math-help

[ember garnet]

yeah it's -4

[dusty current]

yess b is def -4

[soft plover]

Yep I got B=-4

[dusty current]

thankyouuu

[dusty current]

howd you get the 3s in P(1) and P(2)?

[ember garnet]

it's the binomial coefficient. It's how many ways you can choose k objects from n objects.

[dusty current]

ahh okay thankss againn

[ember garnet]

you're welcome

[soft plover]

Anyone can explain 6b

[ember garnet]

It's based on this rule. Integration by parts.

[soft plover]

i tried but didnt get the answer

i ended up in a endless loop

[ember garnet]

The anti-derivative of cos(2theta) is 1/2*sin(2theta). The solution looks right to me. Where is the issue with yours?

[soft plover]

I started with this

[ember garnet]

You only need to do integration by parts to find the integral of theta * cos2theta. After that, you just split the integral in question to the sum of two integrals, 1/2 * theta and 7/2 * theta * cos2theta.

[soft plover]

Like this?

I do a level math and I haven't seen spliting integrals like this before

[ember garnet]

Yes that is correct. Well you don't have to split them but it's easier to see it like that. You can just distribute the theta and keep the two terms inside the same integral but you'll still find their antiderivatives separately. Same thing either way.

[soft plover]

i got it now, thank you so much 😁

[ember garnet]

You're welcome :)

[quasi vale]

my smol brain can't workout how they simplified this

[white sinew]

(-2x)^2=4x^2, you have 2 in the denominator, so you are left with 2 as coefficient

[soft lintel]

Can someone pls tell me how did we come up with this formula Xn=A^nX0

Is it something that I should conclude from the equations or is it some kind of general formula ?

[cinder yacht]

X(n+1) = A X(n)

from this one formula
u can conclude the stuff u circled in red

each time they replace X(..) by AX(.. - 1)

[soft lintel]

Thank you . It worked 🙂 👌

[urban willow]

i hate math

[candid heron]

Hey i need help

[candid heron]

Why the derivative of (x-5) is (x-5)²/2

And not x²/2+5x

[candid heron]

Like this one

I cant figure out why they are differently intregrated 🥲

[ember garnet]

You mean the antiderivative, right? They differ by a constant number, so when you evaluate the definite integral they both give the same answer.

[candid heron]

So if theres a constant number is shouldn't do like (3x²+2)²/2?

@ember garnet @ember garnet @ember garnet

Or is it the same🙄

Tnx in advance

[ember garnet]

No, I didn't mean that constant number. Think about if you were calculating the indefinite integral of x-5. You would say it is x²/2 - 5x + c where c can be any constant number. Alternatively, you could set u = x-5 and since du=dx the integral becomes \int u du which is u²/2 + c. Then substitute x-5 back to it, you get (x-5)²/2 + c. If you expand it, you get x²/2 - 5x + 12.5 + c but 12.5 + c is also any constant number so it's the same as x²/2 - 5x + c.

[dusty parcel]

that was such a beautiful answer

[ember garnet]

thank you :)

[left knoll]

Sameeeeeeeee

[soft plover]

Anyone know hot to do part (c)

[solemn vessel]

first derivative?

idk lol that’s my guess

[soft plover]

They ended up with 3500(1.035)^t ln(1.035)

[tacit crane]

heeelp :c, i know its A) but how do you end up with the result? like.. just visually? lOL

[wispy blaze]

Well we know it can’t be B

[ember garnet]

It is known that sin 30° = 1/2.
Consider the right triangle OMP. The sine of the angle at P (30°) is equal to the opposite over the hypotenuse, so sin 30° = OM/OP -> 1/2 = 2/(2+NP) -> NP = 2

[tacit crane]

THANK YOU : ) , didnt think of considering OP as 2+NP, i thought it would be more complicated than that lmaoo

[ember garnet]

You're welcome :)

[delicate cave]

use intersecting chords theorem or intersecting secant theorem

[fallen galleon]

i looked at the other responses but I think the simplest way is just set up the equation of sin(30) = 2 / x

solve for x (hypotenuse) and subtract the known length of 2

its an iteration of what iamphysics did but i think it makes more sense instead of doing 2+np conceptually

[soft plover]

anyone know how 2u/1+u changed to 2(1-1/+u) for part (b)

[ember garnet]

add and subtract 2 from the numerator
2u/(1+u) = (2u+2-2)/(1+u) = [2(u+1) - 2]/(1+u) = 2(1+u)/(1+u) - 2/(1+u) = 2 - 2/(1+u) = 2[1 - 1/(1+u)]

[soft plover]

How I'm I meant to know I need to add and subtract 2

[ember garnet]

I feel you. I was there once.
You're not really meant to know that, it's basically a trick. But you can see why you would do that in an attempt to simplify the integrand into simpler terms of which you know the antiderivatives.

[soft plover]

ah okay

there's no other methods?

[ember garnet]

you could also set w = 1 + u

[supple island]

the thing you're supposed to ask yourself here is: if i add something can this give me a simpler form to work with?
for example if we have x²-2x we can add and subtract 1 to obtain x²-2x+1-1, which is (x-1)²-1. this is very useful if you're working with a fraction or even better an exponential

like if you want to do the integral of e^(x²+2x) you can instead do the integral of 1/e(e^y²) where y=x-1

[soft plover]

ah okay thank you

[cinder yacht]

2u/(u+1) = 2(u+1 - 1)/(u+1)

[warped wren]

uiii

[cinder yacht]

the way to know what to add & subtract is to force the appearance of "u+1" in the nominator

[warped wren]

hello everyone im from vietnam

[tight rain]

how would i begin this question? pls and thank you

[supple island]

find how to express the gradient

then substitute with the given values

[tight rain]

differentiate?

[supple island]

sure, but why? what's the gradient?

[tight rain]

isnt the gradient of a curve whatever you get from differentiating?

[supple island]

more or less yes but that isn't a great way to say it, differentiating here is correct, but i think you should look up the actual definition

[tight rain]

okay, thank you

[wispy blaze]

Can I get some help pls

[ember garnet]

congruent means they have the same size

you can figure out the side lengths by subtracting the respective coordinates

[grizzled owl]

given that

prove that for n+1

help me pleasee

[fierce spear]

how can i solve this 😣

[stable dew]

here's a hint: you can split the first integral into the sum of two integrals: (integral of f(x) from 0 to 2) + (integral of f(x) from 2 to 8)

[left knoll]

idc about the answer (as ik what that is) how do i work it out as in what is the reasoning

and this one as well please

[delicate cave]

B
(alpha + R cos (theta), beta + R sin (theta))
this is the generation expression for any point on the circumference of a circle with centre (alpha, beta) and R = radius

[delicate cave]

balance components in X and Y direction

[left knoll]

thats wrong btw

[left knoll]

could you expand pls?

[fierce spear]

thank youuu 🤝🏼😎

[delicate cave]

then what's correct?

[left knoll]

C

[supple island]

do the diagrams of the forces that act in horizontal axis and the ones in the vertical axis

then you'll get another equation for the vertical

[left knoll]

but how do i find f1

[supple island]

2 equations 2 variables

[left knoll]

oh so simultaneous?

[supple island]

i mean, all forces are acting at the same time

[left knoll]

no no i meant do i solve with simultaneous equations

acc nvm no

u wouldnt do that

[supple island]

?

you do a system with horizontal and vertical forces

of course they are simultaeous

they are acting at the same time

[left knoll]

im ngl im confused

can you walk me through solving this question

[supple island]

what are the forces on the horizontal axis?

[left knoll]

f1 and 10

[supple island]

not only those, we have horizonal components for both F2 and 3

[left knoll]

oh ok ok yea

[supple island]

so can you write the diagram of the forces on the horizontal axis (as in the equation)?

[left knoll]

yes

[supple island]

do it then

[left knoll]

how many am i meant to have

i have two

[supple island]

show me

[supple island]

no, not really, on the left we have F1, horizontal component of F2 and horizontal of 3. on the right we have 10

[left knoll]

oh

[soft lintel]

I know it's a silly question but how did we get to the second line ?

I tried using the formula of cos(a+b) and i found this :cos(wt)cos(φ)+ isin(wt)isin(φ) but I cannot figure out how to find the exponential function

[supple island]

euler formula

e^(it)=cos(t)+isin(t)

[soft lintel]

But if I use what i found there are other terms aside from cos(t)+isin(t)

should I factor out smthg ?

[supple island]

true but what you do in this case is that you write e^it and you only consider the real part

you can also do this if you're integrating z in a symmetric interval, cuz sin is an odd function

[soft lintel]

You mean cos(t)=e^(it)-isin(t)

[supple island]

i mean Re(e^it)=cos(t)

you write a exponential becaus exponentials are much easier to treat than sinusoidals

like in electromagnetism and generally when we talk about waves we do this a lot

[soft lintel]

Ok. I'll try using that thank you : )

[supple island]

thing is: we just say z=cos(t) and z=e^it.
and we know that we will only consider the real parts

[soft lintel]

Does that mean that ie^it=sin(t) ?

[supple island]

it means Im(e^it)=isin(t)

[soft lintel]

Ok thanks

@supple island That technique turned out to be fast and easy thank you : )

[mellow mica]

Final Review, I forgot how to do any of this😭 final is tmrw too

[stray totem]

If a piecewise function is continuous, but doesn't have the same gradient at the point where they 'intersect' then it isn't differentiable right? Even if it looks like a smooth continuous curve?

[supple island]

correct

[stray totem]

Thanks - then for this question b should not be differentiable right? The thing is, the answer said that it was and so I was wondering if there were potentially a few anomalies.

[supple island]

it is differentiable at x=0

[cinder yacht]

it is differentiable at x=2*

[supple island]

also in x=0

[stray totem]

Wait I think I misread the question entirely whoops

[cinder yacht]

yea

but wasn't the question

[supple island]

ah right

mb

[stray totem]

But how so at zero (that was what I had initially calculated)? Aren't the gradients different?

[stray totem]

And yep you're right thanks

[cinder yacht]

the gradients have same value when x->0

right side derivative, at x=0, is : 4
left side derivative, at x=0, is : 2 * 0 + 4 = 4

[stray totem]

Wait you're absolutely right, ahh I got my working out entirely muddled up whoops xD it's night and the test is tmr - I'm a bit tired studying for it

[cinder yacht]

(when x<0, f(x) = x^2+4x+4 so f'(x) = 2x+4)

[stray totem]

Yep gotcha

[plush plover]

Does anyone have any tips for understanding combinatorial analysis? I understand the theory (I think) but the practice is much more complicated.

[stray totem]

Sorry another question: why isn't the cot graph discontinuous at the x intercepts? Isn't the reciprocal of a vertical asymptote supposed to be discontinuous at that point?

[mellow mica]

For 35. Ik the answer is 7.5 but how do you get it?

I mean answer is 7.2

[limber mesa]

A-is 2.17 and b is 3.1 but how
If you know pls help

[midnight gazelle]

U can calculate using area expressen

P=ab/2=c*hc/2

[mellow mica]

Appreciate it

[left knoll]

what grade questions are these

These are 5th grade questions in my country

:/

[tropic lava]

How many ways can you choose 4 cards from a 52 card deck so that there is at least one queen and exactly one king among them

[frozen parcel]

anyone got a clue what the last part of the question is asking me to do?

first 2 parts are fine, but part c got me stuck

[mellow mica]

9th grade geometry 😂 nvm though I got it it’s pretty easy

[left knoll]

Where are you from

[left knoll]

i tried closing the loop here by making sin x my u

and e^x my dv/dx

didnt work

can someonw explain this please

[supple island]

this is a technique you can use when you integrate by parts, basically when you have 2 functions that are infinitely derivable (like e^x and sinx), you integrate by parts 2 times, and on the right hand side of the equation you'll find something similar to the original integral, (here you find exactly the intergal of e^x sinx, sometimes you can find the same integral multiplied by something), you put that to the left and you sum it to the starting integral.
now you'll have (k)* starting integral=something, (where k is a constant, here it's 2) so the starting integral=something/k

[edgy sun]

how to do this?

[ember garnet]

Assuming you found that q and r are 1 and 3, f(n) is written as (n+1)(n+2)(n+3) + 3. Now, exactly one of (n+1), (n+2), (n+3) must be divisible by 3. Therefore (n+1)(n+2)(n+3) is divisible by 3 and so (n+1)(n+2)(n+3) + 3 is also divisible by 3.

[left knoll]

You guys are so handsome

Thank you for your help

[meager sleet]

can someone explain this please and thankyou

[vale tide]

first step=> you add 8 on the LHS and the RHS
second step=> you multiply with 5 on both the LHS and the RHS
thrid step=> you divide the LHS and the RHS with 3
and you should get the ans
X >= 25

https://cdn.discordapp.com/emojis/940368955678285855.webp?size=64

[meager sleet]

ok thanks

[left knoll]

Hello. May I please ask what steps I should do to factorise this, and for any other similar equations in the future?

[supple island]

this isn't an equation

there's no equal sign

[left knoll]

I meant expression - I apologise

[supple island]

i mean once you have that what do you want to do?

what's the context? are you trying to do a second degree equation? are you trying to draw a parabola? do you want to complete the square?

[left knoll]

what i understand from what my teacher has given me is that i need to put it into double brackets

[supple island]

can you show the assignment?

[left knoll]

this is what it says on the top of it

actually, here is the entire box.

[supple island]

oh i see what they mean

they want you to express that as a product of 2 binomials

like (ax+b)(cx+d)

(ax+b)(cx+d)=acx²+(ad+bc)x+bd
=4x²-23x+15 in this case

[left knoll]

I believe I have gotten a hang of it now - I did a couple of things wrong. thank you for taking your time in explaining

[vale tide]

you can also just apply the expression to the quadratic formula and the more simpler expressions can also be solved by splitting of the middle term

[left knoll]

Can someone help me with this question? I can't solve it.

[ember garnet]

for DE the lower bound should be 35 cm. For EF I'm not sure because it says correct to 2 sig figures when 16.6 has 3 sig figures. So are we supposed to ignore the .6 or what?

[left knoll]

no dont worry about EF i did it but DE i didnt, Thanks!

[ember garnet]

cool, np :)

[left knoll]

for this

why did they make u=cos x

how r u meant to know what to make ur u for substitution

[ember garnet]

It's about finding ways to simplify the integral into something you know how to integrate easily (in this case, a polynomial). It takes some creativity and experience to do this on your own.

[fierce spear]

For its only critical point to be a relative minimum, "a" has to be higher than… ?

can someone help me to do this? 😔 is from a test that i have to do now

[acoustic heron]

hi, does anyone know of a good/recommended way of studying calculus?, i've been struggling the past few months and wanna know how other people do it, if anything dm your recommendations plss

[left knoll]

khan academy is a good choice for beginners, the calculus books by james stewarts is also recommended (this one is more challenging than the courses in khan academy)

[supple island]

did your professor recommend any books?

[gritty grove]

do you still need it?

[fierce spear]

i did the test already but i would like to know how to do it hajfsjjf

[left knoll]

can someone give me the reasoning for why the answer to this question is B

[ember garnet]

I think it's D. Find the signs of f(0) and f'(0).

[left knoll]

no its B

[supple island]

pretty sure it's D

[left knoll]

Its B

dont know what to tell u

but thats what the answer says

[supple island]

well, the sign of f'(0) is negative, it's decreasing

[left knoll]

that my teacher gave me

ur reasoning acc makes sense

ok what

now im confused

how do i argue d with my teacher

[supple island]

f(0) is positive, f'(0) is negative, it's D

[left knoll]

ok ok ty

wish me luck for arguing

[rustic shuttle]

Agree with @supple island , i think its D

I cant think of a way to make it work to be B

[left knoll]

how do i do this one

[ember garnet]

by using this rule

[raven wyvern]

Umm u can use the Casio calculator to do it faster

[spice basin]

I’m currently trying to learn calculating the volume of a figure created by connecting multiple surfaces and I don’t understand one thing: we are supposed to calculate the radius of the upper intersection of two surfaces and it just so happens that the two equations of the surfaces can be written as a quadratic equation which has 2 different solutions (3 and 4). But of course one circle can only have one radius. During the lecture our professor said that in this case it has to be 4 rather than 3, but I don’t understand why. Maybe I overlooked something, idk. I’ll be really thankful for any help (also sorry for a terrible drawing)

[spice basin]

Nevermind, I figured it out 😅

[left knoll]

Haha

[near verge]

how can i get with polar cordinates?

[stoic fog]

Hi, does anyone know how to find p value on excel with ANOVA test? for stats

[ember garnet]

Given its definition, isn't D the circular sector of the unit disk starting from theta = 45° up to theta = 135° ?

[near verge]

Yep, but for the finally u need to get in the final the 2 integrals with 0-1 and 0-1 (sorry for the eng)

[vagrant moss]

hiii

can someone help me with a problem of lineal algebra using mathematica

the problem is the next

Find an invertible matrix P and a diagonal matrix D such that D=P−1AP

S is the next matrix = {-3, 2, 0, 0}, {2, 4, 0, 0}, {0, 0, -5, -2}, {0, 0, -2, -2}

[supple island]

<@&942391219206647828>

[left knoll]

This question pls

[fiery widget]

Can anyone help me with this?

[ember garnet]

@near verge ^^ after that, maybe change theta to {u*pi/2 + pi/4} to get the integral limits from 0 to 1?

[ember garnet]

Coordinates of P can be expressed as (x, x) and Q is (0,4). Distance QP is equal to sqrt{ (x-0)² + (x-4)²}. Set that equal to 6 and solve for x.

[fiery widget]

ahhh okay that makes sense

cause I tried doing as P can be expressed as (x,y) but then I would have two variables which didnt work

thanks alot

[ember garnet]

yw

[ember garnet]

Vector CF is -2c + 2f. Using the theorem given without proof, vector WZ is parallel to that and of half length, therefore vector WZ = -c + f

[balmy light]

need help with this proof 😞 not homework or graded

[floral star]

Not that good at writing proofs tho

[fiery widget]

how would I do c) ?

I know that the the coordinates for A start off as (-2,y) and for B it is (6,y) but Im not sure how to find the y values for each

[floral star]

From the fact that PA = PB = the radius of the circle, u can solve for the y value

[fiery widget]

AH IT JUST CLICKED

thank you

[floral star]

Welcome

[left knoll]

<@&942391219206647828>

[final flume]

Hey yall

Who can help me on maths

I really need help

[cinder yacht]

r goes from 0 to 1 and theta goes from pi/4 to 3pi/4

oh it was alrdy answered my bad

[floral star]

Ask here and whoever knows will help u

[cinder yacht]

you know Stirling formula?

if u know it u can use it to mention that n! / 20^n - > +infinity when n->infinity

and so, there exists c such that for every n>=c, n!/20^n >= 1

[final flume]

But i have exam at 3p.m

[subtle tartan]

depends what you need help with

[supple island]

just ask

someone will answer

[left knoll]

Help pls for ii) and iii)

[ember garnet]

for ii) equate the coefficients of the i and j vectors?

[left knoll]

I think it’s more than that

[ember garnet]

I think that's it really, by equating them you calculate the time that the ball strikes the hill and with that you can easily calculate the speed for iii)

[near verge]

if someone know how to get the new jacobian later of this and can teach me, i will apreciate

[civic forge]

Hello guys, does anybody here know statistics and how to use ibm's SPSS? This software is above my level of understanding and I need a bit of help

[junior egret]

Not sure how to do b

[supple island]

do you know what a basis is?

[junior egret]

Yeah think so... just the transpose of a vector * another vector has to have a sum equal to 0

And then they are in the same basis

[supple island]

one of us is very confused, because i have no idea what you just said, either way, that doesn't seem like the definition of a basis, i suggest to look it up some more

[junior egret]

https://en.wikipedia.org/wiki/Basis_(linear_algebra)#:~:text=In mathematics%2C a set B,vector with respect to B.

[supple island]

With that knowledge you should be able to answer ii)

just to be super clear:
a basis is a collection of n linearly independent vectors, each one with n components, that's because the linear combination of those vectors can give any vector of n components

so what you're asked to do in this exercise is: find a so that all 3 vectors are linearly independent

[junior egret]

I know but the "a" is giving me trouble

[supple island]

how so?

[junior egret]

I for some reason am not able to sole the system of equations properly

I ended up with a=-4/3

[supple island]

find the coefficients for which the first ad the third row of x¹ and x³ give the first and the third of x², then a is whatever number for which the second row of x¹ and x³ don't give x³ (using the coefficients you have found)

[junior egret]

Not quite following

I might just ask my prof. but thanks for trying

[supple island]

@junior egret

Oh i sent the same thing twice lol

[junior egret]

Alright thanks a lot

[ripe bay]

If the message above contains a link to free nitro, it is most likely a phishing link. Please DON'T click on it to protect your privacy. You can notify the peeps by tagging them ( @peeps ) and they will take care of it as soon as they can. Please don't ping them if someone else already did in the chat thank you.

[hot moth]

Find all the natural n, for which
n-2=a, n+24=b, n+24=c
are true, where a, b, and c are prime numbers

[cinder yacht]

c=b

so it's n=a+2 and n=b-24
so a+2 = b-24
so b = a + 26, & b and a are prime

so a can not be a multiple of 2, 13 (which are divisors of 26) (cuz otherwise b would be a multiple of those too, and therefore not a prime). same for b

that's all I can think of, rip

a=3 seems to work, a=5 too, a=11 too,..

[vague dagger]

do u guys know what area of math are my lessons is?
Distinguishable and Circular Permutations
Permutation
Principles of Factorial
The Addition Rule
The Multiplication Principle
Linear Diophantine Equations
Congruence and its Properties

im in a adv math class

[left knoll]

the range is tripping me up

[left knoll]

cant figure out c how u do it

[supple island]

<@&942391219206647828>

[ember garnet]

I think the first three are part of Discrete Math.

[steel berry]

p sure most if not all r discrete math

[ember garnet]

you have to find the minimum and maximum of h(x). These are located where h'(x) = 0. So if you calculated h'(x) from (b), equate it to 0 and solve for x. You get two solutions, call them x1 for the minimum and x2 for the maximum. The range is the closed interval [h(x1), h(x2)].

[left knoll]

ahhhh

u so smart

mr zoro

[cinder yacht]

not exactly

by looking at sign of h'(x) FOR X>=0, h is increasing on [0,a] then decreasing on [a, +inf) where a>0 is the POSITIVE solution of h'(x) = 0

so the range is the union of [h(0), h(a)] and ( lim (x->+inf) h(x) , h(a)]

[ember garnet]

I didn't see that h(x) was only defined for x>=0. But also, lim(x->+inf) h(x) is zero right? So the range is simply [0, h(a)]

[mild oyster]

Point (–3, –2) lies in the quadrant??

plz tell

exact

[ebon relic]

yes

It lies in quadrant 3
If neither the x coordinate nor the y coordinate of the point is zero, u can say that it lies in the quadrant

[wintry carbon]

Provided that n is an integer, prove that n^2+n+16 isn't divisible by 49
pls help, thanks in advance!

[cinder yacht]

yeah ur right cuz h(0)< lim(x->+inf) h(x)

[mild oyster]

thanks

[cinder yacht]

if divisible by 49
then n^2+n = 49k-16 where k€N
so (n+1/2)^2 = 49k - 16 + 1/4
so (2n+1)^2 = 196k - 64 + 1 = 192k - 63
= 7 [28k - 9] where k € N
so (2n+1)^2 is a perfect square, and 7 is a divisor of (2n+1)^2
so 49 is a divisor of (2n+1)^2
so 49 is a divisor of 7 [28k-9]
so 7 is a divisor of [28k-9] (where k € N)
so 7 is a divisor of 7 * (4k - 9/7)
so 4k-9/7 is an integer : that's absurd
meaning our initial assumption is false

there are probably much faster ways, im not used to number theory questions sry

[soft lintel]

hey i have a question. How do we know the class of a function? like a polynomial function is of class C∞ but is there a specific rule to which we know this ?

[cinder yacht]

there is a bunch of functions that's C infinite

and sums, compositions and products of C infinite functions are C infinite

so when u see a function u need to see how u could construct it form sums, compositions and products of those usual functions

[cinder yacht]

also to prove that f is C infinite at x0, u need to prove by induction that it's Cn at x0 for every n€N

Cn at x0 means that it's derivable n times at x0 and that it's n'th derivaticr is continuous at x0

[soft lintel]

thank you : )

[empty vessel]

someone can help with Statistics Exam? (it’s in portuguese but i can translate to help)

binomial distribuction and poisson

[left knoll]

what do u need

[left knoll]

Hey could someone help me with some recurrence relations cause Im kinda confused

Looking for the solution to these

And if you could tell me how I'd go about solving them id appreciate

[cinder yacht]

T(n)
= 16 T(n/4) + 24
= 16 [ 16T(n/4^2) + 24] + 24
= 16^2 * T(n / 4^2) + (16^1 + 16^0) * 24
=...
= 16^k * T(n / 4^k) + (16^(k-1) +... +16^0) * 24
= (4^k)^4 * T(n / 4^k) + 24 * (16^k-1)/(16-1)
= (4^k)^4 * T(n / 4^k) + 24/15 * [ (4^k)^4- 1]
for every integer k such that n / 4^k >= 1

so u apply that to k such that n / 4^k = 1
meaning 4^k = n (we only consider the values of n that are powers of 4 here)
that gives u
T(n) = n^4 * T(1) + 24/15 * [n^4 - 1]
= n^4 * [T(1) + 24/15] - 24/15

[left knoll]

❤️ ❤️

Thank you!

[dreamy oasis]

The derivative function of f is drawn above, at how many points does the local extreme point exist? Sorry for my bad english

[cinder yacht]

f' is strictly positive everywhere except at two points

so f is a strictly increasing function

so it has 1 minimum, at the start, and 1 maximum, at the end (assuming f is defined on a segment like [a,b] and not on all of R. If it's all of R, then no extrema)

[dreamy oasis]

That is, is there an extreme at x=0 in the function of the derivative of f drawn here? How do we know if a function has an extreme in its graph? I'm pretty confused.

What I am wondering is that the local extrema points of f'(x) , not of the function f( x)

[cinder yacht]

ohhh

I thought u wanted local extrema of d

f*

4 is a local maximum (at x=0)
0 is a local minimum (at x=-4 and x=2)

[vestal marten]

Can someone explain the working please I applied L'H rule 2 times still 0/0

[winter grail]

3 times then?

[vestal marten]

But my answers isn't correct after 3 times too
I'm getting 1/24 lol and the answer is 1/16

[ember garnet]

you must be making some mistake, I got it right after doing it 3 times

[vestal marten]

What are you getting after doing it 3 times?

[ember garnet]

@vestal marten

[ember garnet]

that's after 2 times

[ember garnet]

and that's after 3 times @vestal marten

[vestal marten]

I got
1/6 lt x-->pi/2 (-2cosecx cot x+cos x)/2(pi-2x)(-2)

Then I got 12
Oh ok I got it
Ty💗

[dreamy oasis]

At first I thought the same as you. But if you pay attention to the graph, point 4 is hollow, so can we accept this point as the extreme point?

[ember garnet]

yw :))

[cinder yacht]

i dont know what hollow means to me

[dreamy oasis]

that point on the graph is empty, sorry for my bad english hope u understand me now

[cinder yacht]

for me, f has a maximum at x=a if and only if there exists a neighborhood of a, such that for every x that is in both that neighbordhood AND the domain of f, f(a) >= f(x)

and that is the case here : f is higher at x=a than at every value of x surrounding it

[ember garnet]

I think the value of this function at x=0 is 2 though

[dreamy oasis]

But if the point is empty that means there is no extreme points or maybe i am wrong?

[cinder yacht]

ah it is?

i dont know that graph convention, in france we represent things differently

if f(0) = 2 then there is no local maximum

if f(0) = 4 then there is a local maximum

[dreamy oasis]

Yeah i am talking about this

[cinder yacht]

ok then yea no local maximum

[dreamy oasis]

So that means we have just 2 exttreme points in this graph right?

[cinder yacht]

ye

[dreamy oasis]

Thanks for helping Colyy!

[crystal patio]

anyone have much experience working with the Taylor series? was studying with a friend and he just doesn’t quite understand the significance/application of it

[tight salmon]

Taylor series is a sumatory that represents a polynomial function that if is infinite can be equal to the function

In that specific point

[crystal patio]

I see, so it seems like it has a very niche purpose

wouldn’t the type of questions that can be tested for a topic like that be very limited then?

[tight salmon]

Sometimes for example, in an exam, it appears "find the result of this f(a) using taylor order 4"

[tight salmon]

Well in my career we didnt dig deep about taylor so i don't it's actual importance,

At least for me wasnt

[crystal patio]

ahh gotcha

[crystal patio]

I understand

thank you for your help, I appreciate it

[faint star]

can someone help me I have a test ques

[supple island]

are you doing a test right now?

[left knoll]

help with this one pls

[ember garnet]

without strictly proving it, it's B because in that case the denominator's absolute value is greater than 1 and so each subsequent term will get smaller and smaller. This is not guaranteed in the other cases.

[left knoll]

Ty

[left knoll]

how would i graph, x^3-3x^2-9x+4

[ember garnet]

You mean without using a computer?

[left knoll]

Yes

[ember garnet]

you can start by calculating the first and second derivative of the function, finding the local extrema and the inflection points.

[cinder yacht]

and look at limits at +infinity and -infinity

[left knoll]

Is there no way to factor it?

I have all of the min and max already

And I have inflection point

How do I find x intercept

[ember garnet]

solving a cubic equation is generally not an easy task

[left knoll]

But how would you do so

[solemn vessel]

@left knoll

[left knoll]

Damn

Ummm

Yea nvm

[ember garnet]

Yeah, so if you want the exact analytical solution, it's gonna get ugly. Otherwise, you can just find numerical approximations. Depends on what you need.

[cinder yacht]

or sometimes u can test replacing X by a few values x0 (0, 1, - 1, for example) and see if it gives 0

if it does, that means that u can factor it by (X-x0), and then it becomes easier to factor the rest cuz it's a polynomial of degree 2

here I tried some values and didn't work, so RIP

[candid rivet]

why does the number of paths of length 2 in any graph is equal to the sum of the degrees squared ?

[left knoll]

thank you for trying tho!

[solemn vessel]

@left knoll Out of curiosity since I see you posting here a lot ,I am wondering if you are a student of if the questions you pose are from self-studying

[left knoll]

ello lads

with the change of 10 to 9.5 why would that be necessary

isnt 10 already the lowest value so why would continuity correction be needed

[left knoll]

how u from antartica

[ember garnet]

if the weight of a cat to the nearest kg is 10 kg, the real value could be anywhere from 9.5 to 10.5 so that interval must be included too

likewise, the last class would have boundaries from 18.5 to 20.5, with a class width of 2 though

[left knoll]

thank you miss ellish

zorro

[solemn vessel]

big ass coat

[left knoll]

https://tenor.com/view/kumalala-kumalala-kumala-savesta-kumalala-kumala-savesta-thoms-gif-25640000

[cold raptor]

there is a difference if the weight is given to be 10.0, right?
It's 9.95 to 10.05 or am I tripping?

[ember garnet]

yes, that's right. 10.0 has 3 significant figures

[cold raptor]

hmm thanks

[crisp ocean]

is there a major difference in calculus in college and calculus BC in high school?

[left knoll]

Yes I am a high school student, but I like doing hundreds of practice problems as that is what I have found to help me achieve high marks. My apologies if I post too much 😁😁

[left knoll]

Some of them are self studying

[solemn vessel]

cool, just wondering

[fierce spear]

hello can someone help me to search the volume formula for this? i found one that had a coefficient in it, but my professor said i needed to justify it by using the area (??

[left knoll]

wbu?

[solemn vessel]

Ah you see Im from antarctica!

[left knoll]

Are you being serious???

[ember garnet]

The function (call it f) has to change its sign 3 times. Since the limit of f for x -> -inf is -inf (negative), going from -inf to +inf on the x axis f must go from - to +, then from + to -, and then from - to + up to +inf. Now that you know how cubic functions are graphed, you know that f goes from -inf to a local maximum, then to a local minimum and then to +inf. Therefore, to change its sign 3 times, f must be positive at the local maximum and negative at the local minimum.

[ember garnet]

Another way to think about it is that f is increasing from -inf to x1 (local maximum), decreasing from x1 to x2 (local minimum) and increasing from x2 to +inf.
Given that f(x-> -inf) < 0 and f(x-> +inf) > 0, for f to change sign three times, it must be f(x1)>0 and f(x2)<0.

[unborn mulch]

Can someone help me with my calc assignment

how do I find c

solve for x ?

[ember garnet]

the critical point is where the derivative is zero

[unborn mulch]

i keep getting it wrong

i got 0.60

[ember garnet]

do you know how to find the derivative of the function?

[unborn mulch]

yes i found it

then set it to zero

[cyan night]

yea

what did you get

[unborn mulch]

i got

4 - log (x) / 4x^1/4

[cyan night]

yea set it to 0

what did you get for x

4-ln(x) = 0

x=e^4 right?

[unborn mulch]

yea makes sense

ur right i fucked up my algebra

[cyan night]

its alright

sometimes you can check with a computer

[unborn mulch]

what about

[ember garnet]

critical points are where the first derivative is zero, inflection points are where the second derivative is zero.

[unborn mulch]

which statment is true tho

[ember garnet]

I'm trying to help you without doing your homework for you.

the graph is that of the first derivative

therefore its zeros correspond to the critical points

[cosmic sorrel]

volume of this shape?

[candid rivet]

Can someone explain to me why the number of "walks" of length 2 in a graph is equal to the sum of the degrees squared ?

[fierce spear]

yes!!

[ember garnet]

do you have a more detailed diagram of that pool?

[fierce spear]

no but is supposed to be a pool 🧐 i founded that pic from google cause i needed to search for different pool shapes (?

the idea of the problem is to find a way to maximize the volume of a pool

so far i optimized the volume formula for the rectangle pool, and now i wanted to try with this one

[ember garnet]

maximize the volume with respect to what? The surface area of the pool? You need either the surface area or at least some relation between the different edges of the pool. Otherwise you'd have to make some assumptions. How did you do the rectangle pool btw?

[fierce spear]

the area of the mosaics (?? or whatever is called is 100 m2 in total

i know the steps i need to do to optimize it but i need the formula first 😭😭

i was about to send pic of what i did with the rectangle but is in spanish 😭 i dont know if is understandable

[ember garnet]

send it anyway

[ember garnet]

ok, so you need to write the volume with one variable if you want to optimize it

and see they gave you b = 4m, otherwise it wouldn't be possible to write V with one variable

That's why I'm saying you need a bit more information for the oval pool too

if you could constrain one of the sides it would be possible

[fierce spear]

i mean i understand what i should do to optimize and all, but i need the volume formula of the oval pool and i suck at it 😔 i doubt that is gonna be V= abh again

[ember garnet]

Are the curved sides of the pool semicircles?

[fierce spear]

and i need the area formula as well

[fierce spear]

yes!! that’s what i thought too

[ember garnet]

if that is the case, here is what I drew

[fierce spear]

OMG 🥺🥺🥺🥺 thank you so much i was really stuck with this

i think i love you

[ember garnet]

you are welcome 😊 😊

[left knoll]

part b an c please

not part a

[ember garnet]

b) The interest for the n-th month will be I_n = A_n-1 * 0.005
c) Write A_n as an expression of just n, (no incurrence). Try to find A_3 from part (a) without calculating A_2 and A_1; just replace them until you get to A_0, then expand and group similar terms and try to find a pattern (you'll have to use a geometric series too).

[left knoll]

could you specify part b please?

[left knoll]

also i have another q

based on this data

[mild patrol]

How many pairs of natural numbers (x,y) satisfying that 3x+4y=100?

Anyone please

how many quadratic polynomials with real coefficients exist with-1 and 2 as zeroes

[delicate cave]

f(x) = a * (x + 1) (x - 2)
a can take any real value (except 0) and the roots would still be -1 and 2,
so infinite such polynomials must exist

[ember garnet]

The first month's interest will be the money that was in the account before the first withdrawal times the interest. So I_1 = A_0 * 0.005. In general, I_n = A_n-1 * 0.005. Calculate I_1, I_2, I_3 and add them.

[ember garnet]

If you write it as y = 25 - 3x/4, you can see that for y to also be natural, x can only be multiples of 4 and less than 100/3.

[vernal pagoda]

@ember garnet hello i have a question for you ,cuz you are so smart,
what are you studying for?

mathematics teacher؟

[left knoll]

well is it not obvious that they are studying physics

[vernal pagoda]

yeah but i think this is just nickname or some think,thanks

[ember garnet]

I'm a physics student

[vernal pagoda]

Good luck

[ember garnet]

Thank you :))

[vernal pagoda]

your welcome

[ember garnet]

K(t) is basically modeled as [K(0)+K(6)]/2 + [K(0)-K(6)]/2 * cos(pi * t/6). Write a similar equation to model W(t).
The constant term in the equation corresponds to the average daily max temp.

[proud nymph]

heisphysics

[vestal marten]

Anyone knows how to do this

[winter grail]

df/dg = df/dx * dx/dg = f'/g'

[vestal marten]

Oh alright ty

[sly island]

could someone help me with these question on call or something?

[stone wren]

is there a good website to help with learning derivation?

[rain tendon]

guysss pls help me w this problem

its solve : tan3x.tanx=1

[winter grail]

transform into sin/cos and use some sincos formula

[soft plover]

Anyone can explain part (b)

[supple island]

what is it that you're not understanding?

[soft plover]

i got the acceleration but markscheme used velocity and then worked out distance

i'm not sure how they did it

[supple island]

isn't it just d=h/sin(a) ?

[soft plover]

d>1.5h

i got the acceleration 0.4g

but the rest i don't know how to get

[supple island]

oh i see what the question is

[soft plover]

i think i figured it out

but have no clue why it is that method

[quartz scroll]

c + |c| = 2+ 8i, how much is |c|^2

[delicate cave]

17

[ember garnet]

the square of that

[delicate cave]

yea ... that's |c|

so what you can do is

take c = a + b i

a + b i + root(a^2 + b^2) = 2 + 8 i

=> b i = 8 i
so b = 8

=> a + root(a^2 + b^2) = 2
(a - 2)^2 = (a^2 + 64)
so a = 15

[soft plover]

anyone can explain the -6/5g-2g/5=2a onwards

[quartz scroll]

ty

[ember garnet]

-6g/5 g is the parallel to the plane component of the weight force while the -2g/5 is the friction force.

at the next step, this formula is used

A will have traveled h meters when B hits the ground, and then you find that it will travel 1/2 h more until its velocity becomes 0. Therefore d > h + 1/2 h

[soft plover]

ah okay

thank you

anyone can explain (a)

[ember garnet]

do a diagram of the forces at the points A, B, C and at the center of the ladder (its weight). At point A there is a vertical force (reaction) and a horizontal force (static friction). At point B there is only the reaction force which is horizontal (no friction because the vertical wall is smooth). Then try to balance the forces, vertical and horizontal, so that the ladder doesn't travel and also balance the torques so that the ladder doesn't rotate.

[soft plover]

i'm not sure where the 45g comes from

they did pivot at A but they summed up all the equation into one and idk where 6root3/2 comes from

[ember garnet]

from the equation above. 3 x 30 / 2 = 45

[soft plover]

i'm not sure how they got to that tho

i did 30gX3 + 70gX2 as my clockwise momentum

idk anticlockwise momentum

[ember garnet]

you also multiply both by cos60 which is 1/2

when calculating the torque, you take into account the component that is perpendicular to the rod.

[soft plover]

I Got 90% of it just i'm stuck on the 6root3/2 N

ik its sin60 X 6 X N

But idk how to tell it's sin60

i drew out the triangle but not 100% sure it's correct

[ember garnet]

The force Nsin60 is applied at point B and is perpendicular to the rod, not how you drew it

[soft plover]

But where's the right angle

So is it like this

[ember garnet]

yes thats right

[soft plover]

thank you

[cold raptor]

If someone could just appreciate the awesomeness of this question, don't need help tho.

[cosmic sorrel]

Tigers in hospitals 🤣

[twin sinew]

LMAOO

[main prism]

😭

[low patio]

does anyone know the solution to this?

[ember garnet]

should be 25

[low patio]

can you explain how u got that?

[ember garnet]

you need to complete the squares and write the equation in this form: (x-a)^2 + (y-b)^2 = r^2

point (a,b) will be the center of the circle, and radius r will be an expression of k. For the circle to have exactly three points of contact with the axes, it must meet one of the axes in two points and the other axis must be tangent to it at one point. So the radius must be equal to the largest of the distances from the center of the circle to either axis (i.e. max{a,b})

[ember garnet]

it must look something like this

[sly island]

is this correct guys?

[low patio]

got it tysm!!

[fringe timber]

Hey i have 2 questions!

Question 9 asks in what quadrant of the argand diagram do you find z^5 if z=cos.... Motivate your answer

Please help me!

[winter grail]

use eulers formula

[fringe timber]

Ahh nice i got it

[left knoll]

what are the answers?

[vestal marten]

Can someone explain where 2^y go?

In the 4th step

[supple island]

you're resolving both integrals, one on the eft, one on the right

[vestal marten]

Oh, I meant by the integral of 2^y

Oh ok

I get it thank you

[winter grail]

oh wait i was actually wrong u should use substitution

pls forget what i wrote up there 😭

[vestal marten]

Ok

[left knoll]

what is the value of c here

i got 1/2

[supple island]

i'd say 0

oh wait

it's x²/2

yeah 1/2

@left knoll

[left knoll]

The answer does say 0

[supple island]

hmmm

cuz you should get y=tan(x+x²/2+c) right?

yeah

yeah here c1=2c so for y(-1)=0 c1=1

[fiery birch]

any ideas?

[winter grail]

what is the question? find y?

[fiery birch]

yes, it's differential equation

[ornate ravine]

A car loses part of its value every year. A car that costs €15,000 new is already worth 30% less after one year. The following year, the value falls by another 25%.
By what percentage has the value decreased after two years?

Round to 1 decimal place.

---

Anyone understand this????? ive asked everybody i know

[weak surge]

you just need to multiply the og cost to 70% and 75%

actually, you dont even need the 15000 euro cost to find the answer. So the value of the car from the start is 100%, after 1 year - decrease 30% mean it have 70% original value (100% * 70% = 70%), same with the 2nd year you have 70% * 75% = 52.5% original value so the value had decreased 100% - 52.5% = 47.5%

[earnest surge]

Does anyone know why b was subtracted from the denominator and what happened to its coefficient??

[granite tinsel]

we know that 1/2^b is equivalent to 2^-b then 2^a * 2^-b = 2^a+(-b) =2^a-b

In this example, u have 2^2a-b (I forgot to mention 2)

[vapid spruce]

B-7?

Nvm it was just A

[earnest surge]

Ahh I still don’t understand. Thank you for your reply tho

[winter grail]

Because it has the same base like x^a/ x^b = x^a-b

[cold raptor]

Can someone help me out here, I mean I have a general idea of what to do but things don't seem to be panning out.

[ember garnet]

they are exponent properties, check out this table: https://mathinsight.org/exponentiation_basic_rules

[cold raptor]

Thanks Mr.Physics

[left knoll]

For differential equations, you know when you are doing the initial value problem and you are solving for the unknown constant

On which side do you put the constant when you split the DE into its components

As i have found that can change the answer

For example

Y’=-2y

I speak in regards to this

As it is evident my exponent would be -ve

[ember garnet]

that integral is hard to compute analytically

[ember garnet]

it shouldn't really matter, if you apply the initial value condition the final answer (the function to be found) should be the same

[left knoll]

then why is the answer different for this case

if you take c on the other side (on rhs) then the 2c becomes +ve

but its negative when on the lhs

[ember garnet]

First of all, what is the initial value? Second, shouldn't it be |y| = e^(-2n+2c) ? If you apply the initial value condition, y can only be one particular function. And it is y that you want to find, right? Not c which is arbitrary.

[left knoll]

sorry i dont understand the question

[ember garnet]

Your problem is y' = -2y. What is the initial condition?

[left knoll]

oh y(0)=1

@ember garnet

[ember garnet]

ok so after you write ln|y| = -2n -2c, next step should be |y| = e^(-2n -2c). Now apply y(0)=1, you get: |1| = e^(-2 * 0 -2c) --> 1 = e^(-2c) --> c=0. Therefore, |y| = e^(-2n) and since y is positive at 0, then simply y = e^(-2n)

it doesn't matter if you would put c on rhs and write -2n+2c = ln|y|, final answer would be the same.

[left knoll]

oh ok ok yea

ur right

lol i was being dumb af

i forogt the condition

[ember garnet]

and not because c turns out to be 0, for any initial condition the final answer for y will be the same wherever you put c.

[supple island]

what do you mean?

[mild oyster]

I'm sorry this physics question i asked in maths

[ember garnet]

the 3 is the mistake, it should be 2

[haughty owl]

3 stays 3

[haughty owl]

yep, its 2 my bad

thx

[ember garnet]

np

[left knoll]

why do we reciprocate DEs

to solve them

[granite tinsel]

any Idea

[tranquil berry]

I guess you need to apply l hospitals rule
First assume 1/x as p so u will get 0/0 form

[winter grail]

solve the integral first then lim

[cinder yacht]

lol the integral is hard to sokve

it's useful to think about how big/small the intwgrand is when t is between 0 and a very large value of x (cuz x->+inf)

and basically (t+1)/(t+2) is a pretty small thing, i mean it never exceeds 1

and since sin(t) is between - 1 and +1, u can see that e^sin(t) is between e^(-1) and e^(+1)

so really the whole integrand doesn't take very large (nor very small) values

between 0 and x

so the integral stays pretty close to x * a constant
so when u divide it by x^2, it stays pretty close to (a constant)/x
so when x->+inf it's basically 0

to sum up : find a lower bound and upper bound for the integrand, and deduce a lower bound and upper bound for the integral, divide by x^2, do x->+infinity

[tranquil berry]

Can some one help me out with this

[left knoll]

(a+1)×(a)! - (a)! = (a)! [(a+1) - 1 ] = (1)! × [ (1+1 ) -1 ] = 1× 1= 1☻

[granite tinsel]

it's hard

[granite tinsel]

thanks, bro

[cinder yacht]

wtf did I read

[candid rivet]

just try to write the first terms and see what cancels out

[tranquil berry]

Yep got it thanks

[fierce spear]

can someone help me to search critical points of partial derivates??? my derivates are too big and i dont have idea how to do it

the online calculators cant solve it 🙁

[ember garnet]

can you send the problem?

[hard light]

how do i solve the intergal?

[left knoll]

"có đồ thị như hình bên" mà bạn cắt mất hình bên thì khó quá

từ đồ thị mới có thể đoán được f(x) => f'(x), thế 2x-1 vào ẩn rồi chia trường hợp tích phân

[south cove]

Does anyone know how to do these?

[candid rivet]

5. these are in the form (n-1)(n+1), n*n, (n+1)(n-1) so the first column is just going from (n-1) to (n+1) while the line is going from (n+1) to (n-1)
6. not sure about what is the exact answer to the two first questions but exp(2x)=exp(x)^2
   for the tangent we have : y=f'(3)(x-3)+f(3) with f(x)=exp(2x) and f'(x)=2exp(2x) which gives : y=exp(6)[2x-5]

don't know how to do questions 3. and 7. sorry

correct me if i'm wrong

[hard light]

ừ mình xin lỗi mình chưa thêm ảnh đồ thị

[left knoll]

Em làm ra =4, ko bt đúng đáp số chưa ạ

[left knoll]

Đồ thị trên góc là của f’

[left knoll]

First question the friction is pointing to the left, magnitude of 1gmk

[solemn steppe]

Can someone help me figure this one out?

I'm not sure as to how the |x| part exactly works and would alter the graph

[ember garnet]

f(|-x|) = f(|x|) so f(|x|) is an even function.

Therefore its graph will be reflected with respect to the y-axis.

[solemn steppe]

thank youu

Anyone know the solution?

[silk tulip]

d i think

[solemn steppe]

THANKS i just got it loll

[solemn steppe]

Anyone know the answer to this one?

[ember garnet]

should be d

[left knoll]

My brain isn’t working i need to isolate A

[unborn mulch]

hello

i have a queastion plz

[left knoll]

Thats a lot of chainrule

[unborn mulch]

nd this as well, not sure what i did worn

wrong*

[left knoll]

Ok so

[left knoll]

Don’t have time so just gonna solve this one

Rewrite 3x+1 as $e^{ln(3x+1)}$

Then you’ll have

I think you can continue the work from that

The e^ whole thing stays

The thing in the bracket can just use prod rule and chain rule

[round crystal]

help pls

[glossy falcon]

how?

[candid rivet]

here c is divided by 2 which means it keeps its direction but its magnitude is divided by two. So it is answer b

[solemn steppe]

Oh, could you explain why its D? ARe you supposed to try and get r alone on the left side of the equal sign?

[ember garnet]

yes, just solve for r

[solemn steppe]

thank youu

is that what like "y as a function of x" means?

You solve for just y?

[ember garnet]

yeah

[solemn steppe]

I see, thank you

[sonic laurel]

Hi, I’m a high school student in France and I have been on this question for several hours , I think the result might be right but I’m not sure so can you help me guys?

[ember garnet]

Looks good to me, except that you should have written (1+x^2)^3/2

The final result is the same though because 1^2 = 1

[agile trench]

its right

[sonic laurel]

Ohh 😮 you are right I dropped it in the midway

Thank you

[left knoll]

a) y=x+2

b) y=4-x

[torn trellis]

thanks

[fallow belfry]

Hello guys, i was wondering if anyone could answer this quest. It'll be big help, ty in advance

[supple island]

remember that x^-n=1/x^n and that x^(1/n)=nroot(x)

[fallow belfry]

so correct answer is 1/9?

[supple island]

correct

[fallow belfry]

thank you ❤️

[ember garnet]

Yeah I think it's C

[solemn steppe]

im very stuck on this one because there are no logs. Does anyone mind explaining how to find the answer to this one? I tried plugging it into my calculator but that didnt do anything

[ember garnet]

An exponential will always grow faster than any polynomial. So you can exclude c, d, e. When you have polynomials, the larger the degree the faster it grows, so the answer here is a.

[solemn steppe]

OHHHHH thank you that makes a lot of sense

[ember garnet]

You're welcome

[solemn steppe]

So just to make sure I'm understanding this correctly, out of c, d, and e, or the entire problem, E would grow the fastest because it is an exponential but also because it's degrees are higher than C and D?

[ember garnet]

When there is an exponential you can ignore the polynomials. E would grow faster because the base is larger (5)

[solemn steppe]

OHHH

Damn bro your so smart

thank you

[ember garnet]

No problem

Also keep in mind that exponentials grow faster only when the base is greater than 1 @solemn steppe

[solemn steppe]

Ohhhh

thank you so much

Does infinity also correlate to DNE? because i got infinite but thats not an option here...

[ember garnet]

Yes. If the limit exists, it must be a real number. Infinity isn't a real number.

[solemn steppe]

I see, thank you

[junior egret]

Could anyone tell me the distributions for a)i and b)i I'm slightly confused in the one in a binomial?

[ember garnet]

for a) i), P(X) = [10 choose X] * 0.15^X * (1-0.15)^(10-X)

[junior egret]

That is binomial or?

[ember garnet]

yes

[junior egret]

and b) i) ?

[ember garnet]

i guess it's P(Y) = 0.85^(Y-1) * 0.15

[solemn steppe]

the picture is unclear but it is lim x->-3^-

[twilit crane]

It's C

[solemn steppe]

Could you possibly explain how you got c?

[twilit crane]

So
Lim f(x)
X-->-3-

Means the limit when f approches -3 from the left

[solemn steppe]

ohh

so all the rest would be wrong because

they all pass -3 from the left correct?

[twilit crane]

Yes

[solemn steppe]

OKAYY THANK YOUU

[twilit crane]

You're welcome

[twilit crane]

Which means that in that case the limit is a real number not -∞

[solemn steppe]

I seeeee

damn these people are all so smart

[twilit crane]

Don't worry mate you will learn all of this and it will be so much easy

[solemn steppe]

thank youuu

[left knoll]

Can someone help me out with this?

[ember garnet]

When the quadratic is written as x^2 + bx + c = 0, if (x1, x2) are the roots, then x1+x2 = -b and x1*x2 = c

[harsh barn]

Help with this pls

[ember garnet]

sqrt(x) is increasing, 2-x is decreasing. They meet at x=1, so x>=1 for inequality to be true.

[hot arrow]

thank youuuuuu

[hot moth]

Prove that for all natural n :
n³+3n²+2n can be divided by 6

[winter grail]

its equal 3(A)-2(I3)

[subtle sequoia]

hi, can i ask something?

what is (m angle R = 60)

[peak gale]

by posing: u(n) = expression(n) , maybe try to prove for n=1 that's working, then find a recurrence like u(n+1)= u(n) + g(n) where g(n) is also divided by 6

[peak gale]

and try to find a basic factorization of u(n) by using the cubic identity

[neat bramble]

that just means measure of angle r is 60 degrees

[left knoll]

Can someone please explain why A & B will be: A(2h,0) & B(0,2k) - Ik the reason for 0 in these coz its obvious but confused with the other coordinates

[ember garnet]

Thales' intercept theorem: if two lines are cut by a set of parallel lines, the segments cut by the parallel lines on one line are proportional to the corresponding segments cut on the other line. So in this picture, AP/AM = BP/OM.

[left knoll]

Oh okayy, thank you! @ember garnet

[ripe bay]

If the message above contains a link to free nitro, it is most likely a phishing link. Please DON'T click on it to protect your privacy. You can notify the peeps by tagging them ( @peeps ) and they will take care of it as soon as they can. Please don't ping them if someone else already did in the chat thank you.

[quasi nova]

I want to be good at math is there any tips

[modest compass]

main thing is practice tbh, but maths take a particular way of thinking which makes your life easier when you think that way

[rigid solstice]

Hi guys I was wondering if anyone could help me with this question. It'll help me a lot. Ty in advanced

But it would be good if you show the solution. I am really appreciated either way 🙂

[sonic jolt]

I'm not a mathematician, but maybe this is correct:
16+4x=14+10
16+4x=24 /*2
32+8x=48
-> 8x=16

[rigid solstice]

thank youuu ><

[supple island]

<@&942391219206647828>

[trail swift]

thanks

[peak bison]

May I ask how old are you?

[prisma jolt]

:<

[winter grail]

1 & 3 could be solved by taking derivative of h(x), then set h'(x) = -0.64 = .... with function h(x) and solve for x and h(x)
2 is irrelevant cause h(x) is a function of a ball
4 find the derivative = 0 and solve for x then there is the maxima

[unborn mulch]

Can anyone help me with this; the maximum value is right but I keep getting the min wrong; I keep getting 0.073, can someone double check to see if I am right or wrong ?

Never mind got it

[pastel pecan]

visualize it
don't just solve problem but understand what the question is asking and what the answer represents

but solve a shit ton of questions

[azure shale]

@forest torrent

[gilded portal]

Does anyone know a specific place whether it be a discord server or a website where i can reach out to and have an online discussion with a person who is experienced in the subject (math)?

Im tryna understand how to prove the chain rule of derivatives using delta epsilon

[rigid solstice]

16 yrs old

can some Americans tell me the name of the math book you use in Grade 11, please? Thanks in advanced

[violet mason]

Hahaha omg epsilon delta stuffs are seriously so hard to understand

If you find the proof please show me hahaha

Im very interested at it

[left knoll]

Delta Epsilon proofs aren't too bad. I would look at stack exchange math for help if you need it

[noble viper]

The picture below is the solution for this question. One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill the cistern in 6 hours and 40 minutes. Find the time that each pipe will take to fill the cistern. I just want to know why we cant just add up the time like x+x-3 = 20/3, why we gotta do 1/x + 1/(x-3) = 20/3

[ember garnet]

if one guy needs 1 day to paint a wall, will two guys need 2 days to paint the same wall?

[noble viper]

probably not

[ember garnet]

so you don't just add them up

[noble viper]

so why do we do 1/x?

[ember garnet]

Power is work divided by time. P=W/t. Pipe 1 has a power of 1 cistern per x hours [P1 = 1/x], while Pipe 2 has a power of 1 cistern per (x-3) hours [P2=1/(x-3)]. When you have both pipes working together, the total power is the sum of their powers, so P = P1+P2 = 1/x + 1/(x-3). Now, the final amount of work is still 1 cistern. So W=1. So if you solve for time in the first equation I wrote, t = W/P. So the time it will take for the two pipes is t = 1/P = 1/(P1+P2). If you invert both sides, you get the simpler form 1/t = P1+P2 -> 1/t = 1/x + 1/(x-3)

[noble viper]

ty

[ember garnet]

yw

[wooden lodge]

does anyone have good resources for learning discrete math?

[peak bison]

In the 11th grade, I studied a math textbook called Algebra and Calculus

[plain flicker]

hello every1 this one's simple but I just couldn't wrap my head around why $3000 has to be deducted??

[ember garnet]

she gets 4% of sales over $3000. If the sales were less than $3000, she would get nothing. If the sales were $3001, she would get $0.04 from that.

[plain flicker]

made it much easier to understand, thanks!

[ember garnet]

yw

[soft stag]

Is there a way to let my calculator solve this?

Thats the outcome i want to get with my calculator

but it says error

[vocal zodiac]

what kind of calculator do you have

[soft stag]

casio fx-991DEX

not graphic one

would be so big if thats possible somehow

[vocal zodiac]

im unfamiliar but probably not

does your equation say x^(-0.8)?

[soft stag]

im just looking for an easy step by step guide how to get to this one

Yes

[vocal zodiac]

yea!

it helps me to put it into fraction notation first

[soft stag]

How would you do it?

[vocal zodiac]

x (-4/5) divided by x (1/5)

are you familiar with rules when exponents have the same root?

[soft stag]

hmmm but i wouldnt know that ^-0,8 is -4/5 in my exam

[vocal zodiac]

that's fair

let's just work with -0.8 then

[soft stag]

My problem is that i study tax law and this is just a little step for a big calculation but i cant remember my whole math in school lol

[vocal zodiac]

yea i gotchu

[soft stag]

i need the easiest way it doesnt matter if its long

[vocal zodiac]

so when you're dividing by exponents with the same root, you just subtract the exponents

i.e. x^b / x^a = x^(b-a)

in your case, x^-0.8 / x^0.2 = x^(-1)

[soft stag]

Couldnt i just use 1 instead of x and put it then into my calculator? because 1^-0.8 / 1^ 0,2 = 1 so i would know its 1/x?

I know that i need this calculation 100% im just afraid that my prof changes the numbers a bit

[vocal zodiac]

yea but with more complex equations and numbers, it will be rough

better to know the formiula

[vocal zodiac]

this one

[soft stag]

But when i get the solution that its in this case x^(-1) i still dont know how to get to 1/x or how to get rid of the ^-1

[vocal zodiac]

anything to the -1 power is

1/that number

6^(-1) is 1/6

[soft stag]

that is all i need

[vocal zodiac]

perfect

[soft stag]

Doesnt matter which numbers he uses i just use your formular and then just calculate it

[vocal zodiac]

bang bang

multiplication of exponents is the opposite

[soft stag]

I really need to repeat those standard math rules. It is so embarrassing

[vocal zodiac]

yea its alright

[soft stag]

Doing high bachelor shit but cant do simple maths

[vocal zodiac]

when you're in the workfield, you'll probably just gogle it

[soft stag]

yeah i just use exel all day

[vocal zodiac]

yea that's dope

[soft stag]

So thanks again! Have a great day man

[vocal zodiac]

you too bro.

glad I could help

[ember garnet]

110

[ember garnet]

he probably just meant the absolute value of the slope

[ember garnet]

Numerically, yes. But, usually, when you compare slopes you refer to their steepness, so their absolute values. For a certain distance in x (run) L2 will have a greater change in y (rise), in absolute value at least. So L2 is steeper than L1.
I'm not a mathematician, though. If someone knows better they could give you another opinion.

yw :)

[left knoll]

https://www.youtube.com/watch?v=9O8LaUhluHI

[leaden shoal]

can braking distance only be found on a diagram?

[twin bloom]

Hi! I am 18 years old and I want to learn math from 0.
I graduated from high school in philology, where I didn't do math at all. But I like a lot economy and I want to learn math for that.

What should I do?

p.s: sorry for my english

[winter grail]

I would recommend Khan Academy

They have good basic stuffs there

[soft stag]

Is there a way to get a fraction like 3/4 into 1/ something ?

[ember garnet]

with whole numbers, no. Otherwise, it's 1/1.333...

[supple island]

you can write 1/(4/3)

which is basically what he was saying

[soft stag]

How can i solve this?

Because i thought i could translate 3/4 into 1/n then and then just multiplay it with n

it makes me problems that both of the fractions are not 1/n

[ember garnet]

they don't need to have the same denominator to multiply them

[soft stag]

So how do i get the 3/4 to the right side

if it would be 1/4 i would just multiplay with 4

[ember garnet]

multiply both sides with its inverse

that equation becomes y = (4/7) * x

[soft stag]

That is my solution @ember garnet

[ember garnet]

that is correct up to the second line, I don't understand what you did in the third line

why did 4/7 become 16/21?

[soft stag]

wait i have to check

I was wrong

Sorry

[sacred garden]

also remember that x =/= 0

[soft stag]

You helped me!

[twin bloom]

Thank you!

[edgy ridge]

hello can someone help me with this question?

[tranquil berry]

Assume t+1/t as x and u can do by substitution method

[delicate cave]

thank you !

[left knoll]

@balmy star very sorry for ping but what is this

[balmy star]

don't click

[left knoll]

which class level is this?

okk

[muted sky]

https://docs.google.com/forms/u/0/d/e/1FAIpQLSeViAR-ydvcQYu5gbtHgdIVEljOzIetipYaLDGc5I0nEVkq9g/formResponse

respond this thnk u

[solemn steppe]

anyone mind helping me on this one?

[solemn steppe]

I think I got it actually would anyone mind checking?

[ember garnet]

looks correct to me

[solemn steppe]

Thank youuu

[ember garnet]

np

[silk rivet]

anyone mind helping me with this problem?

[left knoll]

answer : a ?