz its normal

but after comma its weird ting

[quasi bridge]

for the 1st part,
average acceleration = (final velocity - initial velocity)/total time
so it'd be (15 - 30)/6 = -15/6 = -2.5 m/s² (the -ve sign indicates retardation)

for the 2nd part,
s = ut + (1/2)at²
in this case,
u = 30 m/s
t = 6 s
a = -2.5 m/s²

[strong stump]

🙏 thank you

[fringe hare]

you keep multiplying by 2 until you find 0 + fractional part, in this example we converted 0.9 to binary:

u only take the integer part from above

[left knoll]

Can someone help with 6th

[left knoll]

ping me when answering

[left knoll]

<@&942391219206647828>

[blissful ridge]

I need to simplify this expression and the topic is inverse Matrix

Could someone help me step by step? Today was the first time i heared about this and the solution key is not helping me

[sly parrot]

Hey guys, I'm studying math again after a long time. I finished my bachelor's in English and I'm currently working in marketing. I'm looking to transition to a data analytics career. And so I've taken a course, currently we're doing things like linear algebra, calculus, logarithmic functions and more. I'm finding it hard to understand the math because I haven't done it in a while. Do you guys have any recommendations on youtube or elsewhere where I can understand the math better?