help-26

[humble badge]

ok

sorry i was doing something'

my options wre

[heavy knoll]

is it an option tho

[humble badge]

2m/s

0m/s

50m/s

20m/s

"?"

[heavy knoll]

I guess put the question mark then?

[humble badge]

ok

[heavy knoll]

because it should be 29.7

[humble badge]

does it not want us to do any equations?

[heavy knoll]

wdym

[humble badge]

im just cuirous why 29.7 wouldnt be an option

[heavy knoll]

don't know, sometimes they wanna trick you

[humble badge]

oh

[heavy knoll]

ok sumbit them did we get both questions right

?

[humble badge]

that was the first quiestion 😭

theres 3 more but its actually where u solve it

[heavy knoll]

well fuck man,

[humble badge]

like no chart

like it give sme values

then asks me what the velocity is

no mltiple choice

[heavy knoll]

ok wait since i helped you with physics can you help me with simplifying exponential expressions?

[humble badge]

🙂

can i see

[heavy knoll]

ok wait

its loading

both these idk how to do the fractions one especially @humble badge

[humble badge]

🥲

[heavy knoll]

u got this right?

🙏

bro...?

[humble badge]

uh

[humble badge]

whens it due...

[heavy knoll]

tommorow

like i got a mid term i am studying it

cuz idk how to do it

[humble badge]

oh

[humble badge]

what time 😭

[heavy knoll]

bro why

so u dont know thisss??

[humble badge]

my precalc class is teaching us algebra 2 rn 😭

[heavy knoll]

bruh what do they teach u guys in the states man

shit man thi is like algebra 4

bye bro i'm jumpin off a cliff nice knowin ya fam

[humble badge]

what 😭

algebra 4?!!?

[topaz sinew]

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[topaz sinew]

Please don't occupy multiple help channels.

[orchid sonnet]

this is correct right?

[floral bison]

Is a just a dummy variable

[orchid sonnet]

yea

[floral bison]

Looks good

Wait

What are the others

[orchid sonnet]

here

out of all these the one i chose is correct right?

[floral bison]

So a and b are cubic thus wrong

[orchid sonnet]

o

so its A?

[floral bison]

You have a quartic

A is cubic

Therefore wrong

[orchid sonnet]

oh i see

[floral bison]

Yeah it looks like D is most likely right

[orchid sonnet]

i see

i also have another question

its 2 degree right?

@floral bison

[floral bison]

Quadratic but it looks real sus because table supposed to be mirrored

Unless parabola is shifted somewhere

[orchid sonnet]

can u make sure its 2 degrees?

im positive with my answer but i cant get it wrong

[floral bison]

I only see a decrease and an increase

Yes it’s quadratic

[orchid sonnet]

how about this

[floral bison]

Find the zeroes

And use them in factor form

[orchid sonnet]

oh alr

whats this

[floral bison]

Reason this one out

[orchid sonnet]

i got x

c

[floral bison]

Correct

[orchid sonnet]

yay

and for this i got

i dont get this

[floral bison]

n is the exponent

[orchid sonnet]

?

[floral bison]

n is the exponent which means n is a degree

[orchid sonnet]

okay how do i find n

@floral bison

[floral bison]

The number of factors equals n

[orchid sonnet]

so in this case what would it be

@floral bison

3?

.close

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[elfin musk]

Guys for the maximum torque

its just the Y point of the vertex

but when I do the vertex formula I dont seem to find the right answer

[radiant tapir]

hi what did you get as the answer?

and can you show your work so we can potentially see the mistake?

[elfin musk]

its so wrong but 144.9055

cause I got -23 and divided by 2(3.75)

then thats X for vertex

then i plugged it in the equation for Y axis

[radiant tapir]

ah see you forgot the negative in (-3.75)

it's this

[elfin musk]

oh yea I put negative

[radiant tapir]

x = $\frac{-(23.2)}{2(-3.75)} = 3.093333333...$

[elfin musk]

yea thats what I did

[thorny flame]

MellowDramaLlama

[elfin musk]

wait so then I just plug it in

the equation

[radiant tapir]

,calc -3.75(23.2/7.5)^2 + 23.2(23.2/7.5) + 38.8

[thorny flame]

Result:

74.682666666667

[radiant tapir]

Yeah the vertex is the point $\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

[thorny flame]

MellowDramaLlama

[elfin musk]

ty bro

.close

[radiant tapir]

yep np!

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[minor cipher]

whats the smartest way to find determinant in order to find eigenvalues

[minor cipher]

like you have to find the determinant by using the general formula anCn...

or is it better to gauss-jordan and get triangular matrix

and then take sum

product*

<@&286206848099549185>

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@minor cipher Has your question been resolved?

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[neon iron]

How can I do a comparison test for

[fierce zealot]

You can make the denominator smaller

Which makes the whole fraction bigger

By deleting a term

Try removing x

Oh yeah right. So you’d be comparing it to a p series which will diverge

So it will diverge

[neon iron]

Doesn’t work

With 1/x

@fierce zealot

[fierce zealot]

The integral test says the improper integral and the infinite series will converge or diverge to the same thing given that your function f(x) >=0 for all x and f is eventually decreasing.

[neon iron]

Is the “integral test” the same as the “comparison test”?

[fierce zealot]

https://tutorial.math.lamar.edu/classes/calcii/IntegralTest.aspx

No

[neon iron]

Oh yeah

Well

I didn’t learn this

I’m expected to use the comparison theorem/test

[fierce zealot]

Hm ok I didn’t see this.

[neon iron]

Or u-sub (and other basic integration techniques)

[neon iron]

Any ideas?

[fierce zealot]

Ok right

So the comparison test says if an<=bn for all n, then if integral of an diverges then integral of bn diverges

Right?

https://tutorial.math.lamar.edu/classes/calcII/seriescomptest.aspx

Here, basically the second point

[neon iron]

Yes

[fierce zealot]

So

[neon iron]

Same idea for convergence right

[fierce zealot]

If we can find an integral of some an, such that it diverges then the integral of bn also will diverge (as in 2)

Similarly, if we can find an integral of some bn that converges, then so is an (as in 1)

[fierce zealot]

We try try to do this one

If you make the denominator sqrt(x^2+x^2) > sqrt (x^2+x) which is what you originally had

Then the function 1/ sqrt(x^2+x^2) < 1/sqrt(x^2+x)

But the lhs is then just integral of 1/(sqrt(2) *x) from 1 to infinity which will diverge

So by (1)

Your function will diverge

[neon iron]

Hence original integral is divergent

[fierce zealot]

Yeah

[neon iron]

How would the same thing be applied to integrals like

[fierce zealot]

Well. Integral test says the infinite series converge iff the improper integral converge

Usually

The integral is easier to compute

So they usually give you a series

[thorny flame]

🌐

[fierce zealot]

Oh

[neon iron]

There’s no obvious function that’s smaller than this

[fierce zealot]

Nope

Ther is

You will get a messier power (not really that messy)

But it works

Like

How about doing the same thing we did with the previous one

In the previous one we replaced x by x^2

[neon iron]

Yeah

[fierce zealot]

Making denominator bigger

You just do the same thing here

You make the 1 to be x^2, x^3 or more conviniently x^5

Which again makes the denominator bigger

Yeah?

Alright. I think I will sleep now

[neon iron]

It’s convergent

Unfortunately

[fierce zealot]

Ok well

Instead of trying for 2, why not try 1

[fierce zealot]

This one

Find a function bigger than the one youre given

If that bigger function converges

So must the function you’re given

There is one very obvious choice

Remember you wanna make the denominator of your new function smaller, in order for the function to be bigger

Ok I need to actually sleep

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

Ok I’ll do this later

Heading to bed too

Thanks for your help

[topaz sinew]

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[last anvil]

hey, i just `have a new questions about Parabolas that i was stuck on

[last anvil]

Consider the parabola given by the quadratic equation y = 2x^2 − 8x + 9.
Use x = − b/2a to determine the turning point.

not sure how to do this is what im asking.

[topaz sinew]

@last anvil Has your question been resolved?

[last anvil]

<@&286206848099549185>

[topaz sinew]

@last anvil Has your question been resolved?

[last anvil]

<@&286206848099549185>

[last anvil]

I just gonna give up

.close

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[turbid sphinx]

Hello, can someone help me with this i need to find the intersections from a parabola.

[turbid sphinx]

a b and e

The question is in dutch in my workbook

i dont know how to start on it like i got things but after i do it i make mistakes and i dont understand it

[twin cloak]

What is it asking you to do in Dutch

[jade thunder]

,rotate

[turbid sphinx]

Bereken de eventuele snijpunten van volgende parabolen.
(Calculate any intersection points of the following parabolas.)

[twin cloak]

You can set them equal to each other

If you want to find the points they intersect at

[turbid sphinx]

yeah i did but i will show u

wait a sec

[twin cloak]

Sure

[turbid sphinx]

thanks btw

Here i get stuck

[twin cloak]

Okay you don’t need to keep y I believe

[turbid sphinx]

ohhw

[twin cloak]

You just need 2x^2 +6x = x^2+7x+6

[turbid sphinx]

yeah

and then?

[twin cloak]

And then you can subtract x^2 from both sides

[turbid sphinx]

yea

[twin cloak]

And subtract 7x from both sides

And 6 from both sides to get an expression that equals 0

You should get: quadratic = 0

[turbid sphinx]

i got that

[twin cloak]

You do not need the y still let me show you what I mean in writing sorry

[turbid sphinx]

okay il wait

[turbid sphinx]

,rotate

[twin cloak]

So you start by subtracting x^2 on both sides

And you should get this

Do you get why?

[turbid sphinx]

so it is easy'er?

[twin cloak]

Yes

Pretty much

And so now with this new one on the bottom

Subtract 7x

From both sides see what you get

Try it the way I did you do not need “y” at all really

[turbid sphinx]

okay wait a sec

[twin cloak]

Yep

[twin cloak]

That’s good yeah!

[turbid sphinx]

Thanks

[twin cloak]

And now if get all the terms to the right hand side you should be able to factor and solve for x

Those x values are the x values where the graphs intercept at

And if you plug them in you can get (x,y) where they intercept

[turbid sphinx]

Ohh

thanks

[twin cloak]

Yeah ofc!

[turbid sphinx]

but actually i need to do it on an other way ig. Or maybe this is a special one. Look the other.

[twin cloak]

Actually you can do them the same way

[turbid sphinx]

MP is merkwaardig product( remarkable product)

Oh yeah but of my teacher i need to do it like that

[twin cloak]

If you need that way I’m sorry I’m not too sure how to do it maybe someone else can help but the way I showed is usually what most people do it solve it

Sorry :((

[turbid sphinx]

oh its okay. I will ask it on her (my teacher) tommorow. Have a nice day! And thanks to make time free for this!

[topaz sinew]

@turbid sphinx Has your question been resolved?

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[spark yew]

i need help with this example please.I do not understand anything and what is the topic called?

[tough cargo]

Indeterminate forms I think, $1^\infty$ in this case

[thorny flame]

992qqoloy

[tough cargo]

U can take ln to rewrite it as like $\frac{x}{\frac{1}{\ln(stuff)}} $ and then that turns it into $\frac{\infty}{\infty}$. Tho u could also turn it into $\frac{0}{0}$ indeterminate Form, I'm not sure which is better here tbh I haven't done all the steps

[thorny flame]

992qqoloy

[tough cargo]

But either way u use l'hôpitals after that

And once u finally have the limit $L$ of that, $e^L$ is ur desired limit

[thorny flame]

992qqoloy

[topaz sinew]

@spark yew Has your question been resolved?

[spark yew]

i don;t think we're supposed to use L'hopital's rule,since we havent passed that topic yet and our teacher have this to us

[tough cargo]

Hmmm

[spark yew]

do you see what we did in class ?

[tough cargo]

Oh I'm dumb ic now

[spark yew]

this is a better pic of the initial example

[tough cargo]

Depends on the value of a1/a2 I think

But taking ln still helps

[spark yew]

i miss numbers when I'm solving these kind of examples

[spark yew]

that's all?

[tough cargo]

Yeah p much, you can keep it as $x \ln(stuff)$

[thorny flame]

992qqoloy

[tough cargo]

And then find the limit of stuff

[spark yew]

thanks then

[tough cargo]

mhm

And the actual limit is still $e^L$, or rather where $e^L$ tends to as x goes to infinity (since L won't always be finite)

[thorny flame]

992qqoloy

[spark yew]

What's l?

[tough cargo]

But it's mostly the same for all positive values of $a_1/a_2$. Actually tho I gotta think about this for negative values with magnitude less than one since $a^x$ is only defined for integer x when $a$ is negative 🙃

[thorny flame]

992qqoloy

[tough cargo]

L is the limit of $x \ln(stuff)$

[thorny flame]

992qqoloy

[spark yew]

right

i have a paper tomorrow and hope we don't get this kind of examples

cause i can solve pretty much everything we have solved till now,but this one cause i jut don't understand shit

it's only this one of this kind

[tough cargo]

yeah this 1 is trickier than what you'd normally find at that point

[spark yew]

thanks anyway dude

[tough cargo]

mhm

[spark yew]

really appreciate

[tough cargo]

ok so the answer is... I have no idea what your teacher wants in the case that for instance, you take the limit of $(-1/2)^x$ as x goes to infinity lol

[thorny flame]

992qqoloy

[tough cargo]

the answer is 0

But that's either a complex analysis question (not a super complex one but it is)

Or you gotta be technical about it and restrict the domain to integers

And then the sequence still tends to 0

If they specified that a1 and a2 are nonnegative or something then it shouldn't matter tho

But if they didn't that's kinda a technical question for intro calc

[spark yew]

@tough cargo look

i have solved it by her model,but got stuck here

[tough cargo]

Gotta multiply both numerator and denom by 1/x

[spark yew]

but is it right till here?

can you help me with 1 more thing tho please ?

[spark yew]

. close

.close

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[astral temple]

!status

[topaz sinew]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[frozen path]

Like completely forgotten

[astral temple]

Okay

Let's start with the table

For an event in probability, we can split the possible outcomes into different probabilities yes? Like if we flip a coin, there is a 50% chance of it landing on either side. As decimals, that is 0.5 for one side, 0.5 for the other

But the total sum of probabilities is always 1 or 100%

Can you extrapolate anything from the table with that fact in mind?

[frozen path]

I remember 1

So it adds up to 1 or 100

Percent

[astral temple]

yeah, sometimes we use percentages, sometimes decimals

The point being, the sum of the probabilites for each side has to be 1 in total

[frozen path]

Mmhmm

Wait it’s a biased dice?

Ohhh

So you’ll add them all up Ig?

[astral temple]

Yeah

[frozen path]

So 1 will be 0.31

Erhh my common sense is confusing me

[astral temple]

Yep that's correct

[frozen path]

Wait lemme think so

U have to

Times right?

@astral temple?

[astral temple]

You're on the 200 rolls part?

[frozen path]

Yh

[astral temple]

Then yes there is multiplication involved

[frozen path]

So u times by 200?

[astral temple]

Yes

[frozen path]

Done

600 in total

Wait a min

Oh lmao @astral temple

So 31 times and 18

I’m guessing

[astral temple]

If you flip a coin 10 times

How many times do you expect to see heads or tails

[frozen path]

Mmhmm

5 and 5

[astral temple]

And how did you come up with that

[frozen path]

Errmmm yk

50/50

[astral temple]

mathematically though

not based on intuition

if heads is .5 and tails is .5

[frozen path]

Mmhmm

[astral temple]

then 10 flips gives us 10*.5 and 10*.5

[frozen path]

Yh

[astral temple]

Now move the same concept over to your dice rolling

[frozen path]

@astral temple

Ohh mb

I timesd wrong

Sos

Lmao

I did 100 on accident

1 is 62 and 36

@astral temple?

[astral temple]

sounds about right

as in 1 is 62 and 3 is 36

[frozen path]

Yh

@astral temple can u help me with another question got an answer need to check if it’s right

[astral temple]

sure just post it

[frozen path]

Alr so ik

It would be 5x and 2x

3/4x2x+117=2x

[astral temple]

You should try to define either child or adult as a variable then define the other as some expression using that variable

[frozen path]

but I don’t get a few step steps

[astral temple]

What do you mean by that

[frozen path]

Alr so

Ik that ur supposed to

Wait I forgot smh

[topaz sinew]

@frozen path Has your question been resolved?

[topaz sinew]

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[neon iron]

i don't understand

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

<@&286206848099549185>

[noble laurel]

.close

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[warped pewter]

i just dont understand how to do it with the definition of the derivative

[barren lion]

do you know the limit definition of the derivative

what have you got so far

[warped pewter]

i think the definition of the derivative we are supposed to use is this thing

but im not too sure

[barren lion]

yes

what do you get if you use that definition for the given function

[warped pewter]

((x+h)^(5/2) - x^(5/2)) / h

but it was at this point i was stuck

because i dont know what to do with the (x+h)^(5/2)

i tried using l'hospitals but i got confused with that too

[barren lion]

tried multiplying by the conjugate?

[warped pewter]

you mean multiplying by (x+h)^(5/2) + x^(5/2) ?

[barren lion]

yes

[warped pewter]

let me try

oh ok

ill try that 2 secs

[barren lion]

okay the original one was correct

[warped pewter]

by this?

[barren lion]

you just have to expand

yes

[warped pewter]

ok wait

[barren lion]

yeah, multiplying by the conjugate works

you unfortunately have to expand and cancel and it works

[warped pewter]

ok ima try it now

so i can go from here?

ok i have it

.close

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[neon iron]

Hello?

[neon iron]

(2x+3)/x differentiation

How would I do this?

[floral bison]

Quotient rule

[neon iron]

Idk what that is

I started high school 5 weeks ago

We started calculus last lesson

[floral bison]

Ok

This requires some memorization

So

[neon iron]

Alright

[floral bison]

Gimme a second to write it down

[neon iron]

Thank you

[floral bison]

,rotate

[neon iron]

Let me see

How would I do f’(x) for 2x+3

?

@floral bison

[finite moth]

power rule

[neon iron]

Wdym

[finite moth]

2x equals 2x^1

[neon iron]

Yeah what about it

Differentiate 2x+3?

So (2x+3)^1

= 2x

If it’s differentiated

Or separately

[finite moth]

separately

[neon iron]

2x^1 differentiated = 2

[finite moth]

yes

[neon iron]

3 differentiated = 0

[finite moth]

yep

[neon iron]

So f’(x) = 2

[finite moth]

yep

[neon iron]

g(x)f’(x) = 2x

[finite moth]

yes

[neon iron]

f(x)g’(x) = 2x+3 * 0 ?

Meaning it’s 0

[finite moth]

times 1 cuz derivative of x is 1

[neon iron]

Oh yeah

You’re right

2x-1

[finite moth]

2x - (2x+3)(1)

[neon iron]

(g(x))^2 = x^2

[finite moth]

that’s correct

[neon iron]

Oh ye

3/x^2?

[finite moth]

-3 but yes

[neon iron]

How’s it -3?

[finite moth]

because you have to distribute the negative to all the terms

including the 3

[neon iron]

The - from 2x - 2x + 3

?

[finite moth]

yea

[neon iron]

Ah okay

[finite moth]

bc it’s -(2x+3)

[neon iron]

OH YEAH

YOURE RIGHT

How do I know I need to use the rule

[finite moth]

quotient rule?

[neon iron]

g(x)f’(x)-f(x)g’(x)
/
[g(x)]^2

That

Idk what it’s called

[finite moth]

it’s called quotient rule

[neon iron]

When’s it used?

[finite moth]

whenever both the numerator and the denominator have a variable

[neon iron]

Just like for

(3x^2 -6) / x

?

[finite moth]

yep

[neon iron]

Time to do it again ig

Hold on

2x+2 differentiated = 2 ?

[finite moth]

yes

[neon iron]

I ended up with that

Where do I go from here?

[floral bison]

If it only asked for the derivative, that’s where you stop

Unless you are asked to simplify

[finite moth]

however ur f’(x)g(x) is wrong

[neon iron]

The answer is 3+6x^-2)

[neon iron]

Huh

No? It’s 2x

[finite moth]

it should be 6x * x not x*2

since 3x^2 differentiated is 6x

and -6 differentiated is 0

[neon iron]

So it’s 6x^2

[finite moth]

yep

[neon iron]

Oh shoot

(3x^2 + 6)/x^2

[finite moth]

there ya go

[neon iron]

Thank you

More questions to go

🤥

I’ll use it again here won’t I

(2x^3 + 3x)/root(x)

[finite moth]

yes

[neon iron]

Dang

[finite moth]

i wonder why ur teacher assigned all this homework about a topic you haven’t covered yet

[neon iron]

Idk

It’s high school

She said we gotta learn on our own

How’s this so far?

How would I simplify this

I’m lost

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[humble badge]

A plane is flying horizontaly with a speed of 172 m/s at a height of 220m above ground, when a package is thrown downwards from the plane at a velocity of 16m/s. If the accel of gravity is 9.8 how much time will it take for the package to reach the ground

[humble badge]

I've already tried it

I don't know if it's correct

What I got was 6.7

s

[fluid belfry]

!show

[topaz sinew]

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

[humble badge]

Ok

I know the delta x for vertical is -220

And the acceloration is -9.8

Then I did

t=sqrt2deltax/a

And I got 6.7

[humble badge]

What did you get?

<@&286206848099549185>

[modern bloom]

,w 16x+9.8/2*x^2 = 220

[thorny flame]

Results provided by WolframAlpha

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

Requested by eleonardo

[humble badge]

how

Can someone explain it

[modern bloom]

You didn't consider that initial velocity is not 0

Initial vertical velocity is not 0

[humble badge]

What formula did you use?

[modern bloom]

$\Delta x = V_0 t + \frac{1}{2}at^2$

[thorny flame]

ELeonardo

[humble badge]

Why would you replace 1 with 9.8

Ohhh

Can you help me with one more

I already attempted it

[modern bloom]

Ok, show your work too

[humble badge]

Ok

A baseball is thrown into the air with a velocity of 21 at a 46 degree angle. It gets to a maximum height before returning to the ground. How long was the ball in the air from the time it was thrown until it returned to the ground

so I set up a chart

And I found what I knew

I know accel for vertical is 9.8

Vi is 0

Then I wanted to find delta x for vertical and horizontal

So I did R cos theta and R sin theta

21 * cos 46

21* sin 46

I got 14.588

And 15.1

Now I knew 3 values

So I used

t=sqrt 2*deltax/accel

And I got 1.755

[modern bloom]

Did you calculate deltax?

Also Vi is not 0

[humble badge]

Yea

Ughhh

[modern bloom]

It's 21 at a 46 degree angle

[humble badge]

For delta x I got

15.1

Oh wait

Is 15.1 the velocity

[modern bloom]

?

[modern bloom]

This is the velocity

[humble badge]

Ok

[modern bloom]

It has x and y components

[humble badge]

X comp is

14.5878

Y comp is

15.1

Are those my veloxoties for vertical and horizontal?

[modern bloom]

Yes

[humble badge]

Ok

[modern bloom]

Now let's focus on vertical velocity

[humble badge]

Ok

[modern bloom]

What's vertical velocity at the maximum point?

[humble badge]

15.1

[modern bloom]

No that's vertical Vi

[humble badge]

Then how do I find that

[modern bloom]

Remember gravitational acceleration goes downwards

[humble badge]

Ok

I don't know the formula

[modern bloom]

so it only affects the vertical component of velocity

[humble badge]

Ok

Then horizontal is constant

[modern bloom]

Yes 👍🏽

Acceleration is related to velocity by

[humble badge]

9.8

[modern bloom]

Vy = Vyi - gt

Does this make sense?

[humble badge]

Sorta

[humble badge]

Why wouldn't it be Vx

[modern bloom]

Its -g because it goes downwards, and we're taking up as positive direction

[modern bloom]

Gravitational acceleration goes downwards

[humble badge]

Ok

[modern bloom]

We're focusing on Vy

[humble badge]

But I don't know Vy

Or t

[modern bloom]

So is Vy increasing or decreasing?

[humble badge]

At the highest point?

[modern bloom]

No I mean in general

[humble badge]

increasing

[modern bloom]

What, why? 🤔

[humble badge]

cause they hit the baseball

and its at a degree thats greater then zero

so wouldnt it go up and increase

[modern bloom]

Well it's height increases, right?

[humble badge]

yea

[modern bloom]

Until it reaches the maximum point

But why would velocity increase?

[humble badge]

so its constant?

[modern bloom]

In that case, the ball would keep going faster and faster

[humble badge]

ohh

its decreasing

cause it goes fast

then slows down to its max point

[modern bloom]

Yes, gravity slows it down

[humble badge]

ok

[modern bloom]

Then what's velocity at the max point?

[humble badge]

0

cause its not moving

so then Vf would be 0

[modern bloom]

Yess

[humble badge]

ohh

[modern bloom]

Ok now

[humble badge]

so then we know Vf

Vi

and accel

[modern bloom]

We can use this formula to find t

That would be the time it takes to reach its max point

Vf = Vi - gt

As you said Vf=0

[humble badge]

0=15.1-(9.8)t

we can do

do we times it by t

[modern bloom]

?

[humble badge]

or no

wait

im stuck

[modern bloom]

Idk what "imes" mean

*means

Oh ok

[humble badge]

yea idk

[modern bloom]

Solve for t in this equation, t is that you want to find

[humble badge]

ok

[modern bloom]

Isolate t

[humble badge]

so is the answer

1.54

wait no

wait yea

wait but

if you divide 9.8 by t

it removes the t

and it goes to the other side

but then wouldnt you need to divide the other side by t

0/t= 0

wait what

im confused now

[modern bloom]

Wait why are you trying to solve it like that 😵‍💫

[humble badge]

How else

[modern bloom]

This is correct

[humble badge]

i used a calculator but how do I isolate t

[modern bloom]

Oh ok

0=15.1-(9.8)t

You can put (9.8)t to the other side, it was negative so now it's positive

(9.8)t = 15.1

Divide by 9.8 on both sides

[humble badge]

Oh

[modern bloom]

t = 15.1/9.8

[humble badge]

..

[modern bloom]

Ok

Well that's the time it takes to reach the max point

What's the problem asking for?

[humble badge]

How long was the ball in the air from the time it was thrown until it was returned to the ground

Do I just do 1.54*2

[modern bloom]

Yes

[humble badge]

ok

Ok

[humble badge]

I have one more

I swear I got it right

[modern bloom]

You can get a useful formula from this

[humble badge]

Wdym

[modern bloom]

I mean, we use 0=Vi-gt to get the time it takes to reach the max point

You can solve for t

[humble badge]

Oh

Does it only work when the projectile lands same y axis as it started tho

[modern bloom]

Yes

Same x axis

Same ground

[humble badge]

Ok

Can u show me 1 more

🙏🙏🙏🙏

[modern bloom]

Ok sure

[humble badge]

k

"

A cat chased a mouse across a 9.9 high table. The mouse steps out of the way and the cat slides off the table and strikes the floor 2.5m away from the edge of the table. The accel of gravity is 9.81. What was the cats speed when it slid off the table?

So

I made a chart

This time

I KNOW VI IS 0 FOR VERT

9.81 accel

9.9 m high table

I then finally can use the formula

t=sqrt2*deltax/a

I then got

2.0204081633

To find the velocity

I need to di

V=

Distance/time

So I know the distance is 2.5

Time is 2.024

I do 2.5/2.0204

And I gey

Get

1.237373733735

Tadaaa

[modern bloom]

XD

[humble badge]

if I get this wrong

[modern bloom]

Yeah that's correct I think

[humble badge]

I'm dropping out

[humble badge]

Can u double check

I just realized

What I did just now isn't the answer I got 2 sec ago

[modern bloom]

,calc 2.5/sqrt(2*9.9/9.81)

What

The bot isn't working (?

[humble badge]

,calc 1*1

[thorny flame]

Result:

1

[humble badge]

,calc 2.5/sqrt(2*9.9/9.81)

[thorny flame]

Result:

1.7597133030954

[humble badge]

Aw what the hell

[modern bloom]

Lol I'm banned

Okno

[humble badge]

That's what I got when I did it before I just tried it

Oh

Wait

Time is 1.4214

Ok nvm

[topaz sinew]

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[peak copper]

Can some explain how it goes from 1- 1/tan to tan-1/tan

[fluid belfry]

thats basic lcm

[peak copper]

I’m slow explain

[fluid belfry]

,, 5-\frac{3}{2}

[thorny flame]

!Yajat!

[fluid belfry]

how would you solve this?

,, \frac{10-3}{2}

[thorny flame]

!Yajat!

[fluid belfry]

like this right?

[peak copper]

Yuh

[fluid belfry]

and what about $1-\frac{1}{\tan{\theta}}$

[thorny flame]

!Yajat!

[fluid belfry]

,, \frac{\tan{\theta}-1}{\tan{\theta}}

[thorny flame]

!Yajat!

[fluid belfry]

is there any difference between these 2?

[peak copper]

Nope

[fluid belfry]

did you get it now?

[peak copper]

Yes thanks

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[keen lance]

Is anyone able to help with quesiton number 22. I am not sure where to start. I understand how to calculate least squares but I am confused by this specific problem.

[topaz sinew]

@keen lance Has your question been resolved?

[topaz sinew]

@keen lance Has your question been resolved?

[keen lance]

.close

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[flint pier]

Guys I need to find the idempotents of Z[i]/13. Here's my attempt. I'd like to check if it's right and if there's a better way to find them.
Z[i]/13 is iso to (Z/13)[i] so check (a+bi)^2 = a+bi mod 13.
distribute LHS we get a^2 + 2abi - b^2 = a + bi mod 13.
So a^2 - b^2 = a and 2ab = b mod 13.
Then 2a = 1, so a = 7 mod 13.
Now for the first eq, we get 7^2 - b^2 = 7 mod 13.
I brute forced b from 1 to 12 get got that b=9 and b=4 works.

[topaz sinew]

@flint pier Has your question been resolved?

[flint pier]

<@&286206848099549185>

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@flint pier Has your question been resolved?

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@flint pier Has your question been resolved?

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[narrow flint]

Hello, I am on the topics of Side-Side-Side or SSS for Geometry and want to know how can I solve this problem or how can I put it into an equation?

🔺ABC: sides of length 8, x - y, and x + y
🔺DEF: sides of length 8, 15, and 17

Will this have a solution?

[narrow flint]

.close

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[mental harness]

There are 5 cards in a bag numbered 1 through 5. Suppose we draw two cards numbered A and B out of the bag (without replacement), what is the variance of A+4B?

[mental harness]

Does it matter the order over here?

i cant tell with the wording, my initial thought is that they are taken at the same time so it doesnt

in that case E(A) = E(B)

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[supple mist]

Are these proofs ok

[topaz sinew]

@supple mist Has your question been resolved?

[supple mist]

<@&286206848099549185>

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[soft marsh]

f

[soft marsh]

12c the second question

i got 2.595 atoms

because 10 divided by 3.85 x 10^-22 = 2.595

its saying

that it is

2.595 x 10^22 atoms

i dont quite understand why there is 10^22 being multiplied to it

@haughty drum

<@&286206848099549185>

@neon venture pls

[neon venture]

what ?

[soft marsh]

pls help me

[neon venture]

the molar mass of the thorium is 232.04 g/mol
the mass of one atoms is the molar mass of the thorium divided by Avogadro constant which is 6.022*10^23

then you know what to do to find the mass

232.04 divided by 6.022 x 10^{23}

[soft marsh]

why would I need to divide this avogadro constant

is it a scientific thing

@neon venture can you also help me with the second one

the 10g of thorium

[neon venture]

you dont need to understand why for now, I think you are learning how to calculate things with power of 10

its basic chemistry so dont bother with it

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@soft marsh Has your question been resolved?

[soft marsh]

@neon venture

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[elfin seal]

In trapezoid ABCD, AB parallel to CD, AB > CD diagonals and are perpendicular. Knowing that CAB = 60 and AC = 6cm and AO = 2* OC where O is the point of intersection of the diagonals, calculate the lengths of the bases of the trapezoid.

[elfin seal]

I've found that AB is 8

using the 30* angle theorem

[gritty mirage]

Great, for the other one, you need to search for a pair of similar triangles

[topaz sinew]

@elfin seal Has your question been resolved?

[elfin seal]

we've got ADC and DCB

[gritty mirage]

Well, only if ABCD is isosceles, which is not given

[elfin seal]

uh...

can't see any other

[gritty mirage]

So, do you know about the intercept theorem?

[elfin seal]

hey man

[gritty mirage]

Write in an available channel

[elfin seal]

get another channel if you mind?

[gritty mirage]

sorry

[elfin seal]

#help-24

[gritty mirage]

Np

[elfin seal]

If the midpoints of two triangle sides are connected then the resulting line segment is parallel to the third triangle side

This one?

it's parallel to the third side and half of it*

[gritty mirage]

There is a more general statement: In your case, it says that ABO is similar to CDO as a consequence of AB and CD being parallell

But if you have not heard of it, it can be quickly shown using alternate angles.

[elfin seal]

Yeah, let's use that.

[gritty mirage]

Great!

I think you can do the rest without help

[elfin seal]

so DOC is simmilar to AOB

and now what should I do next?

[gritty mirage]

You calculate CD as you calculated AB

[elfin seal]

Oh wait.

damn.

that's

amazing!

.close

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[trim epoch]

Hi can someone please explain why the answer is 4? I got 3 as the number of roots because thats what I can see is the function passes the x axis 3 times

[trim epoch]

sorry this was cut out of the top of the question

Oh wait I figured ut out

but I have another question

Where did they get the formula circled in red from

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@trim epoch Has your question been resolved?

[warped pewter]

It's just the formula for volume of a cone, probably from memory or a formula sheet

[trim epoch]

ohh okay ty

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[glass crescent]

$2x^2+4y^2-4x+6y=24$

[thorny flame]

RunaAnn

[glass crescent]

yes but the process is difficult for me

[steady escarp]

doesnt look like a circle

the coefficients of x^2 and y^2 must be the same for a circle

[glass crescent]

ellipse

not circle sori

[craggy haven]

what's your question though

[glass crescent]

changing to standard form

its hard for me

[craggy haven]

first of all I would divide everything by 2

and then complete the square in x and then y

[glass crescent]

$x^2+2y^2-2x+3y=12$

[thorny flame]

RunaAnn

[glass crescent]

correct?

[craggy haven]

yeah

[glass crescent]

$(x-1)^2+2(y^2+3/2y+9/16)=12+1+9/16$