help-42

[radiant sluice]

write the equation of tangent.. find its x and y intercepts.. write the area of triangle... find its maximum

[kind coyote]

let me try

thanks

[kind coyote]

i am not getting it

i think my equation of tangent is wrong

i used point slope form

[radiant sluice]

dy/dx?

[kind coyote]

i got -e^-x to that

wait

nvm

[radiant sluice]

yeah try putting that in y = dy/dx x + c

oh

[kind coyote]

i thought dy/dt

[radiant sluice]

then find x intercept and y intercept

[kind coyote]

yeah but i think something is wrong 3with my equation

tangent

[radiant sluice]

also its e^-x1... not e^-x if you know what i mean

[kind coyote]

i didnt get you

im just a high school student

[radiant sluice]

ahh.. you should get what i mean...

i learnt that in highschool too

[kind coyote]

lol application of derivatives is my weakest chapter cuz i never really studied

[radiant sluice]

the slope of tangent is defined at the point x1,y1 lying on the function

[kind coyote]

and probability too

[radiant sluice]

guess what

[kind coyote]

mhm

[radiant sluice]

you have a problem

[kind coyote]

i know

[radiant sluice]

and you also have a solution

[kind coyote]

what is it

[radiant sluice]

just study the chapter bro

it ain't that deep

[radiant sluice]

soo now you get it

dont mix it up with x and y from the equation of line

[kind coyote]

true......but im thinking of just doing maths during my final test gap

[kind coyote]

yep

[radiant sluice]

math is a good percentile decider for jee if you are going to give it

[radiant sluice]

try solving again

[kind coyote]

over

12th boards

[kind coyote]

well solved 13 in maths

which is good acc to me

[radiant sluice]

thats a good number

[kind coyote]

cuz people solved about 5 to 6 in my shift

[radiant sluice]

dont compare yourself

[kind coyote]

real

you are in uni?

[radiant sluice]

yeah

[kind coyote]

nice

[calm coral]

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[indigo ginkgo]

ighty

so

i put all the terms in one side

and thats f(x)

and then i took the derivative

and then i found the critical point

and the intervals where the function is increasing and decreasing

the critical point is (2- 12ln2)/3ln2

[leaden thunder]

did you do f(x) > 0 or f(x) < 0

[indigo ginkgo]

umm

let me check

its f(x) > 0

[leaden thunder]

yea so you know the critical point c where f'(c) = 0. now f(c) > 0 since it's a local max (double check if you need to using second derivative test)

then check integers n around c until f(n) becomes negative

[indigo ginkgo]

oh god, im not doing the second derivative of this

[leaden thunder]

you know x >= -4

[indigo ginkgo]

its way to painful to do that

[indigo ginkgo]

yesss

oh i see

[leaden thunder]

and c is close to -1

[indigo ginkgo]

rightttt

[leaden thunder]

Then S = -4 + ... + -1 + 0 + ... + N and you just need to find N

[indigo ginkgo]

wait what?

let me check real quick

[leaden thunder]

Same S

[indigo ginkgo]

it doesnt verify for -4

[leaden thunder]

oh oops

[indigo ginkgo]

it does for -3

[leaden thunder]

-3 + -2 + -1 + 0 + ... + N

[indigo ginkgo]

so how do we find that n

[leaden thunder]

.

[indigo ginkgo]

oh right

i see so its until 0

[leaden thunder]

,calc 2 * log(2, 0+4) - 3*0 - 1

[potent lotus]

Result:

0

[indigo ginkgo]

ight so until 1

[leaden thunder]

yea x=0 is not in A

[indigo ginkgo]

its the sum of elements

[indigo ginkgo]

thx btw

[leaden thunder]

[indigo ginkgo]

.close

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[calm coral]

Please don't occupy multiple help channels.

[remote mural]

How do I solve this

[potent smelt]

That certainly is a triangle.

[remote mural]

Using law of cosines

[potent smelt]

Can you state the law of cosines really quickly?

[remote mural]

c squared equals a squared plus b squared - 2ab cosine c

[potent smelt]

If we let AC = a, CB = b, and our angle be angle ACB = C, then can you rewrite the law of cosines to get AB = c?

[remote mural]

I have no clue

[potent smelt]

c^2 = a^2 + b^2 - 2ab cos C

[remote mural]

Yes

[remote mural]

Or in this case it would be 14^2+27^2-2×(14)×(27) cos 108 when plugging it in

[remote mural]

Yes

[potent smelt]

C is the angle of ACB = 108°

So c^2 = 14^2 + 27^2 - 2×14×27 cos(108°)

[remote mural]

Yep

[potent smelt]

The right hand side is just numbers

So you just perform the computation

And take the square root to find c

[remote mural]

I get -52

On my phone calculator

[potent smelt]

Then you've made a mistake of some sort

Can you screenshot your work?

[remote mural]

Here’s a copy and paste

14^2+27^2-2×(14)×(27)

Then cos 108

[potent smelt]

,w 14^2 + 27^2 - 21427 cos(108 pi/180)

,w sqrt(1158.6168)

[potent smelt]

The reason I asked for a screenshot is so that I could confirm you entered it into the calculator correctly

[remote mural]

Yes thank you

But the phone calculator is weird

I couldn’t do that equation with the cosine 108 after

But angle C is 34

No what

Now

[potent smelt]

Worked for me

[remote mural]

Ok

@potent smelt

I solved it

I have another question tho

[potent smelt]

Cool!

[potent smelt]

What's up?

[remote mural]

Same thing using law of cosines btw

[potent smelt]

To find the angles?

[remote mural]

Yes but my calculator isn’t calculating right

I got 6.76

After doing law of cosines

14.3 + 22.9^2+20.3^2-2×(22.9)×(20.3) cos A

@potent smelt

[potent smelt]

What are you trying to find exactly?

[calm coral]

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[cunning trout]

i dont really get how a question like this works

[calm coral]

Please don't occupy multiple help channels.

[cunning trout]

is it cause teh bounds are changed cause x = 2x

[calm coral]

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[inland dew]

I just need to know if im right lr wrong

[shy swallow]

yes it's correct

[inland dew]

Hey im doing b now and im stuck, i have ideas but idk how to start, like for the auxilery line how would i say that if only one side has a letter

Futher more line fe and line fg are congruent through the angles

[inland dew]

Can you help?

[bitter maple]

Which number

[inland dew]

b

[arctic dirge]

which part are you on in b

Do you need help proving the converse?

[calm coral]

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[iron ore]

So I watched a solution video and I am confused. It says lower the log base the faster it increases. How do we know the equation with E is the second fastest if it does not have a base

[kindred estuary]

,rotate

[finite imp]

do you know derivatives

[kindred estuary]

But does havea base

[iron ore]

No

[kindred estuary]

The base is e

[iron ore]

Yea E but we don’t know the value

So how can we determine if e is greater then or less then any number

[kindred estuary]

Yes you do

It's not a variable

,w value of e

[potent lotus]

Results provided by WolframAlpha

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Requested by captainnova22

[kindred estuary]

It's that

[iron ore]

Ohh

We never learned that

I thought it was somthing like any variable like x

[kindred estuary]

Have you learned what ln is?

[iron ore]

Uh I don’t think so

[kindred estuary]

Well ln is just log base e

And ln is natural log

[iron ore]

This unit is alll confusing

I understand the first part but now that we are doing word problems I’m dead

[finite imp]

if you learnt derivatives it will be simple to solve. d(log(a)(x))/dx=1/xlna, so we get it if " a"larger, it gets slower

[kindred estuary]

They said they have not learnt derivatives

[finite imp]

yes i know

[kindred estuary]

So there is no purpose in bringing it up

[finite imp]

yes. but it is a scientific answer, that one log(a)(b) if "a" gets larger then it gets slower is not that correct, you forgot 0<b<1

[kindred estuary]

You're over explaining a simple question they asked. The question was how was the last equation the second smallest and they did not know that e was used as the value of 2.718. You don't need to bring derivatives or the "scientific answer". All they were confused on was what e meant

That's all

[calm coral]

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[finite imp]

oh yes i misunderstood. my bad. thx btw

[calm coral]

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[peak ferry]

can someone explain to me how this is a bijection? Isn't there a number of balanced T6 strings we can make from a T5 string?

[peak ferry]

For example given a T6 string I would need to remove the last digit to make T5. But how would I know what digit to add from the T5 string?

[ashen tangle]

i mean you can always delete 0

lets say it was balanced in T6 but then it has to have some zeros in it

at balanced mean sum is 3

[peak ferry]

Does it?

[ashen tangle]

so even if you try with 1 you have to have some zeros

[peak ferry]

It could be 222222

or 111111

[ashen tangle]

what is the sum now

sure but if you put the condition of being balanced

which the statement of A tells you

[peak ferry]

then the sum would be 12 or 6 which would be an integer multiple of 3

[ashen tangle]

oh shit

i read it as 3

[peak ferry]

or just 000000

[ashen tangle]

hmm

i think it would be helpful to write down the cases for balanced T6

and just try deleting entries

[peak ferry]

even if I did delete entries I would have no idea where to add them back onto on a T5

[ashen tangle]

which b asks you to do then

[peak ferry]

given a T5

can't a T5 yield multiple T6s

So how is this a bijection?

[ashen tangle]

notice that T5 doesnt have to be balanced anymore

well what is bijection ?

[peak ferry]

back and forth 1 - 1 mapping

[ashen tangle]

sure

thats what im aying

are you getting any many-one map

or not preimage of things

which is what you need to disprove

[peak ferry]

well it seems like there are many T5s to a single T6

[ashen tangle]

single balanced T6 you mean ?

[peak ferry]

yeah

[ashen tangle]

damn

well i havent calculated but if you have then there you go

you have disproved

[peak ferry]

like even if it has the same sum we could just switch the order of the digits

then it wouldn't make the same T6

Oh I think I get it now

[ashen tangle]

give me any example of such

[peak ferry]

wait if X = 00000 then there's no digit we can add

oh wait we can add 0

[ashen tangle]

000000

thats what im thinking too

like its a definition thing

zero is mutiple of every number

im trying to have some ring argument but that doesnt matter

they want you to consider that as a map yes

https://math.stackexchange.com/questions/247499/is-zero-a-multiple-of-any-number

take a look amybe

https://tenor.com/view/niku-jan-jan-niku-cat-rolling-up-gif-20050767

i was like why is there a measure theory convo on north

prolly coz eric was here, in anyways no more spamming

[calm coral]

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[haughty hare]

you can find the limit without lopitals? isnt (-1)^inf an indeterminate form

[plain bone]

Either way, (-1)^n is bounded between -1 and 1. but n! approaches infinity

[mortal orbit]

squeeze theorem is how you find the limit is 0

-1/n! <= a_n <= 1/n!

[haughty hare]

sry how did u get the upper andlower bounds

like what happened to the ^n in the numerator

[haughty hare]

ah yeah

[mortal orbit]

(-1)^n is either -1 or 1

so -1 <= (-1)^n <= 1

divide by 1/n!

and voilà

[haughty hare]

ohh thank you

.close

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[mighty crag]

i need help with this math problem because im lost
the question say ,There is two-digits numbers such that the sum of its digits is 6 while the product of the digits is 1 over 3 of the original number
find this number?

[frosty spruce]

just suppose that number has a form of ab
then: a+b=6 and ab=1/3 (10a + b)

[vocal pagoda]

10x gives us the 10th place of the digit.
Like 20, 30, or 40.
+y gives the unit digit.

So xy=(10x+y)/3

[mighty crag]

hold on let me see if i got it

i got it thanks man

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[zenith summit]

https://math.stackexchange.com/a/23163

[zenith summit]

why do we construct a Vandermonde matrix here?

and how do we assume t = 0, t = 1, ..., t = n - 1?

<@&286206848099549185>

[calm coral]

@zenith summit Has your question been resolved?

[glass heart]

the point is that the equality $\mu_1e^{a_1t} + \ldots+\mu_n e^{a_nt}=0$ is an equality in the function space and is an equality of \textit{functions}, so they need to be equal for all values of $t$

[potent lotus]

Denascite

[glass heart]

so you can choose some values of t that you like, plug them in and the resulting values still have to be the same

the values t=0,1,...,n-1 just turn out to be convenient here because if you plug them in and look at the equations you get, you get precisely the system described by the vandermonde matrix

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[opaque yoke]

can someone please explain to me why this is not enough information?

oh nvm

.close

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[blazing coyote]

Trying to find a vector function that gives the curve indicating where these shapes intersect

[blazing coyote]

So to start I was thinking $y= tan^2(t)$

[potent lotus]

What a wonderful world it is !

[blazing coyote]

That's probably a bad idea, is it not

The best I can do is x= rcos(t), y=rsin(t)

so z=r

Alternatively

$z^2=(1+y)^2$
\
$x^2+y^2=1+y^2+2y$
\
$x^2=1+2y$

[potent lotus]

What a wonderful world it is !

[blazing coyote]

so $x = \sqrt{1+2y}$

[potent lotus]

What a wonderful world it is !

[blazing coyote]

Let $x=t$, so $y = t^2-1/2, z = (1/2+t^2)$

[potent lotus]

What a wonderful world it is !

[blazing coyote]

does this work?

tq

.close

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[honest swallow]

i just need a few hints on how to prove this

[sonic sphinx]

9+1 = 8+2

[remote mural]

7+3=6+4

[jaunty snow]

screams pigeonhole principle. assume an arbitrary group of 16. how many possible sums are there for a subset of size 2 of that

[honest swallow]

not like that

how to prove it

[sonic sphinx]

that was a hint

[honest swallow]

number of subsets are 2^16

[west shard]

possible number of sums

[honest swallow]

possible sums for a set of 16 numbers?

16C2 + 16C3+.....+16C16 if im not wrong

[jaunty snow]

we're specifically looking at subsets of size 2. Maybe I worded it poorly, I was just asking how many sums you can make from that set of 16

which would just be 16C2

which is 120

[honest swallow]

oh my bad

[honest swallow]

yep sum of 2 numbers should be that

[jaunty snow]

pigeonhole can't directly be applied here since technically there are ~200>120 possible sums they may or may not take but there's a way to reframe that lets you apply pigeonhole.

the specific thing to do kinda gives away the problem though uhh

[honest swallow]

oh

[jaunty snow]

rearranging a+b=c+d might help(will help)

[honest swallow]

a-d=c-b?

[jaunty snow]

yeah, so instead of looking at sums of pairs, you're looking at differences

[honest swallow]

that should be better

i think its obvious that in 16 there will exist two pairs but i cant really grasp how to prove it

[jaunty snow]

well, you ahve the same possible number of differences from the set of 16, 16C2

but how many possible differences of 2 numbers <100 are there?

[honest swallow]

99C2?

[jaunty snow]

you reckon? I can't imagine subtracting two numbers between 0 and 100 and getting anymore than 100

[honest swallow]

some of them will have the same difference ig

[glass heart]

you are being imprecise here. a-b and b-a are not the same

[jaunty snow]

Well specifically, there are 120 possible pairs of numbers you can make from a set of 16, but you can only get (absolute) differences between 1 and 99

[jaunty snow]

you're right, i wasn't trying to be 100% rigorous but to lay out the guidelines to a proof. we only care about the absolute difference here since you can swap a/b around WLOG

my b

[honest swallow]

how would we get that?

[jaunty snow]

16C2. how many pairs you can make from a set of 16 numbers

[honest swallow]

yep

also what if 2 numbers are equal?

distinct pairs

but can it be c=b i think

not sure

[jaunty snow]

in the set of 16? this is 16 distinct numbers. Or are you talking about the case where you have like 15-10 as one pair and 10-5 as the other, thus ahving the same difference but not being all distinct numbers

[honest swallow]

yep this is the case

[jaunty snow]

I haven't completely thought through this part yet, work with me here. What we should find is that <= 21 such pairs of pairs exist in the set of 16, so that pigeonhole still works.

What can you say about such a pair of pairs?

[honest swallow]

what if we try to apply pigeonhole in some other way?

the pair of pairs are really vague for me

also because of the case where 2 are equal

(a,b) and (c,d) such that a-c = b-d

[jaunty snow]

What i mean here is that we want to show that there's <=21 (a,b), (b,c) such that a-b=b-c

[honest swallow]

i see

so we are trying to limit how many of these pair of pairs are there for 16 numbers

i think one number can be present like that in at most 1 pair of pairs

[jaunty snow]

Yeah, I think thats the idea

[honest swallow]

at most 1

i think ill just ask my teacher later its too confusing for me

thanks a lot for your help by the way

.close

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[ionic orchid]

hi, i am really struggling with the concept of level surfaces and how to interpret the calculus geometrically, i am on Q2.3, andi have done the maths however i do not know how to interpret the last few geometrically

[ionic orchid]

this is second year uni maths for physics vector calculus for reference

[calm coral]

@ionic orchid Has your question been resolved?

[eternal shard]

Imagining a function f(x,y,z) is hard, but level surfaces work in principal the same thing as level curve, if that's something you know

[ionic orchid]

something we have been taught, i just find it hard visualizing when its a difficult one

like I get that (a.r) with a level surface of (a1,a2,a3,) is constant, and is like a contour line. but how do we get different heights like where is r so that this changes, if u get me

[eternal shard]

I assume (a,r) is some point of the level curve?

And (a1,a2,a3) some point of the level surface?

[ionic orchid]

yeah

where is r wrt to

[eternal shard]

r has no height

(a,r) corresponds to a point in xy plane

if that is what you are asking

[ionic orchid]

yeah I know that a.r correspond to a point on the plane, but like where is r coming from for vislaizatiln purposes

visualisation

[eternal shard]

When you solve f(x,y) = 0 for example

You get a function y of x

[stoic oyster]

respectfully, gtfo if you just want to troll

[ionic orchid]

so for a.r =0

[stoic oyster]

if you spam 1 other message you'll get modded

[ionic orchid]

they must be perpendicular

[eternal shard]

(a,r) is a point that satsfies f(x,y) = 0

f(a,r) = 0 would be true

[stoic oyster]

go to #chill if you want

[ionic orchid]

so it must be that a and r are perp

[eternal shard]

I don't know of a concept where numbers are perpendicular

[stoic oyster]

a.r is the function adonis

[eternal shard]

oh

[stoic oyster]

first question

[ionic orchid]

r is a position vector and a is a constant vector

[calm coral]

@ionic orchid Has your question been resolved?

[eternal shard]

I feel that I didn't address your actual issue, so I am just gonna leave it and hope someone better helps you

[calm coral]

@ionic orchid Has your question been resolved?

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[ionic orchid]

.reopen

[calm coral]

✅

[calm coral]

@ionic orchid Has your question been resolved?

[ionic orchid]

<@&286206848099549185>

[calm coral]

@ionic orchid Has your question been resolved?

[calm coral]

@ionic orchid Has your question been resolved?

[calm coral]

@ionic orchid Has your question been resolved?

[tiny robin]

anyone who can help with a physics problem help 8 pls

[remote mural]

@tiny robin Which problem

[calm coral]

@ionic orchid Has your question been resolved?

[calm coral]

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[iron oracle]

i got 1/3000 hows the answer b?

[iron oracle]

my solution is the bottom one

.close

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[pallid palm]

I need help figuring out where to plot

[viscid nymph]

Rise/run

Look at anywhere where the tangent line intersects integer points

[plain bone]

I recommend using these two points if you cant figure it out

[viscid nymph]

Ye

[pallid palm]

Got it ty

How do you figure out which points to plot if you dont mind me asking

[viscid nymph]

Nice

[viscid nymph]

Just look at where the line intersects integer points

[plain bone]

I used points that intersect with the lines of x-itude and y-itude

[pallid palm]

oh okay

tysm again

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[noble verge]

If a discontinuity is removable, describe how to redefine the function to make it continuous.

The function is a removeable discontinuity at f(1) however I'm stuck on the redefining part of the question.

[versed trout]

make a piecewise function

at x = 1, define it to be the value that the limit possesses

[noble verge]

Ok, would that be the only way? Is their a way to change the stuff in the cos with like a equivalent fraction or something?

[versed trout]

no u cant redefine it by algebraic manipulation

the original function isnt defined at that point

[noble verge]

Ok then I'll go with that then, thanks for the help

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[noble crown]

can someone help me expand ax^4+bx^3+cx^2+dx-\left(a\left(x-1\right)^4+b\left(x-1\right)^3+c\left(x-1\right)^2+d\left(x-1\right)\right)

[noble crown]

,w expand ax^4+bx^3+cx^2+dx-\left(a\left(x-1\right)^4+b\left(x-1\right)^3+c\left(x-1\right)^2+d\left(x-1\right)\right)

[potent lotus]

Results provided by WolframAlpha

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

Requested by kronium_

[noble crown]

wolfram alpha more like sheep ram alpha

ahh

WAIT IT WORKED

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[remote mural]

can someone explain me this part

[stray basalt]

since $u=\sqrt{x^2+4}$, $x^2+4=u^2$, thus $x^2=u^2-4$

[potent lotus]

DiamondPanda16

[slender yoke]

yeh

when u change the variable to u, you basically try to write everything in terms of u

[stray basalt]

yep

[calm coral]

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[ruby vine]

10.14. The body moves in a straight line with the speed v(t) = 4t 0.4t2 (m/s). Find:

1. the path traveled by the body from the start of movement to the stop;

2. acceleration of the body at the moment of time = 5 s.

[calm coral]

@ruby vine Has your question been resolved?

[ruby vine]

<@&286206848099549185>

[marble pendant]

$v = 4t - 0.4t^2$ right?

[potent lotus]

Wumpus Man

[ruby vine]

I don't even know where to start

[marble pendant]

do you know differentiation?

[ruby vine]

V(t)= that yes

[ruby vine]

Yes

[marble pendant]

what do you think we should do?

[ruby vine]

I need to find the second at which the object stopped moving

I assume I can equal my equation to zero?

[marble pendant]

yes

why?

[ruby vine]

Tbh I'm not really sure, I used to learn math in depth but I wasn't able to continue that course
All I know in this is I'll find out 0 and the other number which is when the object stopped moving

Why I equal it out I do not know

[marble pendant]

yes this is correct

by equating it to 0
we will find the time at whcih the body stops moving

[ruby vine]

Well alr

So that's how I'll get my first step solution

The second step is to find the acceleration at second 5

[marble pendant]

kk

how do you think we should do it

!nosols

[calm coral]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[marble pendant]

!img

[calm coral]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[ruby vine]

I still don't rly get how to find it at the 5th second

Or well a certain second

[marble pendant]

can you find the acceleration as a function of time?

[strange crest]

diff it and then plug in the time

[ruby vine]

As a function of time?

[ruby vine]

Oh like instead of t I substitution 5

That makes sense

[marble pendant]

a(t) = ?

kk

[ruby vine]

I'll try it out on paper rn give me a bit

[marble pendant]

kk

[ruby vine]

t=10

So now I just need to solve this long thing

[marble pendant]

?

[strange crest]

nope

[marble pendant]

what is t=10 exactly?

[ruby vine]

When the object stopped moving

[strange crest]

@marble pendant is hints allowed

[marble pendant]

its incorrect

[marble pendant]

i guess but let them it on thier own

[ruby vine]

Well I solved it and got 0 and 10?

[marble pendant]

can you show your calc?

[ruby vine]

Or wait

0.1

1/10

0.1 is when the object stopped moving?

[marble pendant]

its correct

mb

t=10s is when object stops moving

[ruby vine]

Uh

Ok

Then I'll go on with calculating it?

[marble pendant]

sure

[strange crest]

@marble pendant can i dm you?

[ruby vine]

I got 200/3

66 2/3

[strange crest]

you are right

thats correct!

[ruby vine]

So now I can put in t=5

[strange crest]

yes

[potent lotus]

Indresearch Official

[marble pendant]

this is for the distance one?

[ruby vine]

The first one yea

I think I did something wrong I got 39 1/15 for the second one

[marble pendant]

show your work?

[ruby vine]

2t²-0.4 t³/3
I put 5 instead of t here right

[marble pendant]

that formula is for acceleration?

[ruby vine]

What does the other one look like?

[marble pendant]

how did you get this function?

[marble pendant]

for the second part we need acceleration

so we first need a(t)

[ruby vine]

Alright

How do I find that?

[marble pendant]

acceleration is defined as rate of change of velocity

$a = \frac{d}{dt} v$

[potent lotus]

Wumpus Man

[ruby vine]

so a=t•V?
I'm not very good with formulas

I have t

V(t) as well

Nah idk I'm lost

[marble pendant]

you need to differentate v(t) wrt t to get a

like you integrated v(t) wrt t to get s

[ruby vine]

wrt

?

[marble pendant]

with respect to

[ruby vine]

So into V(t) is where I substitute 5?

V(t)=4t-0,4t²

[marble pendant]

no

first find a(t)

which you will get by differentiating v(t)

then put 5

[ruby vine]

2t²-0,4t³/3 or no...

[marble pendant]

nope

[ruby vine]

I do not know how to continue

[marble pendant]

differentiate

not integrate

[ruby vine]

Can you use a simple example to remind me

[marble pendant]

lets say you have f(x) = 2 + 6x

$\int f(x) dx = 3x^2 + 2x + C$

[potent lotus]

Wumpus Man

[marble pendant]

this is for displacement

part a

$\frac{d}{dx} f(x) = 6$

[potent lotus]

Wumpus Man

[ruby vine]

Why is it +2x

[marble pendant]

^

[ruby vine]

3x² okay I get that

[marble pendant]

$\int (2+6x) dx = \int 2 dx + \int 6x dx = 2x + 3x^2$

[potent lotus]

Wumpus Man

[marble pendant]

get it?

[ruby vine]

No

[marble pendant]

hmm

[ruby vine]

Oh wait

[ruby vine]

2•3x to the power of alpha-1

So yea I got that

Aand

[marble pendant]

kk

now try differentiating v(t)

[ruby vine]

2•1to the power of 2-1

Yea ok

I havent done this in a while sorry

[jovial sedge]

Tell me if y'all stuck somewhere

[marble pendant]

np

[jovial sedge]

Alright

[ruby vine]

4t³ is the first one?

4t³-0.4•2t

[marble pendant]

just for reference $v = 4t - 0.4t^2$

[potent lotus]

Wumpus Man

[marble pendant]

idts

[ruby vine]

idts?

[marble pendant]

-0.4•2t is correct

4t^3 is not

[marble pendant]

i dont think so

[ruby vine]

4t^0

4

[marble pendant]

yup

[ruby vine]

4-0.8t

[marble pendant]

correct

now put t=5

[ruby vine]

0

[marble pendant]

correct

[ruby vine]

Thank you

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[marble pendant]

[calm coral]

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[grizzled coral]

$\frac{x^2+5x}{x}$

[calm coral]

Please don't occupy multiple help channels.

[potent lotus]

Yousif

[grizzled coral]

does this become

$(x^2 + 5x) x^{-1}$

[potent lotus]

Yousif

[frosty spruce]

Yes

[grizzled coral]

ohh so it multiples to both?

[frosty spruce]

wdym, like multiplication distribution?

[grizzled coral]

yes yes

mb

i understand now

thank u

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[dusky copper]

Can someone do number 1 for me its been a while since I have done identities and I am struggling with how to proceed

[tall moon]

which number 1

[dusky copper]

T1 I forgot how to do them been a while I haven’t touched these for a while

[tall moon]

use double angle to get everything interms of sinx

[stray basalt]

cos(2x) is like 1 - 2sin^2(x) right

[tall moon]

think so i forgor

[stray basalt]

it is

[calm coral]

@dusky copper Has your question been resolved?

[dusky copper]

Can you solve it so I can understand how you’ve done it and proceed to the next one I need some ideas to grasp how to do it

[stray basalt]

2cos(2x) = 1 - 2sin(x)

2(1 - 2sin^2(x)) = 1 - 2sin(x)

2(1+2sin(x))(1-2sin(x)) = (1-2sin(x)) by diff of squares

2(1+2sin(x)-1)(1-2sin(x)) = 0

2sin(x)(1 - 2sin(x)) = 0

sin(x) = 0 or 1/2

x = 0, 30, 150, 180, 360

[dusky copper]

Sorry I am not getting the 3rd line

[calm coral]

@dusky copper Has your question been resolved?

[calm coral]

@dusky copper Has your question been resolved?

[calm coral]

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[broken wigeon]

Could y'all help me with question 3

[broken wigeon]

It's kinda up side down sos

[plain bone]

,rotate 180

[broken wigeon]

Ye pls help thx btw

[swift condor]

how far have you gotten

[broken wigeon]

Uhh I'm still stuck on 3

[swift condor]

do you know how to start question 3

[broken wigeon]

I did 36000 minus 11500 but idk if it's correct

[swift condor]

yeah thats right

[broken wigeon]

So what now

Yo?

[plain bone]

So how much money is remaining to be taxed

[broken wigeon]

24500

36000-11500 equals 24500 right?

@plain bone

It's 24500

Ye so how does answer the question

[plain bone]

So which tax bracket are you in for the remaining $24,500

[broken wigeon]

20 percent?

[plain bone]

So how much tax do you pay on the $24,500

[broken wigeon]

4900

Then plus?

[plain bone]

So after paying taxes, how much money does Martha have

[broken wigeon]

Oh uhh

19600

Plus the 11500?

And that's the answer?

Thx

[plain bone]

Yw

!done?

[calm coral]

If you are done with this channel, please mark your problem as solved by typing .close

[broken wigeon]

Oh ye

There is another oroblem

Shucks

Can you help pretty pweaee

[plain bone]

,rotate 90

[broken wigeon]

Yall?

<@&286206848099549185>

[supple ferry]

I think you do 7200-6900 to get 300 units then continue from there

to be honest i dont really understand why you do this since i dont get what they mean by "charge per unit", thats just the step that gave me a correct answer

since starting with 7200 or 6900 units gives you an answer wayy too large

[broken wigeon]

Arghh yea I'ma ask teacher thx anyway

.close

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[zenith summit]

how am i supposed to do this using inner product and cauchy-schwarz

[zenith summit]

i am pretty sure i will have to define an inner product since i don't see how $\langle f, g\rangle = \int_1^\infty f\bar{g}$ will work here

[potent lotus]

carburetor

[sweet stag]

yes

u did show it is a inner product

[zenith summit]

the inner product i gave works here?

[sweet stag]

yes

well thats the standard one

[zenith summit]

what do i take f and g to be then

[sweet stag]

ok quick question

calculate the integral 1/x² from 1 to infty

[zenith summit]

that's just 1 right

[sweet stag]

ye

[zenith summit]

oh ok i get it now

x^2 f and 1/x^2

no wait

[sweet stag]

consider h(x) = xf(x)

then $A = \int_1^\infty f(x) dx = \int_1^\infty \frac{h(x)}{x}$

[potent lotus]

Goëtia

[sweet stag]

square A, then use CS

[zenith summit]

oh never mind i got it

yeah xf(x) and 1/x

[sweet stag]

correct

[zenith summit]

i got confused while taking the norm

i was doing something similar to the euclidean inner product 😅

so i didn't understand how the squares came inside the integral

thank you very much

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[marble pendant]

!xy

[calm coral]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[empty quail]

@fathom shuttle ^

what

are you asking me to solve this

no I don't wanna do your homework unless you need help and show the work if possible

[eternal shard]

!nosols

[calm coral]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[swift dragon]

!noans

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The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

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[unborn sentinel]

no prog

i forgot a few of the steps

therefore, i haven't attempted this one.

help

[plain bone]

Whats the highest number that, when rounded to the nearest tenths place, yields 5.9

[unborn sentinel]

5.94?

wait

[plain bone]

Even bigger

[unborn sentinel]

5.95

that makes 6 tho

[plain bone]

No, that rounds to 6

[unborn sentinel]

to tenths

hmm

[plain bone]

Think about it like this:

Does 1.000009 round to 2?

[unborn sentinel]

no

[plain bone]

Why not? 9 > 5 right?

[unborn sentinel]

yes

[plain bone]

Then why doesnt 1.000009 ronud to 2?

[unborn sentinel]

isn't because it has like 5 zeroes ahead of the 9

ok

[plain bone]

Well not exactly

But mainly because 9 isnt in the hundredths place

So you can technically have 5.94999999999999 (which is bounded from above by 5.95)

[unborn sentinel]

i get what you mean now

the nines could go on forever and it'd still be bounded from above by 5.95?

[plain bone]

Because 5.949999999 approaches 5.95 as you keep adding more 9s

[unborn sentinel]

ah ok

i was thinking of something like this

the 6 at the end looks wrong idk

is this how u do it

[plain bone]

I visualize it at 5.95)

In interval notation, that refers to the smallest number thats less than 5.95

[unborn sentinel]

so like this ?

for example: 62<n<64

but u know the thing after 62, it should have an underscore under it

isn't that some other topic

?

2.85+5.95?

8.8

@plain bone

[plain bone]

Nice, you got it right

!done

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[unborn sentinel]

.close

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[calm coral]

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[restive cave]

how do you find rho for the second integral in spherical coords??????????????????????????????????????????? the answer is right, i reevaluated and checked on symbolab with cylindrical coordinates
just the rho-value for the second integral for the one in spherical coordinates

[restive cave]

i only have one webassign attempt left

[leaden thunder]

did you try drawing the region

why is the upper limit of the radial direction 2

[calm coral]

@restive cave Has your question been resolved?

[restive cave]

i'll restart this later i have something to do

.close

[calm coral]

Channel closed

Closed by @restive cave

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[knotty mulch]

i need help

[knotty mulch]

okay so basically

i need hepl with question 11

im having trouble understanding it

[pallid halo]

can you give a condition for b1 and c1 that implies two real roots for the first equation?

and do similarly for the second equation?

[knotty mulch]

c1 must be less than zero

[pallid halo]

not necessarily

[knotty mulch]

oh

hmm

[pallid halo]

b1 is involved as well

[knotty mulch]

do i have to use discriminant

[pallid halo]

consider the quadratic formula

yep use the discriminant

[knotty mulch]

b1^2 + 4c1 >= 0

[pallid halo]

almost but not quite

should be -4c1

[knotty mulch]

o shoot

[pallid halo]

and also you want > 0

[knotty mulch]

ur right

[pallid halo]

because if it = 0 then you have one real root

[knotty mulch]

my teacher said > is for distinct roots but >= gives u 2 roots distinct or equal

[knotty mulch]

what do i do next tho once i have the formula

[pallid halo]

yea two equal roots, so it depends on whether they are counting repeated roots or not

let's worry about that detail later.. first you need to see how the given condition helps

so you have two inequalities, one for the first equation and one for the second

[knotty mulch]

yeah its basically the same thing tho

right?

[pallid halo]

yep just change the 1 subscripts to 2

[knotty mulch]

ok gotchu

[pallid halo]

one way to proceed is to assume that they're both false, and find a contradiction

then the contradiction means that your assumption is wrong, so at least one inequality has to be true

[knotty mulch]

hmm okay

[knotty mulch]

so this is inequality no 1

?

[pallid halo]

yep

if you assume it's false then you would have
b1^2 - 4c1 < 0

and similarly for the other one

and then take a look at your given condition b1 b2 = 2(c1 + c2)

in particular it has a c1+c2

which suggests what you might do with the two inequalities

[knotty mulch]

we add them?

[pallid halo]

yea

[knotty mulch]

oh wait

i think im getting it

so

u get

[pallid halo]

the idea being, you have two negative numbers, so when you add them together you get another negative number

[knotty mulch]

ahh

u get b1^2 + b2^2 < 4(c1 +c2)?

[pallid halo]

yes

now use the condition that's given

[knotty mulch]

b1^2+b2^2 < 4(b1b2/2)

b1^2+b2^2 < 2b1b2

[pallid halo]

yep

can you simplify that further?

[knotty mulch]

(b1-b2)^2 < 0?

[pallid halo]

yep

[knotty mulch]

so this is false cause its squared?

[pallid halo]

right, the square of a real number can't be negative

so we have a contradiction

our assumption that both of the original inequalities were false, led to this contradiction

so one of them must be true!

[knotty mulch]

OH

that makes so much sense ty

[pallid halo]

yw

[knotty mulch]

.close

[calm coral]

Channel closed

Closed by @knotty mulch

Use .reopen if this was a mistake.

[knotty mulch]

.reopen

[calm coral]

✅

[knotty mulch]

i skipped this one before but idk where to start

it's a lot to look at

[calm coral]

@knotty mulch Has your question been resolved?

Channel closed

Closed by @knotty mulch

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[normal gull]

Can someone give me a suggestion ? On how to solve it ?

[plain bone]

Didnt you just get this solved

!noclopen also

[calm coral]

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.

[normal gull]

I mean he didnot convince me

[plain bone]

1. vertical angles
2. reflexive

[normal gull]

So first one is

SAS

And second

ASA ?

Why ?

Whats the correct and why ?

[plain bone]

Does the congruent side (S) come in between the congruent angles (A)?

[normal gull]

I mean i dont see no side

So i assmued

R , T

Is the side

And it comes in between

?

[plain bone]

There is a side though

[normal gull]

Where ?

[plain bone]

Use the Reflexive Property of Congruency

Or rather

Do this instead

[normal gull]

So the correct congruency is ?

[plain bone]

Draw the two triangles separately

[normal gull]

Okay done

[plain bone]

Show me

[normal gull]

I didit on mobile

[plain bone]

Ok count the total number of sides there are

[plain bone]

So how many sides are there

[normal gull]

3 in each ?

Im sorry im just bad at maths 😄

[plain bone]

In total?

[normal gull]

I mean 6 in both triangles

3 in each triangle

I mean shouldnt the teacher put the equal side sign thingy ?

To know if its

AAS or ASA ?

[plain bone]

No, because you need to know about the reflexive property

[normal gull]

Okay okay so im pretty sorry but

After i seperated

[plain bone]

No need to apologize, everyone's here to learn

[plain bone]

Yes?

[normal gull]

Isnt that the sides ?

[plain bone]

Yes, they are. How many sides are there in total here

[normal gull]

6 ?

If no, how much ?

Okay

Now what do i do

[plain bone]

Here, how many total sides are there

[normal gull]

5 ?

RT
ST
UT
UR
RS

@plain bone hm ?

[plain bone]

[5 sides](#help-42 message) or [6 sides](#help-42 message)

What i wanted you to understand from this is: you basically cloned the side RT when you separated the triangles

So RT in both triangles is congruent

[normal gull]

Which means rt is the side ?

[plain bone]

This is the idea behind the reflexive property

[normal gull]

Okay great

So if we said look

So its pretty much like this

So the side is between 2 angles

Doesnt that mean its

ASA ?

@plain bone

[plain bone]

No