help-27

[humble galleon]

its in the occupied section

[heady plinth]

It’ll go away in a minute

[humble galleon]

alr

[heady plinth]

Don’t stress

[devout snow]

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[grave glacier]

hi

is this true?

[heady plinth]

Never seen it before

The right hand side is just (3n+3)! Which is kind of interesting

No it’s not true I just checked

[thin fern]

No you can just plug in n=1 which is a pretty clear counterexample

[grave glacier]

ugh

im trying to find out how to expand it

the problem has (n!)^3/(3n)!

i want to figure out how to cancel the 3n!

[polar wharf]

What's the original problem?

[devout snow]

@grave glacier Has your question been resolved?

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[winged wasp]

How can i find the shaded area?function r(\theta)=\theta\cdot\sin(2\theta) and it graphed between 0 and pi. I am struggling to find limits of the integral. I know i need to set r equal zero and find the roots. There are 3 roots. 0,pi,pi/2 and i don't know which ones are the limits

[twin hornet]

$r(\theta)=\theta\cdot\sin(2\theta)$

[woven radish]

DJJ

[stable storm]

its most likely between pi/2 and pi, since it is impossible for it to create that curve in the fourth quadrant between 0 and pi/2

the radius can only be positive or negative

meaning that it can either be in the first or third quadrant for all values between 0 and pi/2

[winged wasp]

the area is between 0 and 3pi/2 that's why i kinda thought 0 pi/2 was the answer but can you elaborate on how did you deicde on those values?

[stable storm]

if we consider theta ranging from 0 to pi/2

the radius can either be positive or negative

if its positive, then itll sweep out a curve in quadrant 1

if its negative itll sweep out a curve in quadrant 3

[winged wasp]

i undersand it can be in 1'st quadrant but how can it be on 3th?

[stable storm]

if the radius is negative

itll flip it in the opposite direction

[winged wasp]

wouldn't it be 4th then?

[stable storm]

not exactly

when we graph these lines, we would imagine ourselves drawing a line through the origin

and at each theta value

if it is positive, itll point in the quadrant that theta lies

if it is negative, we go to the opposite end of the line

which would give us the quadrant that is diagonal from our supposed quadrant

you can also test out theta values between 0 and pi/2 as well as pi/2 and pi to check

[winged wasp]

can you suggest me a video that can help me understand this? I feel like dumb rn

[stable storm]

try this

https://www.youtube.com/watch?v=aSdaT62ndYE

wait nvm this one is probably better

[winged wasp]

thanks so you mean 1-3 and 2-4 quadrants would give the same result?

[stable storm]

what do you mean same result?

[winged wasp]

like if we take the limits of the integral 3pi/2 and 2pi we can take them as pi/2 and pi and it would'nt be wrong

[stable storm]

so if you were to graph this on desmos, between 3pi/2 and 2pi, it sweeps out an entire different portion of the graph

when compared to pi/2 and pi

maybe itll help to graph it out on desmos to see how it creates the curve

[winged wasp]

maybe since it is 1 am i have started to loose my marbles. I will check desmos and the video tomorrow

Thanks

[stable storm]

yw!

[winged wasp]

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[twilit estuary]

,rotate 270

[twilit estuary]

i dont get how to do 18

[sterile geyser]

magnitude formula

[twilit estuary]

yea like

di i just

no

[sterile geyser]

yes

[twilit estuary]

wait

i just square root

and

[sterile geyser]

(5^2+10^2+10^2)^1/2

[twilit estuary]

power of two

yesyes

ouuu

omg wjays wronf with me

okayy tysm

[sterile geyser]

npp

[twilit estuary]

.close

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[weak marlin]

how do I proceed with this problem

[stable storm]

so represent it with an integral first

[weak marlin]

I have the interval as 1 to 3

[1,3]

[stable storm]

yep

[weak marlin]

then do I split it up

[stable storm]

well just integrate the function from 1 to 3

no need to split it up

or did you mean to split up the integrand

[rustic mountain]

Oh and what about y do you keep y as just y?

(i am also learning this I don't know how to solve so asked)

[weak marlin]

that becomes Area

[woven radish]

y0shi

[stable storm]

no need for any formulas

[rustic mountain]

Oh so integration of y is area

[stable storm]

yes between the function and the x axis that is

[rustic mountain]

Icic

[weak marlin]

okay so from that I'm a little confused as to how I should start solving

do I do u sub again?

[stable storm]

yep

maybe the u sub isnt too obvious tho

i would recommend moving the 3 from the x^3 out of the ln first

and then sub the entire numerator

[woven radish]

y0shi

[stable storm]

that should be the integral you have right

[weak marlin]

yep

[stable storm]

alright

so yeah move the 3 from the x^3 outside of the logarithm

[weak marlin]

so 1 + 3ln(x) / x

[stable storm]

yep

[rustic mountain]

So will it be 1/x + 3lnx/x integration

[weak marlin]

then do I just plug in the lower and upper numbers?

[rustic mountain]

U integrate first

[stable storm]

you have to find the antiderivative first

[weak marlin]

oh right

[stable storm]

you can definitely split it up first

[weak marlin]

ah okay

[stable storm]

or just u sub the entire numerator

[rustic mountain]

Oh i see

Multiply divide by 3 then it becomes clear

[weak marlin]

so I have ln|x| + (3 (lnx)^2)/2

is that right?

[stable storm]

yep

dont forget the +C

[weak marlin]

I'm confused bc this doesn't allow me to put a C

[stable storm]

oh right

this is a definite integral

so we would have to use the fundamental theorem of calculus

[weak marlin]

wait so what is the difference between this and one where I would add C

I remember that coming up but what does that mean?

[stable storm]

you would add a C when it is an indefinite integral where there are no bounds

since an indefinite integral would represent us trying to find the antiderivative and not area

[woven radish]

y0shi

[weak marlin]

okay

[devout snow]

@weak marlin Has your question been resolved?

[weak marlin]

I did (ln|3| + 3(ln(3)^2)/(2)) - (ln|1| + 3(ln(1)^2)/(2)) and got 1.819
it shows up as the wrong answer tho

what am I doing wrong

[upper schooner]

How are you working out the integral?

[weak marlin]

I split it up into 1/x + 3ln(x)/x

and then I found the derivative for the first to be ln|x|

and the second 3(ln(x))^2)/2

the second might be wrong?

[stable storm]

did you do ln 3^2 or (ln 3)^2

it should be the second one since that was our antiderivative

[weak marlin]

yeah I did the second one

[stable storm]

it shouldnt give you 1.819 then

[weak marlin]

I may have put it into my calculator wrong

let me try again

[stable storm]

i got 2.909 when i plugged it in

alright

[weak marlin]

oh okay I got 2.909 that time

I'm not sure what I did wrong but maybe I didn't use enough parentheses

[stable storm]

yeah that happens

[weak marlin]

.close

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[weak marlin]

yeah lol

maybe I'll use an online calculator bc it's easier to insert parentheses and stuff

especially if you miss them you don't have to rewrite the entire equation

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[near haven]

Is this correct? If yes then how did we derived this?

[quaint citrus]

See if u can establish a pattern with the terms of the series

2^1 = 2

2^3 = 8

2^5 = 32

2^7 = 128

Also, notice how signs alternate, and numerator is always 1

See if u can go from there

[near haven]

I had already noticed all that
But I still cannot figure out how it all came out to be sqrt of 1?

I mean 2

[quaint citrus]

In terms of n, what did u make the pattern out to be

(Or in terms of any variable u want)

[near haven]

I didn't get your question
The pattern is simply just two more to the power of two in denominator with alternating plus and minus sign (if that's what you were asking)

[quaint citrus]

Ok let’s take a different path

Do u know what a geometric series is

[near haven]

Yes I do

[quaint citrus]

Ok, excluding the first term, what’s the common ratio of this infinite geometric series

[near haven]

2^2

1/(2^2)

[quaint citrus]

Ur missing something

What about the alternating terms

[near haven]

What about them?

[quaint citrus]

U have to include the fact that we have alternating signs in ur common ratio. 1/2 * (1/2^2) is not equal to -1/8

[near haven]

So how should have I written the common ratio?

[quaint citrus]

Figure it out: what do u multiply 1/2 by to get -1/8?

[near haven]

-1/2^2

Oh okay

[quaint citrus]

Correct

Do u know the formula for sum of an infinite geometric series

[near haven]

I do not remember

[quaint citrus]

It’s

(First term)/(1-common ratio)

[near haven]

Okay

[quaint citrus]

Plug in and see what u get

[near haven]

2/3?

Oh we are excluding 1

wait

1/3

[quaint citrus]

No

[near haven]

what?

[quaint citrus]

Try again

[near haven]

first term is 1/2 right?

[quaint citrus]

Yea

[near haven]

(1/2)/(1-(-1/2))

= (1/2)/(3/2)
=1/3

?

[quaint citrus]

No

What’s the common ratio

[near haven]

oh wait

4/15

[quaint citrus]

No

[near haven]

Common ratio was -1/4?

[quaint citrus]

Yes

[near haven]

2/5

[quaint citrus]

Good

So we have

Sqrt2 = 1 + 2/5

Is this true

[near haven]

Yes

[quaint citrus]

Why?

[near haven]

We can say that

but it is not correct

because it would be a rational number

and sqrt2 is irrariotanal

irrational*

[quaint citrus]

Yea, or just directly compare the values

Same thing

Got it?

[near haven]

ok

Yes

why is that so? why is it wrong?

[quaint citrus]

I don’t understand your question

U think it shouldn’t be wrong?

[near haven]

Why is this not correct

I mean we used the formula for geomteric series sum

[quaint citrus]

1+(2/5) = 7/5 = 1.4 != sqrt(2) ~1.414…

[near haven]

Is that factorial after 1.4?

[quaint citrus]

No, != means not equal to

[near haven]

Okay

Yes

it doesn't equal

so does that mean the series in my question was wrong?

[quaint citrus]

If u wanted something in the form

Sqrt2 = 1 + series

Then yes the series is wrong

[near haven]

But it does get closer to actual value after every value in the series

why is that so?

[quaint citrus]

Are u asking why infinite geometric series converge to a certain value?

[near haven]

no, I am asking that why is the equation wrong
When we evaluate it, it gives value closer and closer to actual value of sqrt 2 after every term

And why is the equation famous? How and why did this equation became popular when it is wrong? Also do you know how someone would have came up with this equation? If we could see the process behind it, we would answer many things by ourselves

[near haven]

Do we have any equation (maybe an infinite sum series) in maths that gives us answer to any root problem specially when the answer is irrational?

[quaint citrus]

Honestly I’ve never even heard of this equation. Maybe someone else here has and im just in the dark about it. Seems like some approximation for sqrt(2) but it’s more than 0.01 away from the actual value of sqrt(2), so idk why it’s useful

[quaint citrus]

Yea I mean u can express some irrational numbers through Taylor series

[near haven]

oh okay
I just had found this on the internet. I myself wasn't aware of it before as well

[near haven]

not expressing
I meant a equation that works for any root of any number?

I would just have to insert the values and it gives me the nth root of the specific number

How does our calculators operate the roots? What principle do they use?

[quaint citrus]

Not too sure honestly, maybe someone else who knows the answer can come along and help

I’m sure Google has some answers too for this kind of stuff

[near haven]

I couldn't find it on google so I thought to ask here
but thanks for the help

[quaint citrus]

Yea maybe open a new channel and ask those questions

[near haven]

okay

.close

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[restive river]

I need help with this question

It didn’t make sense to me since the cup of the coffee or increment was -4

[polar bolt]

what?

[restive river]

Like when I did it

[restive river]

The maximum value I got was like 1152 but the cup of corfeee was -4 dollars

Which made me confused

[polar bolt]

,w max (1.4+0.05x)(800-40*x)

[woven radish]

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[polar bolt]

,w plot (1.4+0.05x)(800-40*x)

[woven radish]

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[restive river]

Wdym

So my final answer I got was 1.25

But my friend said it is 1.2

I’m confused

It means like they sold 800 cups of coffee a day

For 1.4$

But then after I did the calculations

I got -4 as how much I should decrease the cost

[polar bolt]

Yes so 1.4+0.05*-4=1.2

[restive river]

Yes

So is that correct

[polar bolt]

Yes

[restive river]

Why do you multiply it by four

I just minused it by 0.05 four times

And got 1.25

Like you decrement by 4 times

So 0.05 -0.05x4

[polar bolt]

Huh?

[restive river]

Wut

I thought of it as

0.05 minus 0.05 4 times

Am I thinking wrong

[polar bolt]

Your intial price is 1.4

[restive river]

Yes

[polar bolt]

maximum is if you decrease the price by 0.05*4

[restive river]

This makes it decrease 0.15

[restive river]

Why

[polar bolt]

What?

Thats what we found as maximum?

When x=-4

[restive river]

OHHHHHH

I get it

I am so dumb

Thank you

.close

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[short latch]

how do I solve this

[short latch]

do I gotta do the 3 step continuity test?

or is that not necessary for this problem

im used to solving a continuity question in like a piecewise format

[glacial wyvern]

ugh I already hate that problem because the first one isn't defined on that interval

so the question doesn't make a lot of sense

But I think your teacher might think that 1/x is not a continuous function for whatever reason because unfortunately a lot of people seem to think that

[short latch]

key says the answer is E but how

[glacial wyvern]

yeah well II and III are certainly continuous

II is continuous because it's piecewise continuous and at x=0 it's clearly continuous

h is continuous because all root functions are continuous

f is up for debate...

[short latch]

so I just do the 3 step continuity test for each function

if I dont know by just looking at it

[glacial wyvern]

Well if I understand correctly what the 3 step continuity step is then I think it's a test for determining whether a function is continuous at a given point

so for example you could do that test for |x| at x=0

but if you're asked whether a function is continuous on an interval, then you probably have to appeal to well-known results

unless it's a piecewise function, in which case you have to be very careful when the definition changes

[glacial wyvern]

You can tell your teacher that 1/x is a continuous function, meaning it's continuous on all points of its domain, so therefore any problem where you claim that 1/x is, in any sense, "not continuous", is a pedagogical catastrophy

The problem is basically like asking "is 1/x a continuous function on the set of all nonzero polynomials"

but that makes no sense because 1/x is not a function defined for polynomials

And that's a bad example because you could conceivably think of a function that maps a nonzero polynomial p to the rational function 1/p

but you cannot, under any scenario, interpret 1/0 in any reasonable fashion. And as a result, if you remove 0 from the domain, then your function IS continuous on [-1, 1]\{0}

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[toxic monolith]

Can anyone help me ?

I managed to do A, the problem is B, C and D
And I discovered that X≠-5

[toxic monolith]

in question D in the photo it says r but it is X

[magic thicket]

Notice it's actually affine in y
So for a fixed x there's only one real y leading to a solution
When is that y an integer?

[toxic monolith]

In fact, I think that X and Y can be several numbers like these:

( X; Y )
( 2; 7 )
( 3; 25 )
( 7; 227)

[magic thicket]

Well it is asking for the number of solutions
It could even be infinite

[toxic monolith]

Yes I thought about that too but asking "how many" seems like the question wants a specific number

[devout snow]

@toxic monolith Has your question been resolved?

[toxic monolith]

<@&286206848099549185>

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@toxic monolith Has your question been resolved?

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[mystic jewel]

How do you find the parametric equations for this curve? I know how to find the equations when it’s a line, but I’m confused how to start

[heady plinth]

looks like an ellipse but i have no idea

[spare crypt]

you usually start with the parametric equation of a circle of radius r, which is (rcos(t), rsin(t))

and just squish it or whatever to make that shape

[restive river]

What’s the equation for an eclipse

x^2/h + y^2/k = r^2

Use that

Maybe

[devout snow]

@mystic jewel Has your question been resolved?

[mystic jewel]

I tried and I sort of got it, but obviously the left side of the ellipse shouldn’t be there

[spare crypt]

that's good, try -pi/2 to pi/2

[mystic jewel]

how do you determine the t values?

[spare crypt]

the curve starts on the right at t=0, and goes counterclockwise and repeats at 2pi

so bottom to top is -pi/2 to pi/2

[mystic jewel]

👍 thank you

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[vivid hill]

can someone explain to me how they got this as the answer ??

[devout snow]

@vivid hill Has your question been resolved?

[vivid hill]

<@&286206848099549185>

i’m also confused on this one

[devout snow]

@vivid hill Has your question been resolved?

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[rugged sparrow]

The number of integral solution of the equation:\$x^{3}-8xy+x^{2}y-8x^{2}+xy^{2}-8y^{2}+y^{3}-8=0$\ is?

[woven radish]

B-eard

[rugged sparrow]

Help

It doesn't seem to be factorable

the options are
(A) 2
(B) 4
(C) 12
(D) 3

The polynomial is symmetric

so option D is eliminated at first glance

[late rose]

hey

you can factor it

[rugged sparrow]

oh can I?

[late rose]

yeah

[rugged sparrow]

,w factor x^3-8xy+yx^2-8x^2+xy^2-8y^2+y^3-8

[woven radish]

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[rugged sparrow]

erm

[late rose]

the last term

looks like sum of cubes

umm

hold on

ah nvm

[devout snow]

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[rugged sparrow]

<@&286206848099549185>

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@rugged sparrow Has your question been resolved?

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[dry iron]

im abit confused. how did they see that the 5th score and 6th score is 11? and 10th and 11th score is 12?

[hushed lance]

you can imagine the data listed out completely so it would look like
10 10 10
11 11 11 11 11
12 12 12 12
13 13 13 13 13 13
15 15

then just count

[dry iron]

thanks

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[devout snow]

@fossil moth Has your question been resolved?

[fossil moth]

<@&286206848099549185>

[fossil moth]

<@&286206848099549185>

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@fossil moth Has your question been resolved?

[fossil moth]

<@&286206848099549185>

[fossil moth]

stupid question but whats the difference between ill and well conditioned? how do i recognize it

i also see moderatly ill conditioned
and i mean, how do i look at a matrix and see it? i have the proper definition but what do i actually look for
i see the larger the number, the more ill conditioned. but what is it in reference to?
whats the comparision?

why us 21 considered close? what is it relative to?

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<@&286206848099549185>

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[atomic torrent]

is there an easy way to prove that cos(sqrt(n)) does not converge for naturals n?

[atomic torrent]

or actually, that floor(cos(sqrt(n)) doesn't converge

[stone stump]

you would just need to show that its not always positive or negative. that feels doable

[sand dove]

there is a quite beautiful way using subgroups of R, are you familiar with group theory?

[atomic torrent]

yeah a little

[sand dove]

ok

then the schema for proving all your assertions would be :

• A = {n+2pim | n,m integers} is dense in R
• {cos(n) | n natural integer} is the image of A by cos, thus is dense in [-1,1]
• then cos(n) or floor(cos(n)) doesn't converge

[stone stump]

I mean showing that A is dense is harder than just showing this

[sand dove]

but that's overkill

yeah

you can also reason by absurd I think, and if c is the limit of cos(n) then apply trig identities

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[lusty geode]

I need to know what im missing here, The question asks for the curvature and radius

[lusty geode]

First pic is the question itself, 2nd pic is the answer and 3rd pic is one (out of many) attempt

The vector T seems very hard to derive, and I don't think I'm in the correct path to the wanted result

[lusty geode]

(In the point P = (2,2))

Question 147

<@&286206848099549185>

[devout snow]

@lusty geode Has your question been resolved?

[lusty geode]

<@&286206848099549185> (pretty please)

[strange moss]

This thing is in Portuguese?

[lusty geode]

Yes, but I'll do my best at translating if needed

[strange moss]

Go ahead!

[lusty geode]

147. Find the curvature and the radius of curvature of the curvature parameterized by r(t) = ( 2e^t , 2e^(-t) ), at P = ( 2 , 2 )

Crude translation but I hope you can get the ideia

[strange moss]

Find the curvature and the radius of curvature of the curve parametrized by $(\sigma(t) = (2e^t, 2e^{-t}))$ at the point $ P = (2,2)$.

[woven radish]

Hass_sml

[lusty geode]

That's it!

Any idea on what to do to get to the √2/4?

[devout snow]

@lusty geode Has your question been resolved?

[lusty geode]

<@&286206848099549185> I'm following the 15 minute rule, someone pleeease help

[kind anchor]

What is it

The problem

That you need help with

[lusty geode]

.

[lusty geode]

This is the question

The expected answer is k = √2/4

[devout snow]

@lusty geode Has your question been resolved?

[devout snow]

@lusty geode Has your question been resolved?

[lusty geode]

<@&286206848099549185>

[lusty geode]

.

[lusty geode]

.

[buoyant flume]

do you know the standard formula for this?

there is one for curvature of parametrized curves

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[restive river]

hi! can any one help me make a product/grid table or tree diagram for this question?: “the mathematics club of a school has three members. how many ways can this club select a president and secretary if everyone is capable but no one can hold both positions?”

[restive river]

do you need to draw one of those?

because otherwise the problem is straightforward to do

[restive river]

yes

ok just do a tree diagram

you can have one of three choices for the first stage (president)

then one of two choices for the second stage (secretary)

do yk how to begin to draw one in that case?

[restive river]

yes so how many tree diagrams are there supposed to be?-

just 1 right?

yes

so first I start with president?

then what do I branch that with?

[restive river]

u have three choices

call the dudes idk

A, B, C

u can branch to either 3

okay so
president -A
-B
-C

what do I branch that with now?

[restive river]

if u picked A then u have B or C to choose from

if u picked B then u have C or A to choose from

if u picked C then u have A or B to choose from

you get the idea

Oooh okay

so I branch A with B and C?

okay okay

OKAY I GET IT NOW Thank you!!!

.close

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[restive river]

help

.reopen

[devout snow]

✅

[restive river]

wot

I FORGOT

how do I unclaim this

eh?

u did

just

type .close

and it will eventually close on its own

.close

[devout snow]

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[restive river]

okayyy

[devout snow]

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[viscid goblet]

Hey can someone help me on this

[viscid goblet]

Do I use dy/dx

[restive river]

so the equation of \emph{any} line is given by [
y-y_0 = m(x-x_0)
]

[viscid goblet]

yes

[restive river]

the equation of the \textbf{tangent} line is all the same, but the difference is that the slope of the tangent line IS the definition of the derivative. So we have: [
y-y_0 = \6{f'}{x_0}(x-x_0)
]

[viscid goblet]

yes

[restive river]

right, does this help?

[viscid goblet]

So i need to find another close cordinate to find the tangent line?

[restive river]

no the point (2,5) is all you need

[viscid goblet]

ok give me a min let me try to solve it now

[viscid goblet]

is the answer the first one

y=10x-15

I used dy/dx to find the slope

the slope was 10x

and then I applied (2,5) to y=10x+c to find c

and c was -15

So the answer should be y=10x-15

@restive river just let me know if I got it right

also Thanks by the way

yep it was correct

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[fathom maple]

Ello

[fathom maple]

So i recently found this reel

https://www.instagram.com/reel/C3gA-_IqjT7/?igsh=cWxqMHV6b3BwNDAx

alevelmaths2024

A-Level Maths 🧮 Mechanics: projectile motion ⚽️ can you use your knowledge of projectile motion to calculate the speed you must kickable to hit the crossbar in a crossbar challenge? 💭

#Mechanics #ProjectileMotion #Projectile #Student #Engineering #Physics #messi #crossbarchallenge #Math #Mathematics #trigonometry #alevelmaths #alevelphysics

Likes

6666

Instagram

What do they use cos and sin in there?

Why*

[smoky eagle]

because you kick the ball horizontally and vertically and the same time

so the velocity vector has a x and y component

Vx = Vcostheta

[fathom maple]

i dont get it..

[junior chasm]

resolution of a vector

[rigid pewter]

Ax, the horizontal speed, tells us how fast the ball reaches the net
Ay, the vertical speed, tells us how high the ball is when it reaches the net

[fathom maple]

Ohhh

How do they know its 30 degrees tho btw

[rigid pewter]

it's a given

[junior chasm]

whats 30 degrees?

[rigid pewter]

the question is to find the kick speed

[fathom maple]

So it could be any other angle

[rigid pewter]

yeah

[fathom maple]

Ahh i see i see

[smoky eagle]

wouldn't give the same answer tho

[fathom maple]

also what is -g and

a

a is acceleration right?

And also u

[smoky eagle]

yes

-g is the vertical acceleration, or gravity in this case

[fathom maple]

How about u?

[smoky eagle]

it's negative because it accelerates the objects downwards

u?

do you mean v?

[fathom maple]

no u

It says

u = v.sin 30

[smoky eagle]

oh ok

it's the vertical component of the velocity

it's the same as Vy

[fathom maple]

Ahh i see i see

[smoky eagle]

here it's called u for some reason

[fathom maple]

also doesn't the ball experience deceleration

?

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[hasty crane]

Is the way I solved correct

[hasty crane]

.close

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[devout snow]

@undone stump Has your question been resolved?

[undone stump]

<@&286206848099549185>

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@undone stump Has your question been resolved?

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@undone stump Has your question been resolved?

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[restive river]

I just can't solve this question

like

ik we have to v^2 = u^2 + 2as

but idk what value i should substitude

[elfin atlas]

um you should use \newline
$h = u_y \cdot t - \frac {1}{2} \cdot g \cdot t^2$ \newline
$u_y = 14 sin(\alpha)$

[woven radish]

penguin

[elfin atlas]

It's a projectile motion under the influence of gravity so the horizontal velocity remains the same in the entire process @restive river now try on your own

You're not supposed to write the answer sir, let them try

[heady cloud]

oh sorry i've not seen the "occupied"

[elfin atlas]

no worries

[heady cloud]

😅

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[glass perch]

hyatt

[glass perch]

someone help plz

[glass perch]

gyatt

[restive river]

goddamn

light mode

[buoyant holly]

Pass

Thats killing my eyes

[devout snow]

@glass perch Has your question been resolved?

[glass perch]

y’all so weak even light no diffs you

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[jaunty abyss]

Hi

[lofty glacier]

@jaunty abyss post your question

[jaunty abyss]

Is number 14 correct?? How did I get 5

[jaunty abyss]

I first write hi so nobody takes the channel

I was writing my question

Thanks for your patience 🙏

[lofty glacier]

dont worry of you posted a question no one can take your channel

[upbeat ember]

Tried to many times and had it stolen smh

[lofty glacier]

14th i think is wrong

[lofty glacier]

ight i ll raise this matter to mods and see if we can do something about this problem.

thanks for pointing it out

[jaunty abyss]

Yeah it didn’t seem right

[lofty glacier]

its the 6th root of the inside term

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[jaunty abyss]

3 I guess

[lofty glacier]

ight

so when it comes to these type of question.

just write it like this

$(5x^4)^(1/6)

like this

now do what is, that if the terms inside are in multiplication then you can split them like this

@jaunty abyss this is your answer

[jaunty abyss]

Oh ok

I see now

And 4/6 becomes 2/3

[lofty glacier]

yes

if your doubt has been resolved then free this channel, if not then post the doubt here
thanks
and keep doing maths

[jaunty abyss]

.close

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[frank halo]

Jordon scores the 53 on his math test. the class averages 57 with the standard deviation of two points. How many standard deviations below the main does Jordan score?

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[inner ibex]

exucse me does anyone know how i can input this into my calculator

[inner ibex]

its only worth 1 mark so i think they want us to use calculator

[rigid pewter]

do you know the magnitude formula

[inner ibex]

yes

but i want to use my calculator to do it

cuz we dont get marks for working out

[rigid pewter]

i doubt your calculator has a vector magnitude feature built in

[inner ibex]

it does

i saw my teacher use it lol

[rigid pewter]

oh wild

[inner ibex]

i think i found it

is norm the same as magnitude

[rigid pewter]

yes

[devout snow]

@inner ibex Has your question been resolved?

[inner ibex]

omg i found a nifty tool lol

[devout snow]

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[spark kite]

HELP

[spark kite]

i need help with this question

this is financial maths

[devout snow]

@spark kite Has your question been resolved?

[spark kite]

im still waiting

[ocean charm]

Ok

Hi

What part are you on

Hello

@spark kite

@spark kite

@spark kite

@inner ibex

[spark kite]

yes

[ocean charm]

<@&286206848099549185>

[spark kite]

stop pining

[ocean charm]

Ok

[spark kite]

and start helping

[ocean charm]

Ok

What part

[spark kite]

im still confused abt

[ocean charm]

Ok

[spark kite]

how to figure how many hours are worked on the weekdays

i tried some weird working out but my answer was still wrong

[ocean charm]

Her wage is the same

For Saturday

[spark kite]

yep

for saturday it's 5 h * double time pay rate * $13.74

[spark kite]

but the real challenge is here ^^^

[ocean charm]

I will get the senior manger in this

Just get a good night sleep

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[red spire]

If f is a linear map with f : IRn → IRn and Kern(f) = {o}, then
the mapping matrix A is invertible.

is this statement true or false?

Can you help me, I don't really know how I can argue. matrix A is invertible could mean that the rank is equal to n

[red spire]

and Kern(f) = {o} means the only vector I can insert in the mapping matrix is 0 to get the zero vector, all other vectors I insert get me a different vector

oh okay, so a possible mapping matrix is injective because of Kern(f) = {0} and surjective because of IRn -> IRn. And a bijective matrix is invertible, so the statement is correct

[devout snow]

@red spire Has your question been resolved?

[sullen island]

yep

[devout snow]

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[light niche]

can someone explain how to do part c ?

[regal moat]

You can write A(t) as a function that describe the amount of water in the pipe

Then the least amount of water in the pipe will make dA(t)/dt = 0 and d^2A(t)/dt^2 > 0

[light niche]

I worked with that, sorry i didn't mention it but my graphing calculator doesn't have a CAS

[light niche]

how would i write that into a graphign calculator?

[regal moat]

A(t) = 30 + R(t) - D(t)

[light niche]

let me show you the problem i am having with that

[regal moat]

Then solve for t base on these condition

[light niche]

it want sme to specify a value for x at which i want the result of the derivative

[regal moat]

You need to solve by hand

[light niche]

it's a pyq from AP calc AB, it's supposed to be done with a grpahing calculator, 2 questions with four parts each in just 30 minutes by hand is not possible

[regal moat]

Then im not sure then

Can it graphs like Desmos?

[light niche]

i think so

[regal moat]

Cause u can graph it like Desmos then u can graph this and "see" at which t, A(t) is minimum

[light niche]

let me see

[light niche]

it becomes 0 at a negative value of time 😐

[regal moat]

What do u mean?

I've never touched a graph calc before

[light niche]

A(t) = 0 at like -30 or something

[regal moat]

Thats not possible?

[light niche]

how can time be negative?

[regal moat]

.

[regal moat]

Can u restrict it? 0 < t < 8

[light niche]

i can

but even in what you did with your function there

the answer is incorrect

[regal moat]

Whats the solution then?

[light niche]

i don't know

i just know the answer

[regal moat]

Yeah what is it?

[light niche]

it's 3. something

[regal moat]

Bruh

I know whats wrong

@light niche

t=3.272 and A(3.272) = 27.96499

[light niche]

Hmm yea I think this works actually

But I would have to check if my graphing calculator would accept input like this

Thanks I will close the thread, I am outside so if I need help I’ll reopen when I get back home

.close

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[kind wasp]

I have difficulty understanding this problem: Given a binary event $A={0,1}$ with $P(A=1)=0.75$ and a set of finite events $B_i$, $i=1,\dots,n$, mutually independent. Also given the probabilities $P(A|B_i)=\alpha_i$ and $P(B_i)=\beta_i$, $i=1,\dots,n$. How can you calculate $P[A|\bigcap_{i=1}^n B_i]$?

[woven radish]

lobbst

[kind wasp]

Is P(A) = P(A =1) = Probability that even A happens?

[jaunty mantle]

no

{A = 1} is the event

use the definition of conditional probability

[kind wasp]

And can we deduce something like P(A) = \alpha ?

[jaunty mantle]

no

[jaunty mantle]

do this

[kind wasp]

Okay I can get that but what is mean by P(A | B_i)? Probability that B_i happens given … what?

[jaunty mantle]

no

probability of A given B_i

Let (A, B) be events. Define
$$P(A|B) \coloneq \frac{P(A\cap B)}{P(B)}$$

[woven radish]

Frosst

[jaunty mantle]

if P(B) = 0, define P(A|B) = 0

[kind wasp]

The part that I don’t get is that P(A) is not an event by itself. I need to calculate P(A) \times P(B_i). But is it P(A = 1) \times P(B_i) or P(A = 0) \times P(B_i) ?

[jaunty mantle]

P(A) is not an event it is a number, A is an event

where do you need to calculate P(A) * P(B_i)?

[simple torrent]

could i get help

[jaunty mantle]

#❓how-to-get-help

[kind wasp]

yes I meant that A is not an event

[jaunty mantle]

yeah i dont think A is an event either

[kind wasp]

because of this

[jaunty mantle]

i dont think P(A|B_i) is well defined

the first slot of P( • | • ) needs to be an event

[kind wasp]

yess you see the problem too now

that’s why I don’t get the question

[jaunty mantle]

well me neither

maybe ask your teacher

[devout snow]

@kind wasp Has your question been resolved?

[kind wasp]

I’m not a student, just preparing for an exam by myself

<@&286206848099549185>

[devout snow]

@kind wasp Has your question been resolved?

[devout snow]

@kind wasp Has your question been resolved?

[devout snow]

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[restive river]

how did they turn the first one to the second one?

they factored

I can't see how

[fresh elbow]

Subtract dy/dx from the first equation

what do you get

[restive river]

e^2 x dy/dx - dy/dx

oh

cool thanks

[fresh elbow]

👍

[restive river]

.close

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[zealous umbra]

i dont get it, the question was

[zealous umbra]

i get the second line, how does it go form the second to the third?

[devout snow]

@zealous umbra Has your question been resolved?

[devout snow]

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[unborn atlas]

Am I doing this right so far and if so what’s my next step?

[lost laurel]

yes

partial fractions

[unborn atlas]

So

I need to take the antiderivative of it

And so I tried ln|x|

But I don’t see how I can

[mossy dove]

I can't read the starting integral @unborn atlas

dz?

[glad patio]

You can do it by doing this

$\frac{1}{(u-1)(u)} = \frac{A}{u-1} + \frac{B}{u}$

[woven radish]

TayBee

[glad patio]

After you do that ln will work nicely

[unborn atlas]

Yes

[unborn atlas]

Huh?

How

[mossy dove]

wait a sec

ok

Im not english native so i can't explain properly, here is the method... i can try to explain if you have any questiosn

@unborn atlas

idk if you did sub for u, just revert to z

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[fervent dragon]

Given a boundary box with known side lengths that fits an ellipse that is tangent to all four sides and the ellipse is at a known angle theta, solve for the lengths of the semi-major axis and semi-minor axis

[fervent dragon]

Pretty much every resource I've used to try to get a formula uses a rotated boundary box, but I need a formula to get the axis lengths when the boundary box is aligned with the x and y axis

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[modern spear]

How they did this?

[covert root]

What are the key theorems for logarithms

How do you simplify equivalent fractions

[modern spear]

So they just multiplied both sides with log

And got x^2 and on the right got 1

[covert root]

I think the RHS should be 10 for the second equation

Wait let me think

What is written in the picture does not look correct

We would have log_10(x^x)/40 = 1 as the final equation if we want the RHS to equal 1

[modern spear]

It’s bad writing but I got right answer

It’s x^ not x*

.close

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[hearty nexus]

https://discord.com/channels/268882317391429632/903486480985489478

[hearty nexus]

it got locked

so I'll continue here

this is the question

[covert root]

What is 2^5

[hearty nexus]

my answer is -2.5

but in the answer key, its 2.5

I don't know why

[covert root]

Have you check with calculator?

!show

[devout snow]

Show your work, and if possible, explain where you are stuck.

[hearty nexus]

see #help-28

last messages

[final scarab]

32 = 2^5

[hearty nexus]

I know

I checked with a calculator, both 2.5 and -2.5 give wrong results

[final scarab]

hmm

[hearty nexus]

,w 2^(2.5^2) = 32(2^(4 * 2.5))

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rynitee

[final scarab]

show your work

answer shouldnt be 2.5 or -2.5

[hearty nexus]

$\log(2x)^2 = \log[32(2^(4x))]$

[woven radish]

rynite

[hearty nexus]

then

$\log2^x + log2^x = log32 + log2^{4x}$

[woven radish]

rynite

[hearty nexus]

$x\log2 + x\log2 = \log32 + 4x\log2$

[woven radish]

rynite

[hearty nexus]

$2x\log2 = \log32 + 4x\log2$

[woven radish]

rynite

[hearty nexus]

$-2x\log2 = \log32$

[woven radish]

rynite

[hearty nexus]

$-2x = \frac{\log32}{\log2}$

[woven radish]

rynite

[hearty nexus]

$-2x = 5$

[woven radish]

rynite

[hearty nexus]

$x = -2.5$

[woven radish]

rynite

[hearty nexus]

@final scarab

[hearty nexus]

$\log(2^x)^2 = \log[32(2^{4x})]$

typo

[woven radish]

rynite

[hearty nexus]

so what's wrong now?

[covert root]

The issue is with exponentiation

You have worked with (2^x)^2

You should instead work 2^(x^2)

[hearty nexus]

isn't that equivalent to
2^x + 2^x

[covert root]

no that is not related to what I have written

To give an analogy: calculate 2^3^2 on a calculator the answer will be 2^9. Instead in your scenairo we are treating it as (2^3)^2 or in other words 8^2

[hearty nexus]

huh

I thought

$(2^x)^2 = 2^x + 2^x$

[woven radish]

rynite

[covert root]

(2^x)^2 = 2^x * 2^x

[hearty nexus]

OH RIGHT... I understand my mistake now :)

[covert root]

If we applied logs then we would get 2log(2^x)

[devout snow]

@hearty nexus Has your question been resolved?

[hearty nexus]

alright ill solve it again

[hearty nexus]

$x^2\log2 = \log32 + 4x\log2$

[woven radish]

rynite

[hearty nexus]

is that right so far

[devout snow]

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[hearty nexus]

.reopen

[devout snow]

✅

[sturdy mirage]

Take a slight step back. Let's go back to $log (2^x)^2 = log(2^x+2^x)$.

[woven radish]

Narutoes

[hearty nexus]

I got a right answer though

[sturdy mirage]

Oh, why'd you reopen it then?

[hearty nexus]

like just now

sorry lol

[sturdy mirage]

All g

[hearty nexus]

.close

[devout snow]

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[hasty crane]

I’m stuck on final step

[hasty crane]

Why did the 1/4 become 4

Blue is my solving and black is the solution

[safe fractal]

If you have an expression like 1/4 * x the it becomes x/4... is that what you're asking?

[hasty crane]

An no I mean in the denominator

There’s a 1/4 and then the root

How is it that in the black instead of 1/4 they have just 4

[safe fractal]

Oh, you mean how the fraction exponent turned into a root?

[hasty crane]

My answer is identical except for that one

[hasty crane]

Nooo the other thing

Wait I’ll draw it

[tame matrix]

It's -3/4

It went in Denominator

[tame matrix]

You took 1/4 in Dr

[safe fractal]

(a/b) * (c/d) = (ac/bd)

[tame matrix]

See the first step

When you take 1/4 down