math-help

[fair pecan]

i think there's a typo. The f(x) should be P(x), unless im overlooking something

[undone ledge]

Omg phew, I was staring at it for 20 mins frustrated I was thinking it was a typo too I will ask my teacher thanks!

[rare schooner]

try solving it with P(x) to confirm if its a typo or not

[undone ledge]

yeah it was haha.. thanks!

[rare schooner]

Good to hear 👍🏻

[rare schooner]

anyone have an idea whats the answer

[gloomy fiber]

How can I draw this function? Can't I just divide it by e^1/(x+4) and draw the f(x)=(x+3)/(x+4)?

[candid rivet]

i don't think you can be really accurate, but the idea would be to graph x+3 / x+4 and then multiply it by exp(1/(x+4)) which you can say is a function having certain limits on ±infinity and around 4, so in the end it is a function that you kind of know the shape and the limits.
If you want to go further you could calculate the second derivative to know if it concave/convex

[barren ferry]

if you want to draw the function you can use this code :

import matplotlib.pyplot as plt
from math import exp
import numpy as np

N = 1000

function

def f(x):
return ((exp(1 / (x + 4))) * (x + 3)/(x + 4))

x = np.linspace(-1,1,N) # modify this interval
y = np.empty(N)

for k in range(N) :
y[k] = f(x[k])

plt.plot(x,y,"-",label="function")
plt.xlabel("x")
plt.ylabel("y")
plt.legend()

[rocky moth]

The sum of the squares of two positive integers is
208
. If the square of the larger number is
18
times the smaller number, find the numbers.

should the no be x, 208-x

??

[candid rivet]

x<y
x²+y² = 208
18x=y²

so x²+18x=208 which implies x=-26 or x=8, but by definition x is positive, so x=8

Hence 8²+y²=208, y²=208-64=144, y=12 (and not -12 because y is positive)

[rocky moth]

thanks but i wanted it to be in 1 variable

but thanks

[hushed condor]

hello anyone can help me with b and c for this question?

[viral gorge]

Hey there, is there any German speaker here who has probability and want to study with me 😭 , dm me 🙏

[mellow glacier]

Anyone from poland here?

[rare schooner]

anyone know the solution?

[dull bear]

Did you try to multiply the terms and then solve them individually?

like first you would simplify the algebraic stuff

and then put a differential on each term

and then use the power rule, product rule & stuff

IDK for sure i'm taking a guess here

[rare schooner]

Yeah I tried it thanks

[lusty moon]

Does anyone have a book suggestion for self studying statistics and probability at undergraduate level?

[rare schooner]

uh i'd suggest this.. i hear my friends saying it helped them begin their stats so..

https://books.google.co.in/books/about/Introduction_to_Probability_and_Statisti.html?id=Fw7vOXESqwsC&source=kp_cover&redir_esc=y

hope it helps

[worn rune]

Thanks

[untold comet]

Is there something wrong with my setup

[meager valve]

chat
whats a overly complicated way to get 9 as an outcome from an equasion thats not like 6+3

[nova mist]

idk how to simplify this.... :((((

I did the derivative correctly, I checked on mulitple calculators online

but I can't seem to get from that point to the correct answer which is apparently

this is the original problem....

[rancid olive]

How do I do this???? I'm so confused...

[echo birch]

I dont understand help-

ap stats is making me explode

[vale oyster]

brainly.com

[vale oyster]

found this on quora, interesting honestly

[coarse vault]

anybody good at precalc trig dm me por favor

[left knoll]

why we use parametric form ? when we use it in parabola why do we take at^2 and 2at and not somthng else like Y^2/4 nd Y^2

[left knoll]

y² = 4ax
in parametric form, we try to represent x and y in terms of a single variable which satisfy the equation of parabola
it need not to be (at², 2at) it can be something like (a/t², 2a/t) as well

the standard parametric form is (at², 2at) just cause it somewhat easier to solve?

[left knoll]

oki got it

[vale oyster]

what do you need help with

[vale oyster]

you applied the formula wrong in the 2nd line

[left knoll]

the question was to find derivative of (x² + 3x - 4)/(x² - 1) :P

[left knoll]

x² + 3x - 4 = x² + 4x - x - 4 = (x - 1)(x + 4)
f(x) = (x² + 3x - 4)/(x² - 1) = [(x - 1)(x + 4)]/[(x - 1)(x + 1)] = (x + 4)/(x + 1)

use quotient rule from here
f'(x) = [(x + 1) - (x + 4)]/(x + 1)² = -3/(x + 1)²

which is just -3/(x² + 2x + 1)

[left knoll]

is that chatgpt?

[vale oyster]

yeah, i just simplified for easier calculation

[left knoll]

you've found derivative for completely different function ;-;

uh, the first line-

[left knoll]

this was the original question

[vale oyster]

thats the same function, i just simplified it

[left knoll]

and they've got this via online calculators (most prolly chatgpt)

[vale oyster]

wait ill put it on a calculator for you

[left knoll]

;-; welp, alright ig so

[left knoll]

mhm

[vale oyster]

was afk mb

https://www.symbolab.com/solver/step-by-step/\frac{d}{dx}\left(\frac{-3x^{2}%2B6x-3}{\left(x^{2}-1\right)^{2}}\right)?or=input

[left knoll]

well, i didn't mean that you've done something wrong. you've solved for the wrong question T-T

[vale oyster]

man are you trolling me or something

[left knoll]

smh ;-;

[left knoll]

...

nonetheless, ig it's just turning into meaningless discussion

[vale oyster]

ohh my bad , its just popping me the first pic so i didnt notice

[left knoll]

no worries

[timid delta]

Nice

[left knoll]

What do I do when I can't solve a qsn

🥺

[hasty badge]

Get up turn go to bed and sleep ✨✨ haha

[undone ledge]

Hii can someone help me with qo8

Question 8*

Sorry if the picture is blurry I can retake it if you can’t read :>

[eager palm]

@undone ledge

[left knoll]

That doesn't help on exam

🥺

[hasty badge]

Oh then take a nap 😭😭😭

Idk tbh i’m not even god a math i hate it actually so

I say u google it or smth

[left knoll]

Sure if my invigilator decides to let me live after the nap

I m very bad at math

Hehe guess I haven't worked enough

[hasty badge]

😭😭😭

[hasty badge]

Oh no u did look ur trying by even asking ppl

[left knoll]

Nono I haven't practiced it enough thsts why

[random atlas]

help

the answer is 0
i confirmed it through python

def sin_sum(x):
  """
  Calculates the sum of sine of x, sine of (2pi/3 + x), and sine of (4pi/3 + x).

  Args:
    x: The angle in radians.

  Returns:
    The sum of sine of x, sine of (2pi/3 + x), and sine of (4pi/3 + x).
  """
  return math.sin(x) + math.sin((2 * math.pi / 3) + x) + math.sin((4 * math.pi / 3) + x)

# Calculate the sum for x = 0
x = 0
result = sin_sum(x)

# Print the result
print(f"sin(x) + sin((2pi/3) + x) + sin((4pi/3) + x) = {result:.4f}") ```

[severe cosmos]

ia there latex here

$$

$$ \fract{1}{2} $$

$$ \frac{1}{2} $$

nope

[ebon osprey]

Hello can anyone help me pls Im having trouble with this problem

[undone ledge]

thank you so so much!!

[left knoll]

sin(4π/3 + x) = sin(π + (π/3 + x)) = -sin(π/3 + x)
sin(2π/3 + x) = sin(π - π/3 + x) = sin(π - (π/3 - x)) = sin(π/3 - x)

sinx + sin(π/3 - x) - sin(π/3 +x)
sinx + sin(π/3)cosx - sinxcos(π/3) - sin(π/3)cosx - sinxcos(π/3)
sinx - 2sinxcos(π/3)
sinx - sinx = 0

[random atlas]

Thanks

[cobalt mural]

hey i got a) already i just dont understand b)

this is the answer in the back of the book but im not rly sure how they got that

[candid rivet]

by definition the equivalence classes are the sets of elements that are equivalents.
Hence x is in the equivalence class of y if and only if (x,y) is in R, if and only if f(x)=f(y), if and only if x is in f^(-1) (b) where b=f(y)

[wary mason]

@everyone! Telegram Premium giveaway and bitcoin prediction in our telegram channel!

https://t.me/cryptoo_n3wss

[candid rivet]

looks like a integration by parts, but there are probably properties/identities with the bessel function that I don't know

[candid rivet]

if it is a homework, keep trying if you have ideas, and once you're out of ideas read (and understand) the solution, and maybe a day or two later try to do the exercicse again without looking at the solution (and most importantly remember the techniques and tricks. For example, "to show this, i first prove this and then do that" )
If it is on a test, if you're stuck,give yourself 5 more minutes in which you read again the last questions, maybe also read the next question, and try solething if you've just got an idead. If not, skip the question. If near the end of the test, if you still have time or don't have enough time to start a new set of questions, come back to the questions that you've skipped.

[plucky mango]

I know that ai = (3,2,4) .
Which is the value of ak?
(i and k are indices)
🤓

[thorn wolf]

hello, anyone got some tough analysis exercises (last year hs level) to practice? thank you

[candid rivet]

(a) P(X<=2)=P(X=1)+P(X=2) =p+pq
(b) P(X=4)=pq³
(c) 1-P(X<=4) = 1-P(X=1)-P(X=2)-P(X=3)-P(X=4) = 1-p-pq-pq²-pq³

i hope i'm not wrong it's been a while I haven't done probabilities

[candid rivet]

Is that all ? It lacks of information to be solved

[plucky mango]

Yes that's why I cannot solve it

[zenith pond]

No it’s right I did it 3 hours ago

[undone ledge]

Hey guys can someone check my working out? I don’t have the answers with me…

We are supposed to differentiate

[left knoll]

yep correct

[undone ledge]

thank you so muchhh @left knoll

[fickle oriole]

pls solve this :(

[rugged portal]

can i get a check?

[limber niche]

can someone explain to me how to slove this question

the answers is in the boxes

[small temple]

which letter?

[limber niche]

abcd lol

suppose to use this right

[umbral nest]

im in highschool, need help understanding how to use this formula in word problems

i understood the geometrical sequences right away but couldnt get the hang of arithmetic 😩

probably makes sense since i prefer multiplication to addition

one of the questions is
an architect is designing a theatre

• there have to be at least 1000 seats
• the first row has 16 seats
• every next row adds 3 seats
  how many rows are there?

id like to use the formula but cant understand what n and an would be

[umbral nest]

i keep getting 329 rows 😭

so does chatGPT and wolfram alpha wtfff

the actual answer is 22 but i dont understand how to get there 🥲

[left knoll]

the answer is probably wrong

the answer would be 329

[umbral nest]

yup

actually

ive solved it with the help of some friends

[left knoll]

wait

[umbral nest]

i used the wrong formula 💀

[left knoll]

ah

in total 1000 seats

it'll be 22 then

im sorry

[left knoll]

gotta use S_n formula instead of a_n

[umbral nest]

yes

[umbral nest]

yup 💀

learned that now 😅

then use the weird formula with the discriminaTION??

THE thingy

and then yeah

you get two answers but one is negative and the other is like 21.4

smthg

yay

[left knoll]

discrimination 💀

lmao, it's discriminant

[umbral nest]

thank you 😔 im studying it in german, they sound similar and idk the english names lol

[left knoll]

ah, no worries

[left knoll]

<@&942391219206647828>

[hazy wedge]

bruh how tf you supposed to know if the coefficient factored out what is this

[candid rivet]

i think the easiest is to evaluate for x=0 (or x=another value) an then try to see what the function should be equal for this x. For instance, in your first example f(-1) is the point where the graph changes, so the graph on the right, which you know is in the form y=2f(-x+c) with c a constant, has this same point for x=3, meaning that -3+c=-1, so c=+2

Try to graph f(x)=x and g(x)=x-1 and notice how the -1 is actually translating the graph of f to the right (and not left !)

[hazy wedge]

ive lost all hope

[silver pier]

Can anyone explain me how C's conditional probability is solved

Can anyone explain what is means

[red bolt]

The diagonals of the hypotenuse quadrilateral ABCD intersect at point S. If BC=CD, SC=4 and CD=6 then AC=?.
The solution to this problem is AC=9.

does somebody know how to do this

[maiden epoch]

what do i do with sin^2(x) in this case? if it was just sinx then the result of substitution would've been t^3 dt

[fair pecan]

im assuming the power of cos is 3 because i cant make it properly. You can do cos^2(x) = 1 - sin^2(x), that way you will have one cos(x) and (1-sin^2(x))*sin^2(x). Then just do substitution with t = sin(x), and dt = cos(x)dx

[snow merlin]

its 10 fam

[random atlas]

i have not studied this topic in depth, so i don't know how to proceed furthur, should i open it up and then approach from a diff pov ?? HELP

[vale wyvern]

does it have any info related to x?
if not, I can just tell you to expand and use the infinite GP sum formula, can't go any further

[candid rivet]

Yes you can work with a finite sum (n=0 to N) and then take the limit as N->+infinity. If x²>=1 it diverges and if x²<1 it converges to 1/(1-x²)

[random atlas]

actually I found this sum in a question of center of mass, the x here was the coefficient of restitution

value of it was given 81/100

[vale wyvern]

i wrote already "if you dont have any info on x"

you are basically making cases based on assumptions but yes its correct indeed

[vale wyvern]

oh its easy then

you got the answer right?

[random atlas]

Yes

[undone ledge]

Hii can i please get some help on question c

[sick portal]

I fucked up my final

[left knoll]

Can I know how do I solve this type of questions

[vale wyvern]

can you send the whole question?

[vale wyvern]

dont give up! learn and prepare for the upcoming exams

[undone ledge]

Omg sorry I didn’t realise it was cropped

But questions c

I) and ii) I’m struggling with..

[vale wyvern]

um, my moms calling, I will get back after some time, sorry

[undone ledge]

That’s all good :))

[sick portal]

Will try to lock in and actually put some effort next semester

[vale wyvern]

in this equation if you put
f(x) = 0
you get x- 3 = 0 -> x =3
x-1 = 0 -> x =1
and x^2 + 3 cant be equal to zero cause it will give out answer in complex numbers and it is given in the question that the range should be a real number,
so the graph should look somewhat like this

dont see the y intercept or the most bottom point here, I didnt make the exact graph

its like a rough

so the point of the graph is you see the graph is cutting x axis at 1 and 3 in the original equation

and if you remember in a equation if you add "d" (any number) to x (which has happened here as f(x) is turned into f(x + d)) the whole graph moves "d" units to the left

now you gotta move the graph to the left so that 1 x axis intercept remains at the positive side and the other goes in the negative x-axis side

I hope you understand now, try to do it once, if you have any doubt just ping me

[left knoll]

is the answer A?

when you expand the summation/sigma, you'll get these sorta terms

C0C0 C0C1 ... C0Cn
C1C0 C1C1 ... C1Cn
C2C0 C2C1 ... C2Cn
and so on

in this question, we've a restriction on i and j that i ≠ j. in the table-ish form of expansion which we've wrote down, let's see the sum of each column with that restriction taken into consideration.

for the 1st column,
C1C0 + C2C0 + ... + CnC0 (there is no C0C0 term)
C0C0 + C1C0 + C2C0 + ... + CnC0 - C0C0
C0(C0 + C1 + C2 + ... + Cn) - (C0)²
C0(2^n) - (C0)²

and similarly for 2nd column, you'll get the sum to be C1(2^n) - (C1)²

when you add everything,
(2^n)(C0 + C1 + C2 + ... + Cn) - ((C0)² + (C1)² + (C2)² + ... + (Cn)²)
(2^(2n)) - 2nCn

if you're still confused, watch this video

https://www.youtube.com/watch?v=Y9piMmg1cIs

writing down terms in that table format method works for almost every double sigma problem

[left knoll]

Yea the ans is A . Thanks for helping

[pliant flax]

Can anyone suggest a nice book for matrices and determinants for engineering mathematics with lots of solved examples

[naive dew]

You can look up ‘Advanced engineering mathematics by Erwin kreyszig’. It has a chapter on matrices and determinants but I’m not sure about the number of examples

[left knoll]

can anyone teach me statistics

[undone ledge]

Ohhhhhhhhh omg thank you so much for taking time to help me!! You are amazing thank you sm 🙏🏽

[vale wyvern]

your welcome :)

[sharp plank]

Can someone teach me 12th maths

[lofty elk]

ther is someone here study computer science first year ?

[vale wyvern]

youtube exists bro, try finding videos in your language and if you have any doubts just message here, we will help

[vale wyvern]

#study-buddies may be a more suitable channel to find someone

[jade drum]

i know this is not a book but u can practise question from it

[dire aurora]

Can someone please help with this question?

[heavy valve]

expand:```
a^2 + 2ab + 2b^2 + 2bc + 2c^2 + 2cd + d^2 = 4ab + 4bc + 4cd

bring all terms to one side:```
a^2 - 2ab + 2b^2 - 2bc + 2c^2 - 2cd + d^2 = 0

factor:```
(a-b)^2 + (b-c)^2 + (c-d)^2 = 0

Notice that each value is squared, and thus must be positive. The only positive value which can be added three times and still equal 0 is 0.

so a-b=0, b-c=0, c-d=0 => a=b=c=d

[undone ledge]

Hii can i please get some help for question 3 a and b

[dire aurora]

ohhh I couldn't find the perfect squares for the life of me because I didnt think to split up the 2b^2 into b^2 + b^2, for instance; where one is the last term of one expanded perfect square and the other is the first term of the next expanded perfect square.

a^2 - 2ab + b^2 + b^2 - 2bc + c^2 + c^2 - 2cd + d^2 = 0

(a-b)^2 + (b-c)^2 + (c-d)^2 = 0

[dire aurora]

thank you so much

[left knoll]

y = m - 3x and y = 2x² + 3x - 1
m - 3x = 2x² + 3x - 1
2x² + 6x - (m + 1) = 0

if the line "cuts" the parabola then the above equation will have 2 real and distinct roots so discriminant > 0

[undone ledge]

Hmm.. I did that but the answer says it’s “m>-11/2

I understand how to get to that point I’m just a bit confused how to get to the end answer..

O.o

[thorn surge]

is this reasonable?

[left knoll]

discriminant = b² - 4ac
(6)² + 4(2)(m + 1) > 0
36 + 8m + 8 > 0
8m + 44 > 0
m > -44/8
m > -11/2

[undone ledge]

:OOOO OMG…

THANK YOU SO MUCH ❤️

[signal flax]

how do you type superscript

[left knoll]

im on phone rn and gboard has that feature :P

[pearl gazelle]

¿Does anyone recommend a group theory bibliography?

Or abstract algebra.

[thorn surge]

computer engineer

kiddo

I was in your shoes back in the day

Susanna S. Epp

[candid rivet]

i don't understand the first and third =
but and easy way to solve this is to see that 1/ln(n) > 1/n for n bigger than 2 (and then it is just a comparison test for positive terms)

[dire aurora]

Can someone factorise this fully please?

this is the answer

[dire aurora]

Thank you very much guys

[ripe cargo]

I found log5^e

?

[maiden epoch]

where do I have a mistake? value cant be negative

[fair pecan]

i think the problem is in the way youre trying to find V2

[maiden epoch]

I just made V2-V1 and V1-V2 and got the answer right

[fair pecan]

awesome

[tribal grove]

any tips to be strong in mathematics , when a differen sum pop ups i feel like im blank and i totally forget the basics ? mainly having problem in calculas(lazy to go into the subjec )😭

[vale umbra]

bro..thats because when we integrate, we basically add all points wrt to the axis.. u can see here that the area under y=x2 is greater than y3=x....there u are basically substracting lower value by higher value...therefore u get a negetive value

[random atlas]

it's 1,2 and 3 ryt ?

[naive dew]

Practice like your username

[left knoll]

is the answer D?

[random atlas]

I don't have the answer

Why but 1 and 2 ?

[left knoll]

from the question, we can interpret that fox is a subset of cats but we can't anything about cats and window.

i) "no window is cat" - it means that they don't overlap each other but there could be such a case so it isn't always true
ii) "no cat is window" - it means
that window is a never a subset of cat but there is be a possibility where both window and fox are subset of cat but don't overlap each other.
iii) "some cats are fox" - it is always true as the question itself says that fox is a subset of cats
iv) "all cats are fox" - it can't be always true, as mentioned above there is a possibility where cats set and fox set both are the equal but it isn't "always" true

[bold atlas]

yo peeps , help me out thinking this one out :
no of terms in expansion of 1 + x + x2 to power 11

[random atlas]

Thanks for the explanation

[polar glade]

formula: C(n+r-1,r) n:number of terms in parentheses r:power of number

[bold atlas]

ik the formula but idk how to use in the case of multinomials, i tried making it before square and deducing it to binomial form but didnt get optimum answer.

[left knoll]

hey guys, need help

[left knoll]

is there any restrictions on a and b? i.e whether they belong natural number set or something like that?

[left knoll]

just use the formula and you'd get the answer.
in your case, n = 3 and r = 11
C(3 + 11 - 1, 11) = C(13, 11) = 13 * 6 = 78

[left knoll]

no

[lavish copper]

can anyone help me with this one please

[gaunt saffron]

cos^-1(1) = 0

so 9^0 = 1 and 2(3^0) = 2(1)

1-2+1=0

[left knoll]

take 3^(arccos(x)) = t
t² - 2t + 1 = 0
(t - 1)² = 0
t = 1
3^(arccos(x)) = 1
arccos(x) = log_(3) 1 = 0
x = cos(0) = 1

[dire aurora]

Can someone please help with the above

[gaunt saffron]

let the fathers age = f and the sons age = s

f = s + 24 and f - 12 = 2(s-12)

solving simultaneously,
f = s + 24
and
f = 2(s - 12) + 12
f = 2s - 12

thus s + 24 = 2s - 12
s = 36 years old

[dire aurora]

thank you so much

[dire aurora]

Can someone please help with this?

linear equations

[dire onyx]

part of tank filled in 6 mins = 1 i.e., = full
-> part of a tank filled in 1 min = 1/16 = 1/time taken to fill with inlet valve

part of tank emptied in 10 mins = 1
-> part of tank emptied in 1 min = 1/10 = 1/time taken to drain with outlet

part of tank actually filled = part of a tank filled in 1 min - part of tank emptied in 1 min
= 1/16 - 1/10
= -3/80

thus, part of tank filled = 1/time taken to fill if both working
-> 3/80 = 1/time taken to fill if both working
-> time taken to fill if both working = 80/3 mins = 26.7 mins

answer 26.7 mins

[dire aurora]

the textbook's answer is 15 min

ill check whats up tomorrow morning. Thanks a lot for your help!

[gaunt saffron]

the rate the tank fills per minute is 1/6 (assuming a full tank = 1)
the rate the tank empties per minute is 1/10

thus the net rate per minute = fill rate - empty rate
= 1/6 - 1/10
= 5/30 - 3/30
= 1/15

thus the tank fills 1/15th of its capacity per minute

if a full tank = 1
then maximum capacity after time t equals...
1 = 1/15 * t
t = 15 minutes

neo had right idea just did oopsie for rate of fill

[dire aurora]

oh thanks for that. I knew neo was already right in the way that matters, just didnt have time to look. I didnt think about using rates when I looked at the question because i was hung up about using pronumerals to represent the question as other questions in that set of questions involved.

[rocky moth]

is 1 +sin^2θ =3 cosθ*sinθ then prove that tanθ=1,1/2

PLEASE HELP

[rocky moth]

thank you

[ebon sail]

Please help me with this: Calculate the coefficient of x^50 in F(x) = (1+x+x^2+...) (1+x^2+x^4+...) (1+x^5+x^10+...)(1+x^10+x^20+...)(1+x^20+x^40+...)

I made it up to F(x) = 1 / [ (1-x)(1-x^2)(1-x^5)(1-x^10)(1-x^20) ]

But unable to do anything more

[vale wyvern]

I dont think you do this question using infinite GP formula

rather you would have to calculate each possible variation of powers of x taken from each term, so that when they are multiplied with each other they should add upto 50

It sure will take time, if this comes in my exam I would prolly skip over to come to it at last (if time is left) cause this is surely a time taking question

or maybe there is some another method which I am not sure of

[raw relic]

@ebon sail use the multinomial theorem

[dire onyx]

fuck

[lethal elbow]

hey

i have a problem

hcf and lcm of 72 and 120

[maiden epoch]

The assignment was to calculate the eigenvector and "check for correctness by definition". why did she multiply the original matrix by the eigenvectors to check for correctness and got some random numbers?

I got same eigenvector values, but I dont get that "correctness check"

[deft jetty]

seems like they multiplied the eigenvector by that matrix to see if it produces a scalar multiple of that eigenvector.

If it does then it confirms that it is indeed an eigenvector.

Definition of Eigenvector: Av = lambda*v

[lethal elbow]

hey any body here

A line intersects Y-axis and X-axis at point P and Q, respectively. If R [2,5] is the mid - point of line segment PQ, then find the coordinates of P and Q................. PLEASE SOLVE IT

[lethal elbow]

thank yiu bro

[left knoll]

Hi ,I need Quick help with something (im sick ) my brain isn't working

I need the result in watts

But I got J / kelvin

[small temple]

can someone solve this? the text in english is: If [1º expression], the value of [2º expression] is equal to

[lethal elbow]

hey any body here

Find the ratio in which the line segment joining the points A[6,3] and B[-2,-5] is divided by x-axis.......................please solve it

[left knoll]

there it is :))

[bold atlas]

how do u integrate sqrt[(1+x^2)/x^3]

[vernal osprey]

Does anyone help me solve this

I am using partial fractions

But I think the values of { A=-1 and B=10 } is wrong I guess !?

[left knoll]

This is what I got as the answer, make sure to factorise the quadratic correctly and use an appropriate method to find A and B (I'm using the cover-up method in my example), I'm not too sure how you got A=-1 and B=10...

[vernal osprey]

Yeah my factorisation was correct

But can you explain me the coverup method !?

[left knoll]

Yes, once you have factorised the denominator, remove (cover up) one of the terms and whatever value makes the covered up term equal to 0 you substitute in that value into the rational function, so in the case for A, we cover up (x-2) and substitute in 2 into the rest of the rational function which gives us 4, this only really works when we have linear terms in the denominator.

[vernal osprey]

Ohh

Ok ….so now I get it

This cover up method is different than that I use

[left knoll]

yeah, its just faster and doable in your head

[vernal osprey]

Yeah thank you for your help 😀

[left knoll]

np

[dire aurora]

Could someone help with this one?

[dire aurora]

Also, can someone explain this particular proof by contradiction? i dont understand the contradiction.

[undone ledge]

Heyy… guys im stuck on question d and e could I please get some help….

[dire aurora]

find equation of line RT and then solve simultaneously (i.e by equating the y variable in both equations, or otherwise) with the cubic equation to find coords of P and T, with P being your answer. To do this, you need to the find the derivative of the cubic so you can find the coords of the local max, which is also T as given and lies on the line RT. Since T lies on the line RT, and you have a second point R at (40, 0) that also lies on RT, you can find the gradient of the line RT which lets you form the equation of the line RT in the gradient intercept formula given you have the y intercept of the line. The y intercept is coincidently already found as the y-coord of the local max of the cubic. If there was no such coincidence, you can find the equations of the line RT with the two-point formula of a linear function, or derive it yourself by means of equating two equations for the gradient of a function as the gradient between any two points of a line is the same i.e x1 - x/ y1 - y = m = x2 - x/ y2 - y, with an x and y variable in each equation left unplugged and plugging in the 2 two pairs of coord that you have.

for part e, use pythagoras theorem, where the magnitude of any length is the square root of the sum of the squares of perpendicular lines that form a right-angled triangle with the length. The same applies for the length of PT, where the lengths of such perperdicular lines are x2 - x1 and y2 - y1, where (x1, y1,) are the coords of one point and (x2, y2) are the coords of the second point. these have already been found at this stage as the coords of P and T and it is coincidental that two of the four coordinates for you are both 0 as this makes finding the length more logically obvious.

[left knoll]

@random atlas

Did u find the correct answer about that?

[random atlas]

D

[cursive sun]

hi all, i forgot my book at school and i really need one rn
does anyone have a copy of the as level economics cb?
thx

[undone ledge]

:DDD this is such a huge help thank you so so so much

[left knoll]

This integral is not solvable indefinitely 😦

[forest trail]

Does anyone know how to solve this problem? The answers are on the right corner

[forest trail]

The lowest terms 2 can be described is 2/1 and a^2/ b^2 has to in the lowest terms but b^2 > 1 so it's contradictory

[left knoll]

This is how I did it, the key trig identiy is cos2x=cos^2x-sin^2x, this allows you to get the exponents on the LHS in the same form.

There are also some more solutions but I only provided the exact-form ones like the answer in the question did

[forest trail]

ahh thank you that makes sense now

[left knoll]

np

[dire aurora]

Why is b greater than 1 and not possibly equal to 1 other than for the fact that they say so in the proof? Surely b is any integer not excluding 1

Because the premise is the assumption that root 2 is rational, as in that it can be expressed as a fraction/division of integers

Oh because root two is not a whole number. Oops. That makes sense. Thanks!!

[sleek prism]

hmmmm hi? happy new year first to all of you guys! just got a simple basic question

here is somebody who knows nothing about math not even a single simple thing not even the basics and its the exam year so too bad hah... i was searching but got exhausted of all the info. so my question is, can somebody just tell me where and how to start? good to mention: when it comes to numbers, my brain cells quit their job.

[strong drum]

khan academy

look for the website and they have courses from 0 to university level

so just start from the course you like

[sleek prism]

so i go there and search a course for beginners?

[strong drum]

khanacademy.org

yeah it's all free

you can donate if you want, and yeah there are course for beginners

[sleek prism]

imma check it out

[sleek prism]

thanks a lot for your help 🫶

[dire aurora]

Apologies for typo about the coords of P and T

[undone ledge]

hahah thats okay i figured it out :DDDD

[lethal elbow]

any body here

[left knoll]

me 🖐️

[lethal elbow]

the product of two consecutive positive integers is 306. We need to find the integers please solve this question

[left knoll]

n(n+1)=306, then solve for n

so n^2+n-306=0

n = 17

so it is 17 and 18

I rejected the other solution for n because it states that the numbers have to be positive

[rocky moth]

At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

can anyone please solve it

[left knoll]

can you help me with this?

[acoustic aspen]

Well, i know I'm neglecting my own assumption at the very end but that's the best I have. Even if it's not the correct or full answer, i hope it helps at least in some way

Okay, nvm. I found the correct answer on this site:
https://www.cuemath.com/ncert-solutions/at-present-asha-s-age-in-years-is-2-more-than-the-square-of-her-daughter-nisha-s-age-when-nisha-grows-to-her-mother-s-present-age-asha-s-age-would-be-one-year-less-than-10/

[rocky moth]

hey thanks alot

[rocky moth]

tbh i hate these age-related questions

[acoustic aspen]

yo, same. I remember I was doing them like 3 years ago, so I am a bit embarrassed now that I couldn't make it but it's honestly so confusing. All it takes is a small error at the very beginning and you're doomed

[rocky moth]

actually it was made to be solved in one variable but since they asked 2 ages i was confused since 2 variables were needed to used

also language is kinda bad

[dire aurora]

Would you say this proof is lacking because, even though b^2 is not 1, a^2/b^2 = root(2) or, root of any non-square counting number for that matter, can still be true if a/b when raised to the second power causes the expression to then no longer be in smaller terms and have a shared factor other than 1? Why do you say a^2/b^2 has to be in lowest terms when only a/b explicitly has to be? for the proof to be sound, do you also have to show that if a/b is in lowest terms that (a/b)^2 must also? if so, how could you do this

[dire aurora]

we know that if a is a multiple of an integer, that a^2 is a multiple of an integer too. but that isnt enough to say that if a^2 is a multiple of an integer, that a is also a multiple of something. I feel like that is what the proof needs for it to be sound

ok i have what i need to make the proof rigourous !

lmk if u want to know

[rocky moth]

prove that (tan θ + 2) (2 tan θ + 1) = 5 tan θ + sec2θ . i think this question has a mistake

can anyone confirm this for me

[dire aurora]

sure

[rocky moth]

i think it should be 5tan θ + 2sec^2θ

[dire aurora]

you are correct

question is wrong

[rocky moth]

thank you for confirming

[rocky moth]

hey which software is this ?

[dire aurora]

desmos

[rocky moth]

thanks

[dire aurora]

on browser

Can someone prove this equation? I took a = sqroot(2) b = sqroot(5) and n = 2. Thanks

[rocky moth]

i think this is outta my league

[tribal iris]

I'm not sure, but perhaps one can argue that way. If you add the two inequalities, you get that (p+1)/n < b. In this case, you know that p/n is strictly less than a and p is chosen so that it is the maximum integer close to a. That is, (p+1)\n > a.

[cosmic kestrel]

if p/n<a then p/n+1/n<a+1/n. In the same time we know, that a+1/n<b. So (p+1)/n<b

Also (p+1)/n > a because p is the** greatest** integer that satisfies p/n < a

[left knoll]

Guys, can someone help?

[dire aurora]

@tribal iris @cosmic kestrel Thank so you much

[rocky moth]

which part of mathematics is this ?

[left knoll]

topology/functional analysis

[left knoll]

You need to first construct a function f from \Pi_{t\in T}X_t to \Pi_{s\in S}\left(\Pi_{t\in T_s}X_t\right) that acts by sending each point in the product space to a "tuple of tuples", where each inner tuple corresponds to the coordinates in one of the T_s products. This function essentially reorganises the coordinates without changing them.

Then you need to show that f is bijective, this can be done by showing that each element in the domain has a unique image in the codomain and that every element in the codomain is an image of some element in the domain.

Next you need to show that f is continuous by using the definition of the product topology to show that the preimage of a basic open set in \Pi_{s\in S}\left(\Pi_{t\in T_s X_t}\right) under f is open in \Pi_{t\in T}. Since the product topology is generated by the basis elements that are the product of open sets in each factor space, you can show this by considering the preimage of such a basis element.

Finally, you need to show that f^{-1} is continuous, you need to show that the inverse function f^{-1}, which takes a "tuple of tuples" and reorganises it into a single tuple, is continuous. Again, you would use the definition of the product topology and the continuity of projection maps to show that the preimage of a basic open set is open.

You can conclude from here that f is a homeomorphism and thus the two product spaces are homeomorphic. — [Put the math into a LaTeX editor if you are struggling to read it].

Thank you so much, bro🫂

np

[azure kestrel]

Hii, can anyone help me with this equation?

[loud dock]

I’m not sure but maybe you have to calculate N for t=0 and t=10. Then you do the ratio of N(0) to N(10). All multiplied by 100 and you get the rate of increase. But I’m not sure if it answers to the question (PS : I’m French and I have doubts about my understanding of the question )

[acoustic aspen]

I believe you've got to count a derivative function

[azure kestrel]

i think its derivative function too, but im lost at how to start the equation

[acoustic aspen]

okay, hold up. give me a sec

[azure kestrel]

it's okayy, i have doubts understanding it too T^T but thank youuu

[acoustic aspen]

N(t) = t^2 + 5t + 106

that means your derivative function will be:
N(t)' = 2t + 5

now, as we know, our t is 10, so we put that into our derivative:
N(10)' = 25

okay, well, here it's getting a bit tricky. How do we calculate the percentage rate is essential. I'll try too look it up

[azure kestrel]

could it be like how malo said, find for both 0 n 10 , n then find out the percentage ?

[acoustic aspen]

hmm, i don't think so. In the task it states clearly about the percentage rate in 2010. Year 2000 is only mentioned to set limits in which function operates. But at the same time, I'm not an english native so i might be getting lost in translation here

[azure kestrel]

damn it ;-;

thanks for the help tho, appreciate it

[acoustic aspen]

i've got an idea to solve it but you've got to give me some time xd it's a bit funky way to do it but it might work

[azure kestrel]

sure2, take ur timee

[acoustic aspen]

I am highly suspicious of my answer. I might have only complicated the whole task... Maybe Malo was indeed right oops xd

okay, yeah. my answer is incorrect. if rate can be over 100%, then 90*=/=100%

[azure kestrel]

I like how you put effort into the mini stars 😭 ✋, since I have no idea how to do it, I'll def keep urs as a reference for now. Thanks Lenii!!

[acoustic aspen]

and Malo was completely right haha

[azure kestrel]

😭 its alrightt, i'll double check with my lecturer tomorrow then, thanks to both of you

[acoustic aspen]

no problem, had fun solving it myself haha. I guess you learn something everyday

[azure kestrel]

trueeee, but it def wasnt fun for me ;-; lmao

[acoustic aspen]

qwq oh i'm sorry. It's okay, I'm certain your lecturer will make sure you'll understand it so you don't have problems with such tasks in the future uwu

[azure kestrel]

naurr don't apologise, you tried ur best to help me huhu,im the problem lmaoo anyways~

[acoustic aspen]

studying is process, just because you don't understand or cannot do something doesn't mean you're the problem uwu that's why we study, to be able to do things we aren't capable of yet. Anyways, good luck on your studying! you're doing great work!

[rocky moth]

1st part can anybody solve it for me

[undone ledge]

Hi I’m stuck on question 6 a) the main thing is I’m confused on the negative domain can I please get some help….

[loud dock]

You can try with a draw, you'll see where sin and cos intersect

[rocky moth]

Thank you for solving this question

[cosmic kestrel]

We know that sinx=cosx=root(2)/2 when angle=45°=π/4.
But you can also find out, that sin(x+π)=-sin(x) and
cos(x+π)=-cos(x), so sin(x+π)=cos(x+π) also.
You can see that via trigonometric circle. If we add π to our angle and move to the third quadrant, our point coordinates become negative, basically showing us values of sine and cosine

[rocky moth]

is the answer 68.7

percent

[rocky moth]

thank you

[rocky moth]

sorry it must be 9.7

percent

my derivative calculation was wrong

first put vale of t in the quadratic equation to get 256 then calculate the derivative and after you calculate that put t=10 in equation to get 25

to calculate percentage

25/256 * 100 = 9.7...

so the answer is 9.7%

[rocky moth]

Idk if it is correct

[azure kestrel]

THANK YOUUU 😭

[deep edge]

Hello everyonee! Does anyone of you know how to solve this? Been trying to solve it for hours and I just can't :((

[rocky moth]

i guess you should ask this question in science help section

[acoustic aspen]

that makes so much sense now damn

[grizzled dust]

been trying to study AP calculus for a about an hour and a half later and i feel like ive made nop progress, ive been doing past exam questions and i still cant answer them without looking a the answers anyone got any advice or tips?

[young steppe]

you need to figure out what is holding you back and work on it

what specifically do you struggle on when working on past exam questions

[grizzled dust]

mainly just how to go derivatives

im trying to study implict differentiation

[young steppe]

have you got all your derivative rules memorized

[grizzled dust]

sort of

i keep forgiving the basics

[young steppe]

you need to work on the basics then

the basics are most important part

you're taking AP Calc AB, right?

[grizzled dust]

yea

[young steppe]

ok

for practicing the basics of derivatives i recommend the khan academy practice questions

https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new

https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new

they are not as hard the AP questions but r good for practice

if you are struggling with grasping the idea of derivates and its rules

i recommend this youtube series

https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

it goes over everything you'll lean in calc ab

its like the sparksnotes of calculus

[grizzled dust]

thanks

[rocky moth]

Can anybody solve this problem for me

Q 17

[polar glade]

is anybody know markovchain?

[left knoll]

Can someone please confirm if this is correct for me?

[naive dew]

KE= 1/2 m v^2

Velocity squared

[left knoll]

Thank you

[left knoll]

Area of half circle

Then square

Times one half circle by 4

Add to area of square

Minus from whole square aria

@rocky moth

[rocky moth]

hey thanks @naive dew @left knoll

[left knoll]

@naive dew

What year are you in

[spice girder]

How do I become better at complex math problems? Like competition style?

[mystic thunder]

practice

[mystic thunder]

class 10 ncert?

[left knoll]

It’s already done 👍

[mystic thunder]

I was just asking cuz this is in deleted syllabus😭

[spice girder]

Why are they so tricky

Little tricksters

Evil little jokers

[naive dew]

Ill start undergrad this year

[left knoll]

Idek what that is

It’s diff in my country

[naive dew]

What it's like?

[left knoll]

Never mind

[naive dew]

I'll join college this year

Does that help?

[rocky moth]

exemplar

[rocky moth]

really ?

[rocky moth]

yo this is sad

[undone ledge]

OMG thank you so much for the explanation🙏🏽

[left knoll]

Yh

[amber vapor]

can someone help me with this problem pls

[swift crypt]

https://youtu.be/LmpAntNjPj0?si=WYk3keYRD1lG0RpZ

He will explain better than me, the video is great

[dire aurora]

Ive watched it hahah thanks. I get it now, including roots of any prime number

[swift crypt]

Did you solve this one ? I can help you if you didn't

[dire aurora]

Nope. But i only tried once. I can try again later

[swift crypt]

Soo it is not that hard try to express everything with a, like
c=a/3
b=a/2
And a is just a
and put all of that in equation
And you have
3a²+4(a²/4)+18(a²/9)-4a(a/2)-12a(a/3)
Now you have
3a²+a²+2a²-2a²-4a² and like you see
6a²-6a²= 0

[swift crypt]

Hope you get it 😃

[rocky moth]

I can

do you still need it ?

[rocky moth]

Didnt saw this message

[rocky moth]

Can anybody check my mistake

This is solution from the book and I think it is wrong

[grave elbow]

where does 3/5L and 4/5L come from

[naive dew]

Lsin theta and Lcos theta

The vector components I guess

I’m not too sure

[dire aurora]

Oh i thought you had to make the substitution at the end in order to show that c=a/3 and b=a/2. Are you allowed to substitute at the beginning

[swift crypt]

Yes you can, i done a whole question, as i said it's not that hard

[spice girder]

Is this correct

[candid rivet]

and then you know 3x=4h, 4y=3h, x+y=l
and if you add the pythagorean theorem i think you get the values

[candid rivet]

i'd try with x=y and writing the functions with small o, like sqrt(1+X)=1+X/2 +o(X) or cos(x)=1-x²/2 +o(x²). Not sure if it is enough

[candid rivet]

it's hard to guess what are alpha beta V
yet it looks alright
except maybe for the first one, V/a looks more like a tan(...)

[dim cloak]

I am baffled

I honestly idk if I look stupid or anything

I am just having a hard time understanding

when there is a shape like that

[naive dew]

GHI has the angle H in the middle which is not marked hence the congruent triangle’s middle angle will not be marked that is K. the side marked HI is at the end of triangle GHI’s name hence the congruent side shall be at the end of the name of congruent triangle that is side KL

[dim cloak]

I am sorry I am still confused 😭

I am going to try to watch another video on it

[dim cloak]

wait

could you tell me more about that side thing

[naive dew]

Yeah?

[grave elbow]

tysm ❤️

[candid rivet]

have a look at sarrus rule which is the formula of determinant 3x3

[untold shadow]

thanks i got it

[proper vault]

Does anyone have an idea on how to do Plastic Analysis?

[rocky moth]

Can anyone solve this for me

[naive dew]

The 2nd one?

[rocky moth]

all parts

since they are interelated

[rocky moth]

well ya thats the main one

[naive dew]

@rocky moth

[rocky moth]

really thanks

[tardy hedge]

how do you do this

[tardy hedge]

Thanks👍🏻

[tardy hedge]

why did you take a to be = 0 tho

[candid rivet]

well the formula is often written with (b-a)/n and here we have 1/n
If you compare to the riemann sum formula you have no choice but taking b=k and a=0

@tardy hedge

[pliant valve]

high im just wondering how to do this?

prolly basic but

for question b

disclaimer im dumb sorry

this is the matk scheme

and original graph

[pliant valve]

for (a)

[tardy hedge]

Yea I got it, thanks!

[void grove]

i think its law of ambiguous case

but im not sure how to do it 🥲

[swift crypt]

Try sin and cos thing, something like sin42°=h/10 than cos, you can mark the base of triangle with x and y (y=15-x), cos42°=10/x, than find x, than y, than with cos or sin find the angle

[void grove]

https://tenor.com/view/lucky-star-thumbs-up-cute-wink-anime-gif-17593886

thank u !

[rocky moth]

class 10th ?

cuz if it is then it is out of the syllabus

[candid rivet]

2^x=12 is the same as 2^(x-1)=6 so you want to look at the graph for y=6 and it gives you the value x such that 2^(x-1)=6 and you find x=3,6 approximately (the actual solution being 3.5849625...)

[candid rivet]

thanks for sharing the graph it makes it easier to help

[left knoll]

Depends I’m on a car rn so can’t say for sure but it’s deffo Soh cah toa

Remember it’s ^-1

[pliant valve]

tysm

[grizzled dust]

can someone explain how the top calculation jumps from that to the final answer?

[naive dew]

@grizzled dust

[grizzled dust]

wait how did you get

@naive dew

[naive dew]

Multiply 3y^2 and 1/root2y

[grizzled dust]

wait why do you have to multiply it?

[naive dew]

Wait

Let me send it

LCM

[grizzled dust]

can you also explain how it went from the last step to the answer?

[grizzled dust]

thank you so much, calculus is stomping me since its my first time taking it

[naive dew]

Keep going

And remember calculus is not hard

Algebra and trigonometry are

[acoustic orbit]

Any good youtube playlist for calculus?

[grizzled dust]

https://www.youtube.com/playlist?list=PLF797E961509B4EB5

[acoustic orbit]

🔥

[left knoll]

i need help with math

can anybody help me?

[rocky moth]

yes

[left knoll]

@rocky moth thank you! i'm sending you a dm

[dire aurora]

I don’t think youre supposed to. It said to prove by completing the square. There should be some nice pattern that results.

[glossy loom]

how to do this chat?

im not a math student btw

[undone ledge]

Hii can i please have some help with this question 10 and 11

[glossy loom]

sorry not a math stdent

[swift crypt]

Yes you are right

[blissful ridge]

I need to solve b and it says: Depending on a, investigate whether the corresponding LGS has no, exactly one or infinitely many solutions. Specify the solution set if the LGS has an infinite number of solutions. (LGS) is linear equation system. I have no idea why in the solution they assume a = 0. Can someone explain it to me? My approach was a bit different and i looked for (a+4) and my thought was -4.

Is it just me or is discord not showing the pics?

[weary arrow]

I also can't load images

Thought it was my WiFi but data doesn't work either

[quasi bridge]

the idea for that question is nth term = (sum of n terms) - (sum of n - 1 terms)
S_n = 3n² - 4n
S_(n - 1) = 3(n - 1)² - 4(n - 1) = 3(n² + 1 - 2n) - 4(n - 1) = 3n² - 10n + 7
t_n = 3n² - 4n - 3n² + 10n - 7 = 6n - 7

[ebon relic]

can someone please find R here

[ebon relic]

thanks!

[left knoll]

Given the function:
f(x,y) = 1+xy-x-y

On domain V = {(x,y) ∈ ℝ^2: x^2 ≤ y ≤ 4}. This function f(x,y) with domain V is used in parts a-c.
a) Is the domain V convex? Explain why or why not.
Afbeelding

anyone that can help me?

[somber berry]

inequality in two parts : x^2 ≤ y (1) and y ≤ 4 (2).
If we analyse each part separately :

1. if we consider any 2 points on this curve y = x^2 (=values of y) and draw a straight line between them, it will lie within or on the curve. And so this part of the domain V is convex
2. for the second case, values of y must be less or equal to 4. (in other words it should lie below or on the horizontal line y=4). If you take again two points and draw a straight line, considering the condition, it will always stay within or on the line y=4 (it's like a boundary)
   So both parts of the domain V are individually convex, and their intersections form this domain V, which is also convex.

Is it what they asked?..

[loud storm]

y=-2x^2 +8x-16, find roots

how do i find the roots of these

[somber berry]

couldn't find it bc I always find a square root of a negative number :/

[left knoll]

OMG YES!! YOU.ARE.THE.BEST!! Can you help me with another math question too maybe??? thanks a lot btw!!!

[somber berry]

hahah thank u and ur welcome! yes send me I'll see if I can

[worldly copper]

Hello guys I am trying to solve this integral for over 2 hours now and I’m still getting 0 and the answer is pi/2

Can you help me

[raven lichen]

I've done the inverse, however the mark scheme states that the surd must be a negative. can someone help explain why that is the case?

[severe burrow]

Hi, I am unsure of my working, but is it correct? Then, when it says that the firm contracted to produce 15 goods of either type, does it mean Q1 = Q2 = 15?

[left knoll]

multiply and divide with sec²x which will create sec²x dx in numerator and sec²x + tan²x in denominator

sec²x + tan²x = 1 + 2tan²x

the integral after this step would be (sec²x dx)/(1 + 2tan²x)

after this you can use u-substitution to solve the integral

tanx = u

lmk if you're still confused, i'll send a proper typed out solution

[slate lintel]

where can i find things like this to calculus 2?

[left knoll]

guys, is someone good with Laplace/Fourier transforms? please dm me

[undone ledge]

Thank you :)))

[dire aurora]

Can anyone help with b)?

[lethal elbow]

use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m.

bro any body here

[dire aurora]

Does anyone have a method for answering these?

[proud tundra]

put all the numbers under the root and compare
and the root of the two is approximately equal to 1.4
and the root of 6 = 2.45-2.5

to calculate the root of the number 6, we find the two nearest numbers of which to calculate the root and it will be an integer. the nearest ones to six are four and nine. the root of four - two, and of nine - three, so the root of six is something in between, that is 2.5

[dire aurora]

I used that logic for 14)a) as you can see but it wasnt rigorous enough

Turns out, through the calculator, the difference is so small

[dire aurora]

Oh thanks so much

[proud tundra]

you must use logic with adding to the root when you are given integers multiplied by the root

and if you are adding an integer and a root, then you look for the closest value to the number under the root (example with six)

[dire aurora]

OK thanks!!

Can anyone help with this?

[proud tundra]

• use photomath)
  @dire aurora

[dire aurora]

i dont see how that is to help me. i know the expansions already

[weary arrow]

You use the (a-b)² expansion to solve it.
Set the first to a and the second to b, and you can square it easily

[dire aurora]

I tried that already. I failed to get there

Will try again tomorrow

[blissful ridge]

can someone calculate this? i got the vector (15,7,-3 ) but the solution says 15,-3,-3 and i am so confused why. I even used an online calculator and it gave me the result i got and not the ones from the solution

Omg nvm I forgot a - sorry

then it makes sense i forgot to copy the -5

[left knoll]

literally the same, there's this 5 hour YouTube video called precalculus, just see the topics you are not strong in and watch those

https://youtu.be/eI4an8aSsgw?si=c--gZmJWK1mM4MGc

[plucky sail]

for me i watch professor leonard and spam practice problems

[left knoll]

here it is

[left knoll]

nah that guy distracts me

[plucky sail]

how 😭

[left knoll]

also anybody good at Laplace and Fourier transforms pleasee help mee
i don't even know how to go about understanding these problems

[grizzled dust]

wallahi

[blissful pumice]

Oh, I guess that's normal when you get to university...
Idk about yr professor's style, but don't rely on the professor alone..

You can study the material from an external source!

+make sure to study each lecture after you finish, bcuz if you only attend it or accumulate the lectures and study them once, you won't succeed...

Resolve all the questions you learned and understand why they were solved this way?

also try to solve previous years’ questions for the professor you are studying with, do this before the exam It will help you a lot

Good luck ~

[fast heath]

really need help on this

not sure what the topic is called in english though

[sinful kernel]

Differentiation

[sinful kernel]

Equate them and differentiate on both side
For f(x) use division rule of differentiation

[fast heath]

I get to this point

our teacher skipped all examples of this exact thing so I'm just kinda lost lol.

[fast heath]

I'm mostly confused as to what I'm being asked by f'(x)=f'(1)

biggest issue being that I have a test for this topic tomorrow so I can't ask my teacher

[rocky moth]

find for x ?

[fast heath]

" solve "

[rocky moth]

solve*

[fast heath]

I assume it is for x though

[rocky moth]

is answer given ?

[fast heath]

no

[rocky moth]

see I just learnt differentiation a week ago ill send my answer it might be wrong

[fast heath]

not solve for x just simply " solve "

[fast heath]

thank you:)) I have to go to sleep rn but I'll read it first thing tomorrow morning cause I didnt end up figuring it out

[rocky moth]

i might be wrong calculating f prime of x

ik image is trash

[rocky moth]

can you send your work

[blissful pumice]

the sign of 4 is positive... and here was your mistake.
u did subtraction instead of addition, so you weren't able to solve it, understand?

[blissful pumice]

The derivative of the fraction is not solved this way, you are still at the beginning, enjoy ~ 👀

[rocky moth]

ya that is why i said abt f prime a would be wrold

wrong*

[compact adder]

if the square number is divsible by 3, it is in the form 3m, if the square number is not divisible by 3, the remainder is 1 i.e it is in the form 3m+1

[errant chasm]

Hello everyone.Please , How to find the maximum and minimum values of the following expression: A=200sin(200πt)+210cos(840πt)

[silent storm]

<@&942391219206647828>

[fast heath]

oh you're right!! tysm I totally messed that up ':D

[blissful pumice]

don't worry 👀

[blissful pumice]

any time ~
good luck in your test ~

[rocky moth]

i opened the ticket

[left knoll]

I need a solution if u could pls answer this and mention me (@me)

Find the rank of the word 'MUSTAFA' in the dictionary?
From the chapter Permutations and Combinations

[proper venture]

Anyone have pre-com maths grade 8 last year papers

Or guide

[still nest]

u guys got me?

[coarse solar]

anyone who's done a british A Level Maths, does the SUVAT equations come up in the formula booklet given at the exam.

[bold atlas]

how can we find the point of intersection of a curve and trignometric function? like in this case i need the POI of these 2 curves

if possible tell me how to solve curve and trigno func generally rather than solving the question itself :))

[left knoll]

f(x,y) = 1+xy-x-y on the domain V = {(x,y) ∈ R^2: x^2 ≤ y ≤ 4 }

Find the critical points and the extreme values of f on the domain V.

Anyone that can help me?

[weary arrow]

For intersections you put the two to be equal to each other and solve
It's been too long since I had trigonometry so I don't remember much though

[weary arrow]

Hmm

[left knoll]

idts you can algebraically find the point of intersection. these type of questions are made in such a way that you would be able to guess the point of intersection

in this case, it'd be (√2, √2)

[unborn igloo]

Does anyone have any advice for high school students learning linear algebra,
I watched the 3B1B series, didnt finish it fully tho...

i wanna learn it for CS and Physics, so ig learning theoretical and application side would be nice.

pref not a textbook, just cuz I pref online, lmk tho!

[spice harbor]

im kinda confused on how to do this, the question is find k.

Would be much appreciated if someone could explain

[ember socket]

There should be a equality sign can you send the whole question please

[shy schooner]

Aren't you also supposed to consider the solution when what is inside the square is negative, because √x² = |x|. So I have S={2;4}

These aren't simple brackets, these are the absolute value brackets by the way. I don't know how you say in english.
Like |-x|=x

[shy schooner]

Tell me when you have an answer

[blissful pumice]

Oh, I think you're right :)
I studied this last year so I think I forgot about it, sorry...

[shy schooner]

No worries, it's a common mistake to forget about the other solution ! It's actually one of the first times I don't make it 😭. Thank you, have a good night !

[blissful pumice]

In fact, I was suffering from this problem last year XD
I felt like I wasn't studying well because I always forgot the other solution lol...
It was my last year of high school so I was depressed just because of this problem 😂
good night 👀 ~

[shy schooner]

Same here ! I know right, it feels like a lack of work (and honestly maybe is) but still, no need to put yourself in such a bad mood ! It's just an equation ! 😂
I hope you're good with it now !
Bisous !

[blissful pumice]

Yuuppp!
The problem is that I worry a lot, but that's okay... 😩
I hope you're well too, good luck!

[worldly copper]

Hey guys I’m trying to find the limit but every time get +infinity and the answer is actually -9/2. Can you please help me

[devout hamlet]

does anyone have experience with discrete math style proofs?

specifically logic stuff

[blissful pumice]

like what?

[devout hamlet]

this is a question i put on pause, but im trying to figure out what x should be such that for a>1 and M>0, a^x < M, where a,x,M are all real numbers

[blissful pumice]

oh.. idk... sorry :)

[devout hamlet]

haha no worries thanks anywho!

[left knoll]

50$ from steam
steamcommunity.com/gift/76566894433985451
@everyone

[weary arrow]

^ don't click that people

[weary arrow]

Ohh I vaguely remember this lol can you send the formula for solving limits like this?

[lethal slate]

Dumb question but what’s the best way to do fast mental multiplication

[undone ledge]

Can I please get an explanation for question 7

[left knoll]

is the answer π/4?

[undone ledge]

its A

0.o

[left knoll]

o.o weird gimme a sec

[undone ledge]

heheeh yeahhh... thank you :))))

[left knoll]

oh gotcha!
g(x) = sin(2x - π/3)
g(x) is defined from [-a, a] to [-1, 1] (in the question, it's mentioned as R but it'll be just [-1, 1] as it's just a normal sin curve)

the inverse function of g(x) would be (arcsin(x) + π/3)/2 (arcsin is just sin inverse)
inverse function of g(x) is defined from [-1, 1] to [-a, a]

to find range of g inverse, just substitute x = -1 and x = 1 in g inverse. you'll get it to be [-π/12, 5π/12]

according to the options, π/12 is the only one which satisfies

lmk if you're confused at any step

[undone ledge]

woaaaaaaaaaaaaahhh THANK YOU SO MUCHHHH

[mossy scaffold]

can someone pls help me with this

the answer is supposed to be this but i got a different answer

i got x >= -3 instead of x <= -3

[left knoll]

you're welcome!

[left knoll]

send your working

[mossy scaffold]

I figured out where i made a mistake

this is my working 👆

[lethal slate]

Why write a big x on it?

Just write in red pen at the top then explain why you’re wrong at the bottom

[mossy scaffold]

thats the best advice i've ever gotten for writing notes

thanks

[lucid cairn]

Hey yall can someone help? I really don't know where to start. (If you speak french it would be even more awesome).
The question is:"Show that for two real numbers a and b, suitably chosen, we can write:"

[lucid cairn]

Can I ask you why did you remove the denominators from both fractions? (In the beginning)

[tribal lance]

What exactly is confusing you?
That the fraction was removed from both sides instead of only one or why that is done?

[lucid cairn]

I guess both questions

[calm echo]

There is a rule in mathematics, when there is an unknown value divided by a number and it is equal to an unknown value divided by a number, then you do what is called reflection, you multiply the top with the bottom and the bottom with the top.

[calm echo]

For this, your result it's will be like this

[tribal lance]

Having x insode the denominators is really a pain so we multiply a/(x-1) with (2x+1) and b/(2x+1) with (x-1)
This is valid as long as we multiply the numerator and the denominator

Then all the fractions end up with the same denominator
And we can then just remove the denominator completely

[lucid cairn]

Ok...I see

[tribal lance]

If i say that half of x is equal to half of y: x/2 = y/2
You can just multiply both sides by 2 and the fractions disappear

Then we need to find out what values we need to choose for a and b so that the statement is correct

[lucid cairn]

But in this case the 3 hasn't been multiplied by x-1 and 2x+1, has it?

Oh no wait

[tribal lance]

Well to get the denominator away we multiply both sides of by the denominator so yes kinda?

[lucid cairn]

I got i got it

I just got it now omg thank yall so much

[tribal lance]

There are two distinct steps

1. Change the right side to the same denominator
2. Remove the fractions by multiplying the denominator away

[quasi breach]

[somber berry]

hi, did u find it? bc I couldnt do it too and I would like to know if u get the answer?

[somber berry]

the critical point is (1,1), and then normally u must calculate the curves for y=x^2 and y=4

[amber vapor]

can someone help me with b) pls

[azure kestrel]

Hi, can anyone help me with these phy questions pls 🥹 thanks

C(ii) & Q4 (C)

[sinful kernel]

Do you have the answers?

4- C
Conserve mechanical energy ig
KEi+KEf=PEi+PEf

[simple brook]

Can you show me step by step how to find t in the second equation?

[candid rivet]

2,4 =A log(Bt)
log(Bt)= 2,4/A
Bt = 10^(2,4/A)
t= (1/B) 10^(2,4/A)
where A and B are constant numbers

tell me if you need me to write it down without the use of A and B

[unkempt tinsel]

does anyone know of any good resources to learn university level maths? specifically continuity and convergence at the moment

[tribal lance]

https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity
https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-1/v/convergent-and-divergent-sequences

[unkempt tinsel]

ay thank you so much!

[left knoll]

help. anyone with dyscalculia or learning methods to overcome fear of mathematical symbols and equations, i can do anything in the world but not maths, something inside of me just prevents me, suffering for years

[simple brook]

Thank you so much xoxo

[azure kestrel]

There's no mark scheme for this ;-; but yea it was energy conserve method 😄 thanks

[little hamlet]

anyone know how we go from step 2 to 3 here

this is the whole q

[tribal lance]

they substitute with u=cos(t) thus u'=-sin(t) and du=-sin(t)*dt

du = -sin(t)*dt / divide by -sin(t)
dt = 1/(-sin(t))*dt

take (-sin(t))cos²(t) dt and substitute cos(t) with u and dt with what we just calculated and you get
u² * (-sin(t)) * 1/(-sin(t)) * du
the -sin stuff of course cancels out and you are left with u² du
the integral of the square leaves you with [1/3 * u³]
then you just gotta put the u=cos(t) back

seeing the sin just disappear like that really confused me but its just a byproduct uf the substitution

@little hamlet

[little hamlet]

ayyy thank you so much

[tribal lance]

thank wikipedia, wolframalpha and photomath
i am really rusty with integrals 😅

[little hamlet]

same, i was pretty confused and i thought abt doin integration by parts, pretty stupid yh, i knew it wouldve been a substitution but was too lazy not to do em, never again. really appreciate the help!!

[little hamlet]

u still went out ur way to lend me a helping hand

🤝

[tribal lance]

Oh I just found something super strange
When i set Photomath to german, I can press the little zoom icon and get more detail but the english version has that paywalled

[naive dew]

Interesting, I’ll try it too😃

[undone ledge]

i just wanted to say that i am hella grateful for all the amazing people that help out in this gc, you guys helped me alot YOU GUYS ARE SO AMAZING 🍀 💗

[unkempt tinsel]

no yeah yall are amazing 🥹

[icy dragon]

Hello guys i need help with limits, derivatives can someone help me

[tribal lance]

We sure can if you whittle the problem down a little

[muted grail]

or mention it, at all, lol

[weak lotus]

sent it over!

[undone ledge]

Hey guys how do I do question 8c
Since it’s y=-3 doesn’t that make the gradient 0?
So I used the point-gradient form and I got the answer y=5
But the answer book says “ x=4”

I’m confused……..

[icy dragon]

I need help from the beginning, i thought someone could send me some notes or recommend a course

[tribal lance]

the answer line doesnt have a gradient because it goes straight up along the y axis
y=-3 is along the x axis and any line perpendicular to that is along y
those lines can be described by just an x intercept
so we need a straight line that intercepts (4,5) which is x=4

[undone ledge]

OH MY GOD THATS RIGHT THANK YOU SO MUCH

i overlooked that ahhh......

thanks!!!!!

[tribal lance]

yeah and the -3 just doesnt matter at all
kinda evil red herring

[undone ledge]

so evil....

[gritty patio]

Hi guys, does anyone of you use Obsidian to study Math, and if so, can you explain to me your workflow?

[astral hearth]

hi guys can you help me with the integral of sin(x)/1+x^2. it looks easy but i cant do it somehow

[left knoll]

that integral can't be solved by elementary means

[small vine]

how do I use u-substitution in the integral e^(cosx) sin 2x dx ?
theres 2 chainrules right,,? so im a bit confused

[astral hearth]

do you have the full solution it looks very complicated 🥲

[left knoll]

the integral can't be solved T-T
the solution in terms of iota (imaginary number)

there are few integrals which can't be solved via elementary means

indefinite integrals

[left knoll]

you're familiar with integration by parts?

[left knoll]

btw are you sure that the question was sinx/(1+x²)?

[astral hearth]

yeah it was in one of my past exam questions

[dire aurora]

can anyone help do this one?

[sinful kernel]

What grade maths is this?

[left knoll]

im pretty sure it's wrong cause it can't be solvable. can you check it with your teacher once?

[candid rivet]

was it the integral but between maybe 0 and 1 ? sometime we cannot find a primitive of the function but we can calculate the integral for some values

[wanton cape]

(√2+2-√6)/1

[candid rivet]

you have to use the fact that sin(2x)=2sin(x)cos(x). Then it is a u sub and a integration by parts

[small vine]

Yeah I completely overlooked the sin(2x)… thanks 🙏

[dire aurora]

Whats the working

[rocky moth]

i think answer is x=4

[rocky moth]

just plot the graph

guys I am planning to learn calculus can anybody help me. i started derivatives but couldn't master them because of the log questions

[left knoll]

wdym by log questions?

[rocky moth]

logarithm

[obsidian fox]

Think the ones that involves with logarithms

[rocky moth]

ya

can anybody help me by giving me advice about how to do calculus and logarithms both

[obsidian fox]

these?

[rocky moth]

yes

[obsidian fox]

or are you having trouble with apply the logarithmic rules, sometimes you have to use log rules to split the equation to make the dx easier.

Can you show an example of a problem

[left knoll]

this would be better ^^

[rocky moth]

i guess

like i think i can be able to doit by this rule

the thing I am thinking of going for learning logarithms properly first

[rocky moth]

sorry but i dont have a proper problem

[obsidian fox]

https://youtu.be/H9eCT6f_Ftw?si=nMOxI94EdzEwFno8

@rocky moth are you stuck with these?

[rocky moth]

yes

[rocky moth]

thanks

gotta watch them

[dire aurora]

can some one help with all parts of this question please?

[azure kestrel]

Hi can someone help me with these pls? :"D there's no answer script to refer....I js want to know how to solve them

[iron lance]

for 5 (a),
since the question is asking you to use implicit differentiation to solve, you need to differentiate both sides of the equation w.r.t x and treat y as an unknown function of x.
for instance, differentiating the xy term would involve using the product rule.
d(xy)/dx = x (dy/dx) + y (dx/dx) = x (dy/dx) + y

finally, you need to isolate the dy/dx terms

[azure kestrel]

OH I SEEE- okok now i get the vision : D THANKSSS!!!

[slender quiver]

😻

[iron lance]

glad to help

[vale wyvern]

in 15 a)
if you take LCM and get the equation its something like
((a+d)√c + bd)/(b√c +c)

since c is not a square (a+d)√c will always an irrational number
therfore numerator is also an irrational number

and denominator b√c is also an irrational number
therfore b√c + c is also an irrational number

since both numerator and denominator are irrational number they must be multiple of one or the other to become a rational number overall

so you can just assume the coefficient of √c and constant term are the same in order to be a multiple

so (a+c) = b

bd = c

and you mutliply them to get the equation

in 15 b)
since you already have
(a+d) = b
bd = c

you can put b = 1 to make it the equation in the question
then put in a = 1 -d
and d =c

to make it in a equation with only c
and then you can prove the eqn easily

I have cut short the answer, if you don't understand any part dont hesitate to ask

[dire aurora]

'since both numerator and denominator are irrational number they must be multiple of one or the other to become a rational number overall.' Could you please explain why this is true?

I think thats the only part i dont understand but is what the whole solution rests upon

a rational number to me is a number that can be expressed as an irreducible fraction of integers. Does it have to be integers? I'm not sure; neither sure of whether its relevant but to me i tend to think of it involving integers only bcos of intuition. if it cant be expressed as an irreducible ratio of integers then it must be irrational

are you saying that if the numerator and denominator share a common factor that the fraction is rational despite the numerator and denominator each being irrational? if so, why is that so?

[dire aurora]

ohhhh i think you mean that the fraction shares a HCF that is irrational, while all the other respective factors are rational. so, when the HCF cancels, the expression can be written without any irrational terms.

if thats what you meant i shouldve understood you sooner. gonna try the question again

i got part a! that was so clever im amazed at how you were able to find it. but for part b i somehow proved the equation is equal to 1 and hence rational...

Here is my attempt at parts a and b. If you could please check them for me that would be great. Ill reexamine them tomorrow as well

[vale wyvern]

um I should have phrased it differently, my bad

I meant 'numerator should be a multiple of the denominator or vica-versa'

instead of the 'they must be multiple of one or the other' part

[vale wyvern]

yep

[vale wyvern]

um- something's wrong in the 2nd part
the question says to show that its not rational
but 1 is rational

lemme check after some time whats wrong

[left knoll]

Help with understanding graph functions & piece wise functions, more so the graphing aspect like reading the graph or actually graphing it. For some reason I can understand functions/piecewise when not having to graph it but when it comes to graphing or reading the graph it evades me.

I have Schaums outline for precalc ( I have yet to open the book) intending to tn. If it takes me a while to reply, my apologies in advance I’ll be at work closing tn, but I will reply once able.

[left knoll]

Hello, I can't solve this problem. I need help finding the domain.

[pseudo basalt]

F(x)=√{(x+16)(x-2)+16}/16(x-2)+x²-4

√{[x²-14x-16]/16x-32} +x²-4

Idk bro i am missing something

It is supposed to get fixed so 4(4x-8 )go away

[left knoll]

I think you're right

[quartz dirge]

You have to find the x such that x+16≥ 16/2-x

So the domain should be {x | x≥value}

[keen bay]

Guys

I always take the long path to solve prove that questions in trigo

Any tips?

[keen bay]

Or I js dont generally tend to solve it😔

[candid rivet]

25. Let's write b=f(a). we want to know how many b exist such that f(b)=1. We can see there are 3 solutions (approximately 0.5 , 1.3 and 1.7)
    hence we want to know how many a exist such that f(a) is equal to one of these 3 solutions.
    0.5 -> 3 solutions
    1.3 -> 3 solutions
    1.7 -> 3 solutions
    so in total there are 9 different a such that (fof)(a)=1

[candid rivet]

24. Here it is the same as couting how many 3-tuple of distinct elements of B={1,2,3,4,5,6} which is exactly the binomial factor of 3 among 6, which is equal to 6!/[3! (6-3)!] = 20

[candid rivet]

well first you have to know the trig identities, and then it's just a lot of practice. Also try to understand the solutions : like oh we need to write everything with cosine so these cancel out, or else...
and then eventually you'll recognize some patterns or some problems that look like something you already know how to solve
but really it is a lot of practice to become fast

[novel harness]

need help

anyone?

[rocky moth]

A motor cyclist is moving along the line x-y=2 and another moter cyclist is moving along the line x-y = 4 find out their moving direction

i think the question is wrong

[rocky moth]

yes

[unborn creek]

They are parallel, they can't meet

[maiden hazel]

hi! could someone please help me with this one? i have no idea how to do it and its due today.
Mr. Smith, an entrepreneur, decided to invest a sum of 50,000€ in a bank for a period of 4 months. He reinvested the final amount for 8 months and then again for 12 months. The interest rate on the deposit is 6% per annum. Calculate the future value of this investment and the amount Mr. Smith will receive from the bank. Please consider a 19% income tax.

[young grove]

my name is samir lol

[left knoll]

To remember for tmmrw I’ll help

[serene moon]

Help plzz

@novel harness brooo You need to look at this question, I need a lot of help.

[lyric leaf]

The graph is 3x^2 + bx + c
c doesnt matter because its subtracted from itself in both equations
work out b using what it gives:
3(1^2) + b(1) + c - 3(0) - b(0) - c = 2
3 + b + c - c = 2
3 + b = 2
b = -1
so the graph is 3x^2 - x + c
find
P(2) - P(1)
= 3(2^2) - 2 + c - (3(1)^2 - (1) + c)
= 3(4) - 2 - 3(1) + 1
= 12 - 2 - 3 + 1
= 8

i think so at least?

@serene moon

ya looks about right

[serene moon]

okeyy ım understand thank you broo @lyric leaf

[left knoll]

Can anyone solve this?

[oblique lily]

.

[left knoll]

a=2,b=4 or a=4,b=2

[rocky moth]

show that (a+b)^2 , (a^2 + b^2). (a+b^2) are in AP . i think the question is wrong can anybody check

[left knoll]

the last term should be (a - b)^2

[rocky moth]

yeah thanks

[amber inlet]

im really struggling with multivariable calc rn
do you guys have any good online resources that might help?

[gilded tulip]

Hey guys，r these correct?

[swift lake]

Does my answer to this look right?

[slate spade]

Need some help with number 5

[fickle swallow]

Answers are unknown