math-help

[vocal zodiac]

it is

[vocal zodiac]

i believe 1 is C

unforunately, I am not sure what a space vector is

[vapid ocean]

There you go

By the way I know nothing about this subject going into it

I just know how to learn better and faster then majority of people.

[ember garnet]

I think the answer is 3 for both questions.

If "space vectors" means that they strictly can't be coplanar, then the answer is 4 for the second question.

[sullen musk]

guys how do you do this

[ember garnet]

Use l'Hôpital's rule. I think the answer is -1.

[stuck quail]

Yikes

[plain flicker]

"Effective interest rate: •For the period of a hire purchase loan, interest is paid on the original principal •Effective interest rate averages out the yearly rates" can someone rephrase/re-explain this i understand the word individually but it is not clicking??

[small canyon]

how do u solve these two?

[fallen escarp]

so for the first one i think 'make the quadratics equal to each other' (i don't know how to express this in a better way' then arrange that into a quadratic

then use the discriminant

then if that is negative there are no solutions

the discriminant being b^2-2ac

[naive sage]

can someone help

[fallen escarp]

use the discriminant!

b^2-4 x a x c, where b = (p-3), a = 1 and c = (3-2p)

you know that it has two distinct roots so you can know that b^2-4 x a x c > 0

it's unsurprisingly difficult to do maths in ms paint

and then you can just solve the quadratic to find p

sorry if it is illegible

[small canyon]

thanks alot, it worked using discriminant

[left knoll]

Could someone explain q19 pls

[solemn steppe]

I got 0.763244 for this, does anyone mind checking to see if my answer is correct?

[ember garnet]

I guess 4 of them need to go to the bow side and the other 4 to the stroke side. So find the total number of permutations that satisfy the given condition. I think the answer is 1728.

[ember garnet]

I think it is correct. How did you solve it by the way?

[winter grail]

it means normally effective ir larger than normal ir

[left knoll]

Wait yea how did you work it out?

I don’t understand how to do it

[stray totem]

Is that the actual answer? I messed with some numbers (3! x 2! x 3! x 4!) and got 1728 but I don't really know if it makes sense - I get the 3, 2 and 3 factorial but not the 4

[ember garnet]

For the bow side, there are 4 ways that you can choose 3 places out of 4 to put the bow-only crew members (green).
🟢 🟢 🟢 ⚪
🟢 🟢 ⚪ 🟢
🟢 ⚪ 🟢 🟢
⚪ 🟢 🟢 🟢
and for every one of these there are 3! ways that you can arrange the green members, so a total of 4x3! = 24 permutations for the bow side.

For the stroke side, there are 6 ways that you can choose 2 places out of 4 to put the stroke-only crew members (blue).
🔵 🔵 ⚪ ⚪
🔵 ⚪ 🔵 ⚪
🔵 ⚪ ⚪ 🔵
⚪ 🔵 🔵 ⚪
⚪ 🔵 ⚪ 🔵
⚪ ⚪ 🔵 🔵
and for every one of these, there are 2! ways to arrange the blue members, so a total of 6x2! = 12 permutations for the stroke side.

In total, there are 12x24 = 288 ways to permute the "specific" crew members but for every one of these there are also 3! ways to permute the remaining 3 crew members that can go to either side, so total number of allowed permutations is 288x3! = 1728

Alternatively, it's 4P3 for the bow times 4P2 for the stroke times 3P3=3! for the remaining places, where nPr = n!/(n-r)!

[winter grail]

<@&942391219206647828>

[mighty rivet]

Does anyone know any website that helps with solving math problems step by step?

[vocal zodiac]

depends on for what class

symbolab is dope

chegg also 😎

[left knoll]

Mathway

[mighty rivet]

Thanks

[solemn steppe]

Help pls

[nimble anchor]

Hello

[ember garnet]

Hi

[ember garnet]

Find the first and second derivative and then find the local maxima in the given interval. The local maxima are where the first derivative is equal to 0 and the second derivative is negative.

[green condor]

Is anyone looking for math tutoring work? I'm needing some help with some questions I have. It would need to be over a voice call and I can pay over paypal!

[vocal zodiac]

which questions do you need help with? If you post them, we can answer them for free

haha

[verbal ridge]

Guys need ur help pls

[sage cobalt]

guys I need help

[wide elm]

QUESTION 11
I am attempting the question and am unable to prove the statement by mathematical induction. Also, the second derivative I am finding is different from that I’m getting when plugging n=2 in the formula. Please help TIA

[sage cobalt]

thanks a bunch dude!

[mild oyster]

factorise

4 x square + 9 y square + 16 z square + 12 x y - 24 Y Z - 16 X Z

can you help me with that

[left knoll]

these too please

And the first is 2/4=1/2

[main surge]

hhhhh

[ember garnet]

Multiply both sides by sqrt(x+3) and then square both sides. Then, you can rearrange it into a quadratic equation. x must be greater than -3.

[faint thistle]

I'm just really lost if someone can help me

[main surge]

tbh i got a better/simple solution

[wide elm]

Since alpha is a root, we can rewrite it as x (or z). Now make it the subject and substitute in the original equation and simplify.
PS/ 5z+2=y would’ve been more appropriate but saw the variable later

[candid mauve]

The mean and standard deviation height (in cms) for fifty girls in year 10 at a particular school are 164.3 and 7.49 respectively. The mean height for thirty-six boys is 173.5 cm. If 4 boys of the 36 boys in year 10, are shorter than the mean height for girls find the standard deviation (to two decimal places) of the boys' heights. Assume all heights are normally distributed?

I tried to solve it but doesn't see right.....

[left knoll]

can anyone help with these?

[green condor]

Hi, I'm having a lot of trouble solving this question. If someone could help with this it would be fantastic!

[green condor]

I substituted in the numbers but cannot figure out how to solve a) if I don't know what Ce^k is. I thought i might be able to divide P by something but there is nothing to divide by

[left knoll]

@green condor what did you get after substituting t=0?

[frigid wave]

Small tip, always think about which variable you want to stand alone. Since you want to know C, you have to get rid of everything close to C.
If you still need help, you get the answere by || noticing that k * t = 0 and reminding yourself, that every number to the power of 0 becomes 1. This makes P = C * 1, therefore C = 126000.||

[green condor]

That makes a lot more sense! So e becomes 1 then it's just c*1 = P

Thank you for the help

[brittle timber]

hey guys can someone help me with this question

In a group of 10 players, 5 pass the fitness test. What is the probability that, out of four players selected at random, exactly two and at least two will pass the test?

[ember garnet]

For the exactly two part, let's say we want the first 2 out of the 4 players to be the ones who pass the test. The probability is 5/10 x 4/9 x 5/8 x 4/7 = 5/63. But to get the real answer you multiply that by 6 because there are 6 ways that you can choose 2 players out of 4 (combinations). So the answer is 5/63 x 6 = 30/63 = 10/21.

For the at least two part, you do what you did above but you also calculate the probabilities that they are exactly three and exactly four and in the end you add them up.
For exactly three: (5/10 x 4/9 x 3/8 x 5/7) x 4 (four ways to choose 3 out of 4) = 5/84 x 4 = 5/21
For exactly four: (5/10 x 4/9 x 3/8 x 2/7) x 1 (only one way to choose 4 out of 4) = 2/84 x 1 = 1/42
Final answer: 10/21+ 5/21 + 1/42 = 31/42

[brittle timber]

hey thanks its checking out i confirmed it with another friend too

thanks a lot for helping me

[ember garnet]

you are welcome :)

[median totem]

someone please help 🤠

I don't understand how they solved the problem

[winter grail]

which part you don't understand?

[steep vessel]

does f(1) not exist? because it's a jump discontinuity

[ember garnet]

the limit at x=1 does not exist

[steep vessel]

tyty

[left knoll]

alguien habla español que me pueda ayudar?

Tengo este ejercicio y ya logré sacar los puntos criticos pero no entiendo que más hacer

[solar gate]

how do we plot 5-3x=6 on a graph

?

[left knoll]

is a line, x= -1/3

goes up on y

[solar gate]

thankyou so much!

[median totem]

im confused on how they find x1 x2 and x3. I'm pretty sure the right half of the first equation is the inverse matrix, so I think i have to use that but I'm not too sure.

[winter grail]

you already have x1 = b1 and just solve after x2, x3

[left knoll]

what is value of 4pisquare

4pi^square

??

[left knoll]

Part b please

[ember garnet]

find the area, solve for theta, and substitute it to the first expression of the perimeter

[left knoll]

Ye I got it thanks

[loud sorrel]

koi relations and functions karado

[wide geyser]

can anyone help me with this

I know 1= log a (a)

[ember garnet]

apply the property log_a(ab) = log_a(a) + log_a(b) and then log_a(b) will cancel out.

[prisma cave]

Someone help

[wide geyser]

Oh I see it now, thanks for the help

[ember garnet]

yw

[ember garnet]

For question 10: Find the rates at which the pipes fill the tank. For pipes A, B, and C the rates will be 1/3, 1/6, and -1/8 (in units 1 tank per hour).
For 0<t<=1 (in hours) the total rate at which the tank fills is 1/3 + 1/6 = 1/2, and for t>1 the total rate is 1/3 + 1/6 - 1/8 = 3/8.
So if W(t) is the function that gives the amount of water in the tank, where W=1 would mean that the tank is full, then
• W(t) = 1/2 * t (for 0<t<=1)
• W(t) = W(1) + 3/8 * (t-1) (for 1<t)
where W(1) is the value of W(t) at t=1, which is just 1/2 (half-full). Then, take the last equation, set W(t) = 1 and solve for t. I get t=7/3 hours.

[elfin crest]

Can anyone help me prove that the multiplication of the parts separated by the inner tangent circle of a right triangle from the hypotenus is equal to the area?

[midnight gazelle]

Hey guys, I am looking to help my senior year of highschool sister to pass her Math exam. It would be easy if that would be straight forward math questions. But the tutor often gives on exam Medical oriented questions such as the ones I attached. Can someone help me finding the materials and similiar "Medical" questions ? Thanks in advance.

[zinc comet]

Has anyone taken Probability Theory before?

[left knoll]

Can somebody help me with this one? 😵🙏

[weak agate]

can some one help me with Calculus?

i have a test rn

[supple island]

#rules number 5

[weak agate]

oh sorry man didn't know

[left knoll]

i really need help with this please😭

[elfin crest]

With long and tiring efforts, I think I have an answer. What is the correct answer anyway? According to it, I will bother to share my solution.

[elfin crest]

According to given function:
f(2) = sqrt(2+7) = 3
f(12.5) = |12.5 - 4| = 8.5
f(-3) = 9 - (-3)^2 = 9 - 9 = 0

[left knoll]

oh my god you are a goddess thank youuu

[elfin crest]

You're welcome, glad to help.

[left knoll]

you are so iconic i love you

can you help me with this one? dont tell me the answer just walk me through it

[elfin crest]

Well, all you have to do is applying the rule of f(x) on (x + 3), that's just how functions work.

[thin yarrow]

Can any one help me
I want to solve it with Solution steps

[elfin crest]

Does that big "X" means multiplication? I want to be sure.

[thin yarrow]

Yes

[elfin crest]

Ok

[thin yarrow]

And i also its
n+4 p n-4

[elfin crest]

I guess I solved it. I'll send the solution as a picture so wait a sec.

[thin yarrow]

Its a question about permutations

[thin yarrow]

Ok thanks

[elfin crest]

Here you go

You're welcome ^^

[thin yarrow]

Sorry where is the pic ?

[elfin crest]

Right there, isn't?

[thin yarrow]

Nope didn't get it

[elfin crest]

Ok let me send it again.

[elfin crest]

Now?

[zinc comet]

Has anyone taken Probability Theory?

[left knoll]

Oh I am so thankful for your help and effort 🙏 Actually I will find out the answer this week in my math class so when I do I will share it with you if you are curious of course

[left knoll]

I tried so hard to solve it. Like it took me 2 hours and more and couldn't figure it out. Maybe the tutor made a mistake writing it for us?

[left knoll]

Again thank you for looking at it and I am sorry if it wasted a lot of your time and effort 😞

[fresh cave]

i would also like to know what the answer to that question is. Looked simple at first, turns out to be not so simple :)

[elfin crest]

You're welcome, and of course I'm curious about it, it was a nice challenge for me yesterday. Until then, I can share how I tried to solve the problem so maybe it can give you some ideas. It'll be here soon, I hope.

[elfin crest]

Yeah, it took long for me too but I don't think that there's a mistake because problems like this, usually there is a so called "pro gamer move" that we couldn't figure out (and that's what I like about problems like this), then we may think that it has some mistakes. It may have mistakes of course but in the mean time it may not have.

[elfin crest]

It may seem like a waste of time to someone else but I don't care that much. I do actually but the time I spent on it would have been wasted in worse ways. It's better than nothing you know. And we're talking about math and helping someone here, so how can I ignore it if I can give it a shot. And I did give it a shot, as I said it was a nice challenge for me so even if my conclusion is wrong, no problem. At least I tried and I didn't give up so easily on it, I was like "There must be something else..''. If my answer is right I'd be very happy, if it's wrong then I can see and learn new ways to solve problems like this thanks to you. So thank you already 🙂

[dusty saffron]

I have been trying that question for sometime too now lol and completely agree with you on this one

[elfin crest]

This is how I tried to solve it. While rewriting it, for a moment I thought there was a mistake of mine and believe me I was scared to death 😅 😆 . Thank god, there's no mistake, at least I didn't (and don't) catch it yet.

[thin yarrow]

Go it already thanks

[elfin crest]

It's my pleasure.

[left knoll]

Mhm I agree!!!

[left knoll]

Awww thank you so so so much :)

[left knoll]

Oh my God! That's a smart solution I didn't think of

[elfin crest]

Glad to help 👍

[left knoll]

Actually I solved it like that for most of the part and then I couldn't figure it out haha. Again Thank you so much!!!!

[elfin crest]

I hope this is the ''pro gamer move'' I've mentioned before. If it isn't then this would make me more curious about the correct solution.

[left knoll]

Hahahaha I will definitely let ya know!

[elfin crest]

Thank you 🙂

[rare coyote]

i think this sol is incorrect. from (c-b)(a+b+c) =3.93 and the 2 below eqs, if you conclude that a+b+c=3 then we have c-b=93, c-a=16 and a+b+c=3. Solv this set of eqs then we got a=64/3, b=-167/3 and c=112/3. This root, unfortunately, does not satisfy those 3 eqs of the problem.

what you should consider here is that the value of a+b+c might not an integer. it could be, for ex, 3/2 or any real number.

[elfin crest]

Yeah, actually I found these values for a, b and c. I don't know why but I realized that I really didn't try to add them up. Maybe I didn't care about them that much and tried to solve it the way I think that's easy. Then let's do it and see what happens.

a + b + c = (64 + 112 - 167)/3 = 11/3

Hmm

I don't know how can this value fit in my solution. But as you said if we consdier them all as a real number, this may be right.

[elfin crest]

Wait a minute, there is a contradiction.

[rare coyote]

64+112-167=9

[elfin crest]

Oh ok, sorry.

[rare coyote]

maybe we could use geometric method to solve this problem

[elfin crest]

Well it would be very interesting.

[rare coyote]

have you learnt law of cosines?

[elfin crest]

Err, not yet.

[rare coyote]

hmm then do you know what cosine is?

[elfin crest]

Yeah I know it, and I think I can understand law of cosines if I take a look.

[rare coyote]

yeah okay, i think its pretty easy to understand

so from law of cosines we could deduce that the angles between a and b, b and c, c and a are all 2pi/3

and we got a triangle like this

[elfin crest]

Hmm

[rare coyote]

now you could use the area of the big triangle and three small triangles to calculate the value of ab+bc+ca

[elfin crest]

Very clever, if I understand the law of cosines it would make much more sense to me. If I watch a video about it (with its proof of course) I can understand it and so pieces would fit in my mind better.

You can try to solve it this way while I explore the law personally.

[rare coyote]

i got the answer as 88sqrt(3)

[elfin crest]

Ok, I understood the law of cosines and it makes much more sense now why the angle between them must be especially 2pi/3. Can you explain how did you calculate it?

[rare coyote]

so you have the formula for a triangle with 3 sides as a, b, c that
c^2=a^2+b^2-2ab.cos(a, b)
=> cos(a, b) = (a^2+b^2-c^2)/2ab

apply this to the first eq
we have a^2+b^2+ab=11^2
if we consider a, b and 11 as the sides of a triangle then => cos(a, b) = (a^2+b^2-11^2)/2ab = -1/2

[elfin crest]

Makes sense, and what about 88sqrt(3)?

[rare coyote]

deduce from sum of areas of 3 small triangles=area of big triangle

[elfin crest]

I'm asking that, how can we calculate the area without the knowledge of any other angle values?

[rare coyote]

you know all the sides :v

[elfin crest]

Aahh, right. Heron's formula, I've forgotten about it.

[rare coyote]

yup then the area of the big triangle is 66

area of a small triangle is 1/2.sin(2pi/3).a.b

-> sqrt(3)/4(ab+bc+ca)=66 => ab+bc+ca=88sqrt(3)

that is

[elfin crest]

Oook, everything is much more clear now, thanks a lot (sorry about the slowness of understanding by the way).

[rare coyote]

no prob

[elfin crest]

I wonder what the correct answer is, if this way really worked then I'd be very amazed. One way or another, dealing with this problem was worth it.

[rare coyote]

heh let wait for aphrodite's math class

[elfin crest]

I'm pulling that day with a rope, so to speak.

[rancid sleet]

if only it was diophantine :(

[lost robin]

Hi, does anyone know how you get the answer for this question

[lost robin]

Nvm I got it 😅

[left knoll]

@rare coyote @elfin crest Hello guys!

[left knoll]

This is actually the correct answer

And my tutor actually solved it with the help of geometry

Actually I've never thought of using law of cosines

That was very interesting

Thank you for the help everyone I really appreciate it!

@rare coyote @elfin crest i hope I didn't cause ya too much trouble! But it was a very fun math problem

[elfin crest]

You joking? Of course you didn't cause any trouble, not at all.

[elfin crest]

Wow

[left knoll]

Oof okie :)

[elfin crest]

It was a very clever solution anyway, if that wasn't the solution then what can be? Man, math is full of suprises. It always amazes me.

[left knoll]

SAME. Math used to be my fav subject but once I came across physics I fell in love with it. But still I enjoy math just as I did

[elfin crest]

I love physics too. It's wonderful.

It describes the events that happen with laws, and if you can see what makes those laws true it becomes more enjoyable. If you don't question it that much then it will be boring and a burden on your shoulders. You can't question it forever of course because questions may go to different areas of knowledge but when you understand what makes them true at some point, it is like a game you know, a puzzle. Math has this property too and I love it.

[lean orchid]

anyone understands why is it (u-1)u cuz e^-x is not= u right??

[ember garnet]

e^-x in the numerator goes to the denominator as e^x which is u-1. So e^x * (e^x + 1) = (u-1)*u

[lean orchid]

ahhhhhhh

I took me sometime

thanks mate!

[ember garnet]

yw :)

[lean orchid]

How do you go from a^2-4a+4 to (a-2)??

[neat bramble]

i think it should be √(a-2)^2 which gives a-2 since a²-4a+4 is (a-2)²

cant understand the previous part properly so not sure

[lean orchid]

ohh okayyy

ueah you are right thanks

[neat bramble]

yw

[lost robin]

Can someone help with this?

[ember garnet]

The limit given is equal to f'(c). Since f is odd, you can prove that f'(-c) = f'(c) for any c in its domain. Now, since you know the values of f'(-c) and f(-2) which is -f(2), you can find f(a) and deduce what 'a' is based on the table and the fact that f is odd (f should also be a 1-to-1 function to be strict). It turns out a=1 so you are asked to find the value of f(-3). From the table, f(3) = -81 therefore f(-3) = 81.

[lost robin]

Ohh that's interesting!! Thank you!!

[ember garnet]

you're welcome :)

[elfin crest]

Hi, can someone prove that this area is equal to (a + c)*h/2, or at least explain where does this rule come from?

[steel berry]

its similar to trapezoid area

[mighty knot]

this is supposed to be simple, but can someone find the first derivative of** ln(1/x)** ? my book says it's -**lnx **but when i google it i get a bunch of different results

[left knoll]

i got -1/x

[elfin crest]

Yeah but, why?

[elfin crest]

Chain rule may help.

[barren nimbus]

obviously

[elfin crest]

Well, it's not obvious for me, yet. That's why I'm asking. It's like, the fact sum of all the angles of a triangle is equal to 180 isn't obvious unless you see its proof or some kind of explanation.

[rare coyote]

Try to use arc length and area of circular sector to prove this

[left knoll]

Substitute the α= part into the right above equation and youll have it

And ignore the arc no. 3, i thought id use it but turned out unnecessary

[elfin crest]

Oohh I see now, thank you very much. I tried to prove it like this but I guess I thought too complex about it and couldn't continue.

[left knoll]

Does anyone know how to calculate this?

[frozen meadow]

Cross multiplying and Solving this will give you 0/0. Which means you need to use L'hopitals rule

0/0 means numerator and denominator becomes zero

[left knoll]

Yes

Doesn't L'hopitals rule have to do with sin and cos

[frozen meadow]

Nah. Its got to do with having numerator and denominator both being zero

@left knoll

[left knoll]

I don't think I've been taught that

[frozen meadow]

Thats what i studied. Maybe its has something to do with sin and cos too

[frozen meadow]

Oh

[left knoll]

How do you say this f'(x) in English

Product?

[steel berry]

f’ is the derivative

this is a limit

[frozen meadow]

"F dash of x" i guess

[steel berry]

f prime of x

[left knoll]

Oh yes the derivative

[frozen meadow]

If u havent studied l hopitals try using the properties of a^2-b^2

[left knoll]

Is L'hopitals rule that the lim of f(x)/g(x) is the lim of f'(x)/g'(x)?

[frozen meadow]

Yea

[left knoll]

Hm

[steel berry]

this only works when the limit has indeterminate form

which is 0/0, infinity/infinity, 0^infinity,…

it works in this cade

case

[left knoll]

It is 0/0 here

Yes

[steel berry]

yes

[left knoll]

Ok ill try again later thanks

[frozen meadow]

Derive untill u wont get 0/0

[wanton river]

This limit does not exist

As left hand and right hand limits are diverging to positive and negative infinity.

Also l'hospital is not applicable here as necessary conditions are not met by the functions given after algebraic manipulation.

[left knoll]

(0)^0 = 1 or 0 or not defined

[fair prism]

Can someone help me out I. I have no idea what this information is. It makes no sense how am I supposed to be able to make a bar graph with this information.

[lean orchid]

Given the recursion equation Nt+1=f(Nt) with f(x)=x+r sin(√ x) , r>0. This model has many equilibria. The positive solutions of sin(x)=0 is x=k.Pie with k=0, 1, 2, 3, ... And also: cos(kx)=1 if k is even and cos(kx)=-1 if k is odd.

Calculate all the equations. (3/10 points)
If anyone has some spare time you would be a god sent, if you get this you probs going to get scholarship at Harvard no cap

[wanton river]

Is it mathematical modelling or dynamical systems ?

[dapper tree]

can someone find the derivative of this question

[wanton river]

Put x = tan y

Use trigonometric identity

To get y/2 as end result

Put y = arctan (x)

Then differentiate

Answer will be 1÷(2x^2+2)

[lean orchid]

first one

like i know the first here is x=0 but if it can't be /=0 no idea what to do

[peak pollen]

Can someone help explain number a. ? I’m confused about using the inverse (arc) tangent

[wanton river]

Inverse arctan is a function that relates numbers on real line to angles in general. It's output ranges in +pi/2 to -pi/2.

Use a calculator to find it

Because otherwise it takes a lot of analytical work to find angle values in degree

And after that add pi to it depending on the quadrant the cords lie.

[lean orchid]

all good brother thanks

[sick merlin]

Hi, may I ask how to simplify the left side to the right side's form? Thank you

[wanton river]

Multiply the left side by a number of the format a^2+ab+b^2

Then notice that the denominator after this operation becomes a^3-b^3 format.

And the numerator becomes the right side

[sick merlin]

Got it. Thanks!

[grizzled gorge]

You can re-write the exponential using this property

that should help you figure out how to calculate the primitive

[inland granite]

Brother this is question of integration.
And there is exponential function. I just can't figure out how to simplify it. Only this is my problem

[left knoll]

Whats the “in” part, pls dont tell me its imaginary

[ember garnet]

e^(m*logx) = [e^(logx)]^m = x^m

[inland granite]

Thanks brother

[grizzled gorge]

Oh yeah, I sent you the property you had to use because I thought you were asking for a hint, not the answer

btw, for integrals this is an awesome tool https://www.integral-calculator.com/

it shows you the steps and everything

[echo carbon]

hey, is derivative only to find gradient of an equation?

[wanton river]

No we can also use it to approximate a function , find its curvature and we use it to find curve length as well. It has many more uses depending on the questions asked about a function .

[cursive idol]

Can someone please solve this logarithmic inequality?

[rare coyote]

Put 2log3(x) - 3log3(x) -7 = t
Then the ineq becomes
(t-1)(t+1)>=3
<=> t^2>=4

[cursive idol]

Okay

[raven galleon]

Can anyone please help me understand this, haven't graphed functions for a year or two now and forgot :/

[inland granite]

Hlo brother

You still want aswer

[raven galleon]

all good, thank you!

[inland granite]

Ok

[ember garnet]

Integral of f(x) from 2 to 4 must be equal to 0.5. Same for the integral of f(x) from 4 to 5.

[noble moth]

hiiii is anyone doing a maths degree here?

[left knoll]

Can I put lim on both sides of an equation?
For example the problem gave me this: f(x)=f(x-3) for all real values of x. So f(2)=f(-1). Here can I put lim on both sides?

[wanton river]

Well depends on the question itself.

[left knoll]

Is that even an equation

[wanton river]

Yes it is functional equation

And periodic one

[left knoll]

I can't speak math in English too well sorry

[wanton river]

Well no problem

Just ask

[left knoll]

For it to be periodic it has to be f(x+3)=f(x), no?

[wanton river]

Yes

You can make the shift

As it is true for all x

[left knoll]

What

[wanton river]

Replace x with y+3

You get the form f(y+3)=f(y)

From this you can claim the function is periodic

[left knoll]

Oh

So I only need either f(x+T) or f(x-T) to claim it's periodic?

[wanton river]

Yes

[left knoll]

Damn

[wanton river]

But we do not know about the fundamental period from this data alone.

[left knoll]

What is the fundamental period

[wanton river]

The smallest interval after which the value of the function starts to repeat.

Do you know trigonometry?

[left knoll]

A bit

[wanton river]

sin function has fundamental period 2*pi

[left knoll]

Yes

Well T is the fundamental period

[wanton river]

But sin(x+4*pi)=sin(x) as well

[left knoll]

But it's not the smallest yes

[wanton river]

Exactly that is the distinction between fundamental period and any other period of a function

From f(x+3)=f(x) all we know is that it is periodic but knowledge about T is not given

[left knoll]

True

I don't think I have to claim it's periodic

Seems irrelevant

[wanton river]

Ok

[wanton river]

Well I kind of have one unofficially but I dropped out the course with one sem left. I wanted to join better college.

[late root]

hey

i need help with the trig funcs asap

how am i supposed to calculate sin(60) for example, with just a basic calculator

(without scientific calculator this means i have no sin cos or tan button)

[ember garnet]

there are some common angles of which you are supposed to know their trigonometric values. You can also easily prove them geometrically.

[late root]

yooo i have a lot to memorize and u are telling me i have to memorize that table?! 💀

i mean, its fine

but i wanted to ask u about this method i just found like 2 min ago

look

give me a sec

this works for every case (apparently)

using that method i got the question right

[ember garnet]

yeah with that right triangle is also how you prove them for the 30 and 60 degree angles

Also the table is not hard to memorize. You only need to remember the first line for the sine for example.
It goes √0/2, √1/2, √2/2, √3/2, √4/2.
Then the cosine is in reverse order, and the tangent is the ratio sin/cos

[late root]

okok ik i will try to memorize the table then, just to be quicker answering the questions

thx <3

[ember garnet]

yw :)

[blissful ridge]

Cool profile pic man

Or gurl

[late root]

thanks bro

my fav car, nissan silvia s13

[blissful ridge]

Mine aswell!!!

[noble jackal]

I could do a part of the question

If anybody can explain with reasoning, it would mean tons! Thank you (pls tag me if you answer)

[wanton river]

Notice that BOAC is a quadrilateral

Angle BOA is 360-136=224

We already know angle B , angle C , angle BOA

[noble jackal]

Omg

Thank you!!!

[wanton river]

So angle x is 360 - 224 - 39 - 68 =

[noble jackal]

yup yup tysm

appreciate it the help 🫶

[wanton river]

Harse notice that we can use idea of isosceles triangle to arrive at x as well

Join oc

[noble jackal]

By splitting?

That’s what I was thinking too

But I wasn’t entirely sure

[wanton river]

Notice triangle BOC is isosceles

[noble jackal]

yes

[wanton river]

Then we can find COA as well

Use isosceles triangle property to find x

[noble jackal]

thank you

[untold shadow]

Can anyone please explain what happen from the 4th line

[ember garnet]

there are some mistakes.
the B^2's don't cancel out in the 2nd line.
3rd line should be 25 = 49 - 14B + 2B^2
4th line should be -24 = 2B^2 - 14B (subtracted 49 from both sides)
then 0 = 2B^2 - 14B + 24 -> 0 = B^2 - 7B + 12 -> (B-3)(B-4) = 0

[untold shadow]

THANKS ALOT AGAIN

<33

[ember garnet]

yw :)

[blissful ridge]

Can someone give me a bit of help?

Nvm i solved it myself

I forgot the most simplest rule Lul

[echo carbon]

😎

[left knoll]

Good job, also nice paper

I like the grid lined paper for math. It looks really nice, and it's great for graphs

[broken shadow]

people

need some help with matrix math

[sick trellis]

Lemme see, idk if i could help much

[blissful ridge]

Yea thank you!!! It’s comfortable to write on

[left knoll]

hiii does anyone know parabolas?? please dm me right now because i solved for standard equation and i need someone to check my work hehe thank you

[haughty owl]

can someone solve this integral

the inequality is bounded are on bottom of a screen

[restive wedge]

.can anyone tell me how to solve this

I mean prove

I can't get the numerator right

I think at the end (a+b)^2 identity is to be applied in the numerator but idk how to do that with trig

[elfin crest]

Here you go.

I know it looks messy a little but there is no mistake (I hope), after all.

I really didn't think that I'd be cabaple of proving this, so I feel very good right now.

[rose bobcat]

hi guys i forgot how to find the range can someone pls help

[elfin crest]

x >= 0 ----> x^2 >= 0 ----> f(x) = x^2 - 4 >= -4

It should be like this, I guess.

[rose bobcat]

thank you

❤️

[elfin crest]

You're welcome, glad to help 👍

[grizzled lotus]

Hi how do they know the focal point

[brave rock]

guys how do i solve 2/5 x 1/4 - 1 ... would be glad if someone helped

[elfin crest]

Well, it's basicly equal to -9/10 if that "x" means multiplication (even it doesn't, that doesn't make any sense but I want to be sure anyway.)

No offense but it's too easy, enough to make me doubt.

[brave rock]

yeah i figured it out, ty!

[elfin crest]

You're welcome.

[restive wedge]

this is what I did

isn't that right?

cuz it would form the original fraction when we multiply it by -1?

[elfin crest]

Well, if you decided to turn that into a plus, you have to turn the one that's between the pairs of paranthesis too, and sinθ must be negative. Is this what you meant by that?

At first I solved the problem like I said above, but then I decided to do it like that.

[forest magnet]

can someone help me in b?

[patent mason]

brain is not working today is anyone willing to help? thanks

[azure sierra]

https://www.mathematics-monster.com/lessons/linear_equations_line_between_points.html

[grizzled gorge]

y = -3x -4, I'll send you how I did it in a bit, can't take a photo right now

But it's basically evaluating the general equation of a line with the points that they give you

[left knoll]

DF is perp to DC, so calling D’s projection on CF A, use 1/DA^2=1/DC^2+1/DF^2

[left jay]

Love your username

[forest magnet]

Thankss

[restive wedge]

need help in part b only

I saw the solution online and they took the midpoint of A and B, then assumed it was the point of contact and found out radius using the centre coordiinates

is it because the midpoint of a chord is always perpendicular to the center? thats what I thought

just need to confirm

[left knoll]

Yes you can prove it ||median of a isosceles triangle is perp to the corresponding base||

[blissful ridge]

Can someone show me step by step how to solve it? I‘ve tried 4 times now but I can’t figure it out

[ember garnet]

you can also substitute y=3x-20 into the circle equation (x+1)^2 + (y-2)^2 = r^2 which if expanded will give you a quadratic equation with respect to x. Then calculate the discriminant and set it equal to 0 because you want to have exactly one solution (tangent line), and from this solve for r^2 to find the new radius.

It looks like there are typos, it probably meant to say 2^(x+2) + 2^(3-x) = 33 which is what is written in part b. Just solve the quadratic equation written in part b.

[ember garnet]

what are you supposed to do here? Rewrite it? Because you didn't write an equation. Is it equal to 0?

[blissful ridge]

i need to simplify it and the issue is that i can do that and i solved it with my friends... but the solution confuses nme

it doesnt make sense for me and my friend and we dont know if we forgot something or so

[ember garnet]

well, I got x^2 -8xy +7y^2 after simplifying

[blissful ridge]

yea thats the solution and i also got x^2 but the other two ones i got wrong

[blissful ridge]

could you pls explain me how you got -8xz and +7y^2?

[ember garnet]

just expand like this: (a+b)(c+d) = ac +ad +bc +bd. But be careful with the signs. Then add together the similar terms. After expanding you'll have 2 terms with x^2, 4 with xy, and 2 with y^2, just add the coefficients respectively.

[blissful ridge]

thank you

[ember garnet]

you're welcome :)

[inland granite]

Can someone tell me how to integrate this fictions

[elfin crest]

Can anyone explain why can we define ln like this. I mean, we can prove logarithmic properties using this definition. But why the natural log, why not any other logarithm? I'm very frustrated about this so I really need help here, please.

[left knoll]

Then integrate by part and (theoretically, assuming it can be integrated) youll get it

[left knoll]

I don’t think that’s how we define ln, the correct one should be the logarithm of the base e. And it turns out that science really like this constant, it can do a lot of things when it comes to solving differential equations

[left knoll]

Wait I’m stupid lol

[elfin crest]

Well if you search a little you'll find that it is can be defined this way also, and the Thomas Calculus book has it too. I found a video that explains how natural logartihm defined before e was known. In that video they also kinda explains this interesting definition, so I'm focused on that now. I hope I can understand it this definition there.

[elfin crest]

I mean, it's really weird and strange isn't it? Why integrate from 1 to x and why the function f(t) = 1/t? There must be a very good a meaningful explanation for this definition, I'm sure.

[left knoll]

Before e was known? Not sure why they chose 1/X out of all functions, but I guess ppl were just messing around and found smth cool but decided to not tell anyone

But I can explain how that comes: if you take the derivative of 1/x you’ll get ln(x)

You still have that video?

Make sense, in my country they commonly call ln as “log nepe” (which is supposed to mean log Napier ig)

[bright adder]

first time taking cal in college and im having a lil trouble with my trig review lol. i know how to plug in the values using the trig identity but im not too sure what to do after that :/

[elfin crest]

https://youtu.be/habHK6wLkic
Here is the video.

[elfin crest]

I guess you wanted to say the derivative of lnx is 1/x, anyway I got the point. Well, this definition can be explained by this fact but it's really cool to see how this definition made up, because probably these times were before Newton and Leibniz invent The Calculus © :). Maybe they didn't write it as an integral but figured out that this area has something to do with Napier and other's logarithm table.

[left knoll]

Ah ye (1/x)’ is ln x me dumb lmao

[elfin crest]

And I think, there's a strong relation between this definition and the definition of the number e. I'm working on it now.

[inland granite]

@left knoll brother I have done this. My answer is in terms of ln. But it's answer according to answer key is( c )option that's the problem

[honest remnant]

Determine the recursive equation for the following sequences(4K)(Each is 2 marks)
a. -3, -4, -6, -10, -18, …
b. -1, 3, -9, 27, …

HELP！

❤️❤️

[left knoll]

Well on b you multiply by -3, is that what the question is asking?

And I think on a you add the difference of the two numbers times 2. So the difference of -3 and -4 is 1. 1 times 2 is 2 so you are supposed to add 2 but I guess you add -2 because they are all negative.

[final drum]

I’m taking algebra 2 honors this year quiz coming up Monday any note websites you recommended? Thank you.

[final drum]

Quiz mostly on functions

[final drum]

Ping me if you can help

[honest remnant]

Oh thanks bro 👍🏼I ask it for my friend 😏

[blissful ridge]

Can someone help me with F? The goal is to factories this

[wanton river]

(m+n)(m+n+3)

[blissful ridge]

oke thank you can you also explain why

[wanton river]

Well notice if you takeout 3 from first two expressions from left to right then the part becomes 3.(m+n)

The other part is (m+n)^2

[cold thorn]

that works

[wanton river]

Let me tell you about a theorem

If f(a,b) is a polynomial and there is a polynomial h(b) such that f(h(b),b)=0 for all b , then we can write

f(a,b)=(a-h(b))×g(a,b)

Where g(a,b) is a polynomial

This can easily be extended to n variable polynomial

[blissful ridge]

to be honest i dont really get it

[wanton river]

@blissful ridge do you know about polynomials ?

[blissful ridge]

no

[wanton river]

If you are in school then you will learn about them in appropriate class

[elfin crest]

Wow, is that a multi-variable polynomial?

Actually that's a very interesting theorem. If it does have a name what is it? I'd want to search about it later.

[blissful ridge]

i am from swizerland... idk how its called in german

[wanton river]

No name

Just a very natural observation

@blissful ridge ˌpäləˈnōmēəl

[elfin crest]

I see. Well it'd be nice to see its proof. Do you have it or how can I find it?

[wanton river]

Well I came to know about it from imo training

It is very natural and straight forward observation

@elfin crest well I just came up with a proof . Just use the if condition

Assume it is true and then use single variable polynomials factor theorem to prove the statement

[elfin crest]

Umm actually I didn't study polynomials that deep and never studied multivariable polynomials/functions. Even if I don't understand these that much, seeing a proof makes me feel good. Thanks for the tip anyway, I'll try it when I study them.

[blissful ridge]

now i see it it makes totally sense!!! Thank you

it took me a while but now i see it

[vital lake]

Does anyone here have the may/june 2022 edexcel igcse question papers?

[lean orchid]

How you get those N.N???

[azure sierra]

I dony know if this make more sense to you or not @lean orchid. But from what I see, they make it more simple to N to simplify the same equation as there are sense of similar equation. Also, I guess this is more related to formula explaination? Where the No is the initial compare to N the final

[north harness]

HEHEHEHAW

[kindred peak]

it's sooooooooooo hard 💀

[grizzled gorge]

the forbidden operation

[left knoll]

21

[unborn violet]

9

there is priority in multiplication and division operations. if both are in the problem, the process starts from the left

[lean orchid]

Wow thank you i understand!! ❤️

[blissful ridge]

hello guys i have a question
i need to find whats missing here but i dont know how to calculate it
x^2+14x+__

how do i find the missing gap?

[unborn violet]

i think its 49

[blissful ridge]

it is i checked the solutions cus i wanted to see if i got it right

i wrote down 7

[unborn violet]

(x+7)^2

isnt it?

[blissful ridge]

yea thats what i did to find 490

49

ooo now i saw my mistake

thabk you you helped me to realise it

[blissful ridge]

i have an other question i need to linearfactorise this

4m^2-4m-80

what are the steps in my math book it says that i need to multiply the first number with the last one

which would result in -320

and then i need to find a number set that the multiplication is -320 and the addition is -4

any tips on how i can do that more efficient or so ???

[left knoll]

Quadratic fomula?

[blissful ridge]

whats that

[left knoll]

A formula

[blissful ridge]

i dont know it well maybe i do but idk the english terms good in math i speak german and maybe it will help me if someone that speaks german could explain it

or if you show me an example of that formula i could maybe understand what you mean

[left knoll]

First you can devide by 4

To simplify

[blissful ridge]

oke

[left knoll]

But that's optional

[blissful ridge]

oke

[left knoll]

If you simplify you get this: m^2-m-20

[blissful ridge]

oke

[left knoll]

The formula goes like this: m1,2= (-b±√(b^2-4ac))/2a

[blissful ridge]

oo thats far from my level of math

[left knoll]

Don't worry

All these letters can be replaced with numbers

[blissful ridge]

ooo i see

well i need to eat and i will read your explenatiuon later

thank you in advance

[left knoll]

The general way of writing your equation is am^2+bm+c=0

In this case (after dividing by 4) a=1, b=-1 and c=-20

You can plug those numbers in the formula and you'll get 2 results

m1 and m2

When you replace m with either of those numbers in your equation you will get 0

The factorization formula after you have found m1 and m2 is this: am^2+bm+c=a(m-m1)(m-m2)

The a after the = sign is the same a from before

In this case it's 1 so you don't have to write it

Hope it helped you

[blissful ridge]

Thank you

[blissful ridge]

i have an other question

so

2x^2+x-21

i need to factorise that and idk y but in the solution they say

2x^2+7x-6x-21

well its not the whole solution but its the first step and i dont get why they do 7x-6x and how i should know that

[placid flame]

the reason they did it because theres absolutely no way to factorise that in its first form, and the only way u can come up w that is by "experience" or creativity they call ( you gotta choose the number based on whether u can factorise w it or not for exp if it chose 9x - 8x, you couldn't factorise it) , when u make it 7x - 6x, u can factorise 7x with - 21 n 6x with 2x^2 :)

hope this was helpful

[blissful ridge]

Thx

[placid flame]

np

[final drum]

Really dumb question but my teacher sent these notes to me and he said the graph is shifting left and up but it looks to me like it’s going right and down

[ember garnet]

he probably means that the f(x+1)+2 is shifted left and up relative to the original f(x)

[lean orchid]

I got a math exam tomorrow this was one of the old exams Awnsers how did they get I am stuck on the first formula?

[unborn violet]

there must be a mistake here. the mathematical problem at the top is the opposite of the one at the bottom. if the answer to the top one is L, the bottom one should be 1/L. neither is equal to L.

im not sure also

[lean orchid]

Yeah it could be that i have made a mistake

This is the differiantial equation and you know that k>1 now find the general solution differential equation

[lean orchid]

the last part of is 100% correct but dont know how to get there

[full fossil]

Hello, may anyone advice best online resources for learning calculus?

[raven galleon]

does anyone have any tips to turn a decimal into a fraction mentally and quickly? For instance, .25 = 1/4, .5 = 1/2. I just don't understand how I would be able to recognize that .285 = 2/7

[rancid ibex]

Hello, I'm going to start high school and I really need to revise and do some math exercises. Does anyone have any sites or books or anything else to send me?

[north harness]

PEMDAS

[azure sierra]

purcell book is enough for me, if you cant understand some parts then google it and many resources, i believe you will find some good online resources too

[azure sierra]

you can check #useful-links khan academy and some notes there i guess

[elfin crest]

Thomas Calculus may help you, I'm using that now and I think it's fine. Also the youtube channel Professor Leonard has good calculus lessons.

[full fossil]

Thank u

[full fossil]

thank u

[restive wedge]

need help in part 2

[topaz prairie]

Alternative method is to just use the cross method for factorisation

[restive wedge]

this is the answer

[topaz prairie]

List out the factors of the x^2 terms and constsnt terms and then see which combination gives you the result you want

Feels a lot more intuitive but maybe that’s just me

I was replying to a previous message 😅

[restive wedge]

im dumb

[topaz prairie]

The probability of one church chosen at random having less than 61 people attending is (46+110+122)/500

So you multiply the probabilities together

I just realised I don’t really know how to explain sorey

https://math.libretexts.org/Bookshelves/Applied_Mathematics/Book%3A_College_Mathematics_for_Everyday_Life_(Inigo_et_al)/03%3A_Probability/3.02%3A_Combining_Probabilities_with_And_and_Or

[restive wedge]

I understood now after drawing a tree diagram

[restive wedge]

can anyone please explain both methods of the solution

the second one I did correct but didn't multiply combination at the end

I really don't understand what the first one is tho

[wanton river]

First one is combinatorics

Choose 3 from 13 red Sweets and choose other 4 from 39 other type of sweets .After that use Equally likely case definition of probability.

[magic latch]

how to get the sum of fibonacci?

[wanton river]

Sign of the expression is positive.

As the quadratic is always negative or positive.

To find Fibonacci sum use telescopic sum idea

[wintry olive]

ive been trying to solve this and im confused

can anyone help?

[ember garnet]

do the substitution u=3x

[wintry olive]

ok i did that

now i just have the integral of 0 to 3 of f(u)du with 5/3 in front of it

[ember garnet]

you should also have changed the limits of the integral

with the substitution u=3x, the new limits with respect to u should be 3*0 = 0 and 3*3 = 9

giving you the first integral of which you know the value

[wintry olive]

Ahhh

Ok thank you

[ember garnet]

yw

[restive wedge]

why have they not considered the translation of the y axis?

oh wait

its because y values change with the stretch right?

[acoustic forge]

do you mean "why did it move up"?

[acoustic crater]

❤️

[restive wedge]

ik why it went up but I thought the stretch wouldn't shift the vertex of the straight line up

[acoustic forge]

it will

and on the x the same

you just multiply all the points' y value by 3

in this particular problem

[versed cairn]

Hiii!! Can someone help me with hyperbola problem?😭

I was stuck with this minor axis thing idk how to solve this.

[regal cargo]

This is almost definitely not a hyperbola and almost definitely an ellipse

ellipses have major and minor axes

[regal cargo]

what did you need solved about it

I'll assume you need standard equation for ellipse. You need three things for that: the length of the major axis, the minor axis, and the location of the center. The center is (2,4).

Let a = 2, b =4.

Next, the length of the minor axis. It is 24. Get half of that and square it. 24 becomes 12. 12*12 = 144

Let n = 144. We still don't know if this is in the x or y direction though..... we need one more hint.

The final information is that a vertex is at (-11, 4). Since the y coordinate of this vertex is the same as the center (2,4), you know that this major axis will be across the x axis. What is the length of the major axis (or better yet, half of the major axis)? It is 2-(-11) = 13. Square of 13 is 169.

Let m = 169.

The formula for an ellipse is ((x-a)^2/m) + ((y-b)^2/n) = 1.....

So your specific formula will be:

(x-2)^2/169 + (y - 4)^2/144=1

[mint vigil]

i know it’s a dumb question, but it’s 9 pm and i don’t think anymore, i need to find the x

both c and d

[ember garnet]

you can't really find x, there are multiple values that satisfy these inequalities.

[late root]

can someone pls explain me what do i have to here? :)

[ember garnet]

Find the roots of 2x-5=5 and 2x-5=-5

[late root]

why =-5?

i was thinking of writting numbers that are true for that statement

[ember garnet]

If you have |y|=5 then y can be either 5 or -5

[late root]

oh

true

thx <3

[ember garnet]

np:)

[left knoll]

am i stupid? isn't it supposed to be 68 degrees..?

[late root]

hewo

i need help with this one too :((

i have no idea what to do here

[wheat anchor]

the little circle is basically just a bracket for the next function
so the notation is f(g(x)) for a. and g(f(x)) for b.

then u can just sub them in and simplify if u need

[quasi frigate]

92 is parallel to 2 so 2=92
1+2= 180
1+92=180
1=88

[late root]

oh okok thank you very much~

[left knoll]

im so stupid thank u😭

[quasi frigate]

np :))

[late root]

please if someone knows the answer to this one let me know im so tired my brain is dead

nvm just finished it 🧠

[left knoll]

Can someone please help me with this please

[ember garnet]

a) area of sector: pi * r^2 * theta/2pi, where theta is the angle of the sector (in this case it's 2pi-2pi/3)
b) volume of cone: V = 1/3 * pi * r^2 * h. Replace h and transform the equation into the needed form.
c) maximum is where dV/dr = 0 and d^2V/(dr)^2 is negative.

[slim frigate]

Can someone help me with this pls ?

[ember garnet]

cosec(x) = 1/sin(x) so substitute that into the first equation and solve for sin(x).

[slim frigate]

I tried that but this is what I ended up with , idk how to do it

[slim frigate]

Is this how I shld do it ? Idk

[ember garnet]

yeah that's basically it, just add the "=0" after you move the 2sinx to the left hand side

so you have one double root

[slim frigate]

So like how does that answer the question ?

2^n ?

[ember garnet]

well, first of all, maybe it would be better if you had set sin(x) = u, and then you would end up with (u-1)^2=0

[slim frigate]

I've got my entrance in a few days , and here I am unable to solve even the 1 marks , im doomed lol

[ember garnet]

therefore u=1

and so sin(x) = 1

now since sin(x)=1 then also cosec(x)=1 and then 1^n + 1^n is always 2 no matter what n is

[slim frigate]

Oh ya....

[slim frigate]

Thank u

[ember garnet]

np:)

[slim frigate]

Someone help

Shld I just ignore sin and cos and take it as nrml variables?

[wanton river]

Solve for x and y

Interms of trig functions

Then just substitute

In the given expression

[mint vigil]

can someone help me with this?

[left knoll]

What is that

[left knoll]

can someone help me with this?

[lucid cairn]

Why are the numbers after the comma between parentheses?

I need help please. How do I simplify this?

Here are the different answers:

[left knoll]

is the answer c?

[lucid cairn]

Yes omg thank you so much!!!

[mint vigil]

they’re repeating decimals, idk how they’re being written in other countries tho

[lucid cairn]

Oh I've never done this type of equation with repeating decimals.

[wanton river]

@left knoll use substitution method to find the integral.

[left knoll]

i tried that too, it didnt work

[wanton river]

@left knoll answer is
-(1/3)×log|sec(2-3x)+tan(2-3x)| + c

[left knoll]

can you please send me how you got this answer, im not able to solve it

[left knoll]

and in that way if we differentiate this, we should get the same equation sec(2-3x) right? but in this case its not coming the same

[wanton river]

We do get sec(2-3x)

After differentiation

https://www.google.com/imgres?imgurl=https%3A%2F%2Fd138zd1ktt9iqe.cloudfront.net%2Fmedia%2Fseo_landing_files%2Fintegration-of-sec-x-formula-1629953168.png&imgrefurl=https%3A%2F%2Fwww.cuemath.com%2Fcalculus%2Fintegral-of-sec-x%2F&tbnid=Z9xBXEv8JX5JAM&vet=1&docid=iazPf3CXorOV9M&w=543&h=410&source=sh%2Fx%2Fim

[left knoll]

oh

okayy thankss

[left knoll]

Just put 2-3x = t
The equation becomes
-1/3 ( integrate ( sec(t) dt)

[left knoll]

yes thank you

[left knoll]

Are you in 12th?

Class

Are you preparing for jee?

[stiff isle]

can i have some help with this pls

[left knoll]

yes I'm in 12th rn, preparing for jee 2023

[left knoll]

write 6^2x as 36^x then expand it as 3^x.12^x, now the equation becomes 3^(x+1).12^x=12^x. 12^x gets cancelled.

x=-1 must be the solution ig

[stiff isle]

wait then wouldnt 3^x.12^x becom 36^2x not x

[left knoll]

nope

it would be 36^x

[stiff isle]

is that bc the bases arent the same

or...

[left knoll]

yes as much as ik

[stiff isle]

oh waiut im stupid

i got it now

lmao

oops

thanks a lot btw

[timber night]

My bad

[brazen harness]

{log|sec(2-3x)+tan(2-3x)|}/-3

is it correct?

[left knoll]

yes it is

[timber night]

Lol

[scenic cairn]

does someone have a note about equations

for sat math

[queen herald]

Ho can anyone help me this

[karmic latch]

i think the answer is 10 days

[queen herald]

Thank you so much

[karmic latch]

you're welcome

[lucid cairn]

What type of exercise is this? Is it like sequences?

[azure oracle]

Could anyone help with this? it’s factoring

[iron portal]

first take out the common factor which is y

then ur left with a normal quadratic which you can factor easily

make sure to have the y on the outside

[azure oracle]

would it be y (y-9)^2 as the answer?

[azure oracle]

thank you!

[iron portal]

yep

[azure oracle]

perfect thanks!

[cloud night]

Can anyone help me with this question? The answer is D and I don't know why

[sly island]

i think the ques is incomplete they havent mentuoned the remainder when p(x) is divided by x-3

is it like exactly divisible by x-3

?

[cloud night]

yes

[queen herald]

Sorry but i just read it again, i have a question that why B,C,E must start first?? And why we not plus the day of B C E like : 5+ 2+5+5+3+2??

[karmic latch]

B is completed in five days, C is completed in two days, E is completed in 5 days. It only takes 5 days if they start at the same time. B, C, E must start first because B and C have to be completed before A can be started. E and A have to be completed before D can be started.
B, C, E must start first. B, C, E take 5 days to finish. Then A starts and completes in 3 days. Then D starts and completes in 2 days. 5+3+2=10

[queen herald]

Oh i see thank you so much

[lucid cairn]

How do I solve this? I'm supposed to use the limits and variation tables but I forgot all the different steps. Thank you in advance

[left knoll]

Hello! I am asking if anyone is willing to tutor me pre cal

[silver sun]

is it mandatory to use limits and variation tables ? can you use logarithm ?

[exotic rivet]

any one ?

online ?

RECTANGULAR TO SPHERICAL COORDINATES here

z is ρcosφ
and the whole thing under the sqr root is just ρ

how ρ5

[lucid cairn]

No someone explained to me that no it doesn't need it. They told me to only take the Xs to simplify the task instead of writing all the e. But I still can't figure it out

[fringe current]

I really need help with this

[unreal ore]

halp pls need to find the domain and range

[wild ruin]

Heyy! i'm supposed to calculate the average volume of a cookie in a package. i know that the diameter of one cookie is 8,50 ± 0,02 cm and the thickness is 0,050 ± 0,005 cm. how would i go about solving this? I'm supposed to calculate the error limits for the volume as well.

[steady relic]

(2,4)

[regal cargo]

I honestly wouldn't know because I only did Chem and Bio.

From what I've heard, Math is the only one among those three that requires a knack for pattern analysis. Physics and Astronomy can be learned (albeit with some difficulty, but every Olympiad is difficult to some degree)

nope, only nats

the others are too good

i wouldn't know what's the second difficult one

the odds are against you, keep in mind. It's difficult to be top 20 in one subject in the entire US. You really have to devote yourself to that and that alone

Get rid of that thought immediately

Consider doing your best and becoming the best version of yourself before you start saying "I want to go to this college" or "that college"

Do you know exactly what you're going to get out of MIT?

Do you know why you shouldn't go to UT austin?

Yeah. It's a good school, but you said you want to go to MIT. Why do you not want to go to UT Austin?

Or ASU?

Or heck, why not community college?

So it's about name recognition, not a good start.

Figure out what you want out of college and which college is going to give you that.

Talk to their alumni to learn about what kind of people go to those colleges.

Don't just say that you want MIT because it's famous.

Do you know what you would get out of UT Austin that would make it appealing?

How about UChicago?

Andddddd what do you want to do with that?

Every school has astrophysics as a major.

What is one school giving that another isn't?

UC Santa Cruz may not be famous, but it has one of the best astrophysics programs

why not there?

Sooooooo........ you want to be an engineer. Do you want to work for startups? Do you want to do research? Do you want to work for established FAANG companies or their equivalents? Do you want to be a professor? I literally got nothing out of "I want to be in the tech field"

you can do so much in the tech field and each school will help you do a completely different thing with tech

do you have some idea?

Not what I was asking. What I am asking is "What is your life going to look like 20 years from now?"

Not a good answer. This sounds like a person who has a general interest in a field but has no direction.

Any good college wants talented students, but they want students with direction too.

My friends at MIT have big goals. In 20 years, some want to be venture capitalists for R&D companies. Some want to be professors. Some want to simply have a high paying job and take care of a family (nothing wrong with that either). But each and everyone has a direction to supplement their talents. That's true for Harvard, MIT, Stanford, Columbia, whatever school.

If you don't have a solid direction, Idk why a school should take you

Have some direction! You have an interest, now figure out what you want to do with that!

that's all

Best you figure out which one you want to focus on.... I want to be many things. I can only do them one at a time.

Put it this way: a person can be a great student, have a side hustle and be a great runner. This student is well rounded, but won't be accepted into a T10 school because he has no direction.

But a person who is the fastest in their state is likely trying for the Olympics (a direction)

A person with a 4.0 GPA is likely aiming for academia to be a great professor (a direction)

A person who turned his side hustle into a business is likely going to be an entrepreneur or inventor (a direction)

I'd say do some research into various universities and start talking to their alumni.

When you've made enough stupid mistakes, you learn I guess.

So? Go on linkedin! Make connections! Call the universities to see if you can talk to some alumni!

Can you think of other ways to get in touch with alumni?

[raven galleon]

anyone understand

[regal cargo]

I'll tell you another secret: T10 schools want problem solvers. They want people who can get what they want. I think you have more than enough resources as a high school student (even with age restrictions) to figure out how to do this

[regal cargo]

Application of derivatives and double derivatives:

Relative extrema are are found where the derivatives of the function are equal to 0.

The function is increasing on intervals where the derivative is positive (and negative for decreasing)

To draw the graph, you will also need a second derivative (derivative of derivative to find "inflection points", which are places where the concavity of the graph changes. Using those x values, you can plug it into the original equation, use the information of where it is increasing and decreasing as well as where it's concave up or down to estimate the curves of the graph.

I'm at MIT studying bioinformatics

Well...... if you knew more about me, you'll realize that it's more about experience in life than anything.

[raven galleon]

I'm unsure how the factoring of "3x^2-4x-4". Would it be (3x+2)(x-2) giving me the x-values of -2,2?

[regal cargo]

Went to UCSD for a year, quit college over substance addiction, did some random work, got some ideas, invented something, got a patent, went back to college.

So everyone has rough stories. But we all have somewhat of a direction by the end of it. That's why i'm telling you to explore more and find your direction

[regal cargo]

The factoring is correct, but not your x interesect values.

The two should be x = 2 and x = -2/3

Drug addiction

[raven galleon]

ah, makes much more sense. Thank you!

[regal cargo]

Yeah. Not the best thing in my life.

But again, you learn from mistakes, you learn what life is about, and you start trying to push yourself in a direction you want to go.

When I was in high school, I wish people told me to take literature classes more seriously. You don't learn about life through the sciences. You learn about through reading books and talking to people.

That's one suggestion I'd make to you.

Read more books. Read good classical fiction. It's something that people don't do enough of because it doesn't earn the money.

No.... read them to relax

read them to understand

read them to feel their emotions

read them to learn about the shit that goes on in other people's lives.

Don't worry about that. Just because it's harder doesn't mean it's impossible. You're not the only autistic person in the world, and I wasn't the only drug addict in the world

[raven galleon]

yes

[regal cargo]

A device that can measure a certain biomarker in the blood for acute leukemia

it's basically a blood test

alright, enough of that. I'm going back to work now.

[quiet badger]

First off, try to factorize this cubic function and find the x points. And since it's a cubic function, then there will be three solutions (sketch a rough graph, mark the points of the x axis in the graph). to find the y intercepts, just substitute 0. to find these so called "etxtremas" there is a way but type the equation on desmos (an online graphing calculator).

[gilded narwhal]

been stuck for an hour on this, does anyone understand it?

[south gazelle]

graph the piecewise function first

and then the limit finding is straight foward

if u still needed help

[vast merlin]

tyyy

[south gazelle]

np

We all gotta get through calc

[vast merlin]

yeah

[left knoll]

Need help with a math problem, it's sets

Not so sure how to solve or explain

[feral forge]

share it here

[feral forge]

question

[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.

[left knoll]

hello, I need help, thank you
p/s: sorry for the bad translation because I use google translate as my English level is not high enough to translate these mathematical definitions

[left knoll]

i solved them it’s ok

[left knoll]

Is it asking you to find f'(x0)?

[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.

[sudden parcel]

my results are:
(a) 3
(b) 4
idk if it's 100% correct

[light lagoon]

i need some help on this physics kinematics problem

[twin snow]

Maybe I could try

[twin snow]

(My English level is not adequate for problems in general, so some points may lack clarification)
let T be the time in which both Adam and Besty has run when they reach each other
The stretch of road Adam would have run is 3,2T (w/ 3,2 representing A’s velocity)
The velocity of Betsy when she reaches Adam is 2T
The average velocity of Betsy is (v0 + v)/2 = T (w/ v0 representing her initial velocity, v representing her velocity when she reaches Adam)
The stretch of road Betsy would have run is T^2
The two aforementioned stretches of road have a sum of 26m so:
T^2 + 3,2T = 26
<=> T would be roughly 3,74s
Therefore, Betsy’s speed when she reaches Adam is 2 times 3,74 which is roughly 7,48m/s
and her stretch of road is 3,74 square which is roughly 14m

[blissful ridge]

How do I solve this?

[blissful ridge]

I looked at the solutions in my math book and they confuse me even more

i thought i had a solution but i can understand the way they thought

i got it now $

no help needed anymore

[quaint cedar]

can someone help me with my numerical analysis homework? i need to tabulate the transcendental function, I have the first part of code but i don't understand what's wrong since the summs aren't supposed to be bigger and F(1)~=0.7652. (it's the Bessel function)

[left knoll]

@quaint cedar try tech help

[sullen thicket]

İ need help🥺💗

[hearty estuary]

4,8 can be expressed as powers of 2

write everything as a power of 2 and then add and subtract the powers

2^((17-16)x2-(15-12)x4)) = 2^(2-12)=2^-10=1/1024

[sullen thicket]

Thank u so muck 🥰

[sullen thicket]

can someone look into this question 💗

[left knoll]

in 10 minutes I'll do it for you just to finish my class

C=5

Here you go

[left knoll]

welp

[left knoll]

Guys is 0 the only root of this equation?
e^x=π^x

[left knoll]

In the first question I think it wants you to find the real numbers that are not in f's domain. I don't know what the second one is.

[left knoll]

That s the first sol ofc but what is the second??

[sage coral]

math inductions just dont wanna sit with me

i am going to lose it

[thorny sonnet]

STAY AWAKE

STAY WITH ME

WE DUNT LOSE TO MATH INDUCTION

[thorny sonnet]

maybe I can help u sometimes

if u r doing A-levels Further math P1

I might be able to help

[sage coral]

i understand the steps but its just that i dont know how to progress further in the equations and stuff

[thorny sonnet]

I see

[sage coral]

i guess you could say i dont have the fundamentals

[thorny sonnet]

thats actually a problem

how to say

hmmmmmmm

[sage coral]

i do not understand how this progresses

why is there a 4

[thorny sonnet]

if Im not mistaken, u r asking the 2nd line right

[steep cape]

In theory there shouldn't be other solutions, when you divide a part by the other one you get (p/e)^x=1, that's possible only when x=0 and even if you try to draw on the graph they seem to have onl one common point zero. Maybe you should write xЄ{0}

[thorny sonnet]

the (36 · 6^(k-2))/4

[sage coral]

yes

oh i got it

[thorny sonnet]

if ur asking that, is because originally u have 5 · 6^k which is also 5 · 36 · 6^k-2

[thorny sonnet]

ur number out of bracket is not 20

which means u will times 20 to the number inside

but u dunt want to make any change

u want to maintain the 5 there

infront of ur 6^k / 36 · 6^k-2

so u have to divide by 4, to maintain the number

just like how is there a divide 5 for 5^k

[left knoll]

Thank you. I needed to show that there was only one solution to another equation which ended up looking like that and I wasnt sure if there were any numbers greater than 0 that satisfy it.

[elfin crest]

(Didn't see that someone solved #9 already but anyway, here you go)

[sullen thicket]

Thank you sooo much🥺💗💗💗💗

[elfin crest]

Glad to help.

[sullen thicket]

Thanksss thankss🥰✨✨

[left knoll]

Always 🥺🥺

[manic forum]

1, 0 I think