help-28

[coarse tulip]

yucky

welp i'll figure it out ig

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[unreal minnow]

my teach said to use a thing like this
(f(x+h) - f(x))/h

[unreal minnow]

im right here rn

[tribal steppe]

$\frac{\frac{(x+3)-(x+h+3)}{(x+h+3)(x+3)} }{h}$

[glossy valve]

pubuyun

[tribal steppe]

=$\frac{\frac{-h}{(x+h+3)(x+3)} }{h}$

[glossy valve]

pubuyun

[tribal steppe]

=$\frac{-1}{(x+h+3)(x+3)}$

[glossy valve]

pubuyun

[tribal steppe]

so f'(x) = $\lim_{h \to 0} \frac{-1}{(x+h+3)(x+3)}$

[glossy valve]

pubuyun

[unreal minnow]

oh i forgot the -1 on top

[tribal steppe]

=$\frac{-1}{(x+3)^2}$

[glossy valve]

pubuyun

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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.

[unreal minnow]

thx

also wb this

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[full forum]

@median remnant Has your question been resolved?

[median remnant]

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[full forum]

Please don't occupy multiple help channels.

[glacial pasture]

go to your original channel

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[pseudo notch]

I need help with an ixl

[pseudo notch]

first question

ive been on this for 1 hr+

i really need help

[ripe horizon]

what have you tried

you should be starting by graphing line j using the two points provided

[pseudo notch]

yes but i just dont know how to plot the second point for line k

[ripe horizon]

i see

when 2 lines are said to be perpendicular, their slopes will be negative reciprocals of each other

for example, if you a line with a slope of 8/5

[pseudo notch]

-5/8

[ripe horizon]

the slope of a line perpendicular to that line will be -5/8

yea

now, what do you think is the slope of line j

just remember rise/run

[pseudo notch]

sorry my dc crashed

3/4

i think

[ripe horizon]

are you sure

[pseudo notch]

wait let me write it down

4/3

is what i got

[ripe horizon]

yea thats right

now whats the slope of line k

[pseudo notch]

-3/4

[ripe horizon]

using this

yep

now focus on the point (-4,1)

you wanna rise -3 units, and run 4 units

how would you do that

[pseudo notch]

like that im pretty sure

[ripe horizon]

yea

thats correct

[pseudo notch]

i got it right thank you

[ripe horizon]

this is what is looks like when you graph them together

[pseudo notch]

so this is basically the same thing right?

[ripe horizon]

yep

what do you think is the slope of the y-axis

[pseudo notch]

parallel is the same slope

and i dont think u can get a slope with only one point

so 0 i think

or undefined

[ripe horizon]

if you have a straight vertical line

then its an undefined slope

so meaning, line q must be undefined

so we check 2

[pseudo notch]

1 is wrong since it only goes through -3

so would that mean 3 is right?

[ripe horizon]

are you sure

y=3 is a zero slope

while line q has an undefined slope

but remember

a line with a zero slope is a horizontal line,
while a line with an undefined slope is a vertical line

[pseudo notch]

oh ok i get it

y=3 is a zero slope

so its horizontal and the original one is vertical

[ripe horizon]

yea

meaning they are?

[pseudo notch]

so their perpendiculatr

if line y=-3 the slope would be zero right

so it would be wrong

[ripe horizon]

yep

[ripe horizon]

therefore 1 is also true

[ripe horizon]

and yep, therefore 3 is false

now whats x=-3

what type of slope is that

[pseudo notch]

undefined i think since its x

[ripe horizon]

yes

[pseudo notch]

so it would be a vertical line right

[ripe horizon]

and line q also has what?

[ripe horizon]

correct

[pseudo notch]

an undefined slope

[ripe horizon]

therefore they are ?

[pseudo notch]

parallel

[ripe horizon]

meaning 4 is true too

[pseudo notch]

i got it thankyou

i think i can try to solve this one myself

do i show you what i got or just submit

[ripe horizon]

sure ill check if you got the right answer

[pseudo notch]

alright thanks

this is what i got

[ripe horizon]

correct

did you transformed 4x-3y=15 into y=mx+b?

[pseudo notch]

yes

[ripe horizon]

then yea the slipe will be 4/3

its right

[pseudo notch]

i think i can do this one too

[ripe horizon]

go ahead

[pseudo notch]

ok im a little stuck

i make the equation for line d into slope intercept form

y=5/3x+7

[ripe horizon]

thats right

whats the slope of line e then

[pseudo notch]

and i got the slope for lin e -3/5

[ripe horizon]

knowing theyre perpendicular

yea

but do we know the y-intercept?

[pseudo notch]

thats what im kinda stuck on

[ripe horizon]

yea

we dont know the y-intercept yet

so lets represent it as b

the equation of line e will be y=-5/3 x + b

now, what point does line e pass through

[pseudo notch]

10,-8

so we would plug in 10 i think

for x and -8 for y

[ripe horizon]

yea

you will get the value of b

which is the y-intercept

which is exactly what we need

hold on i need to feed dogs

[pseudo notch]

ok lol

i got -24 2/3

gotta use the bathroom one sec

back

[ripe horizon]

thats not right

[ripe horizon]

oops this shouldve been -3/5

[pseudo notch]

oh ok

let me try again

[ripe horizon]

-8 = (-3/5)(10)+b

like that

[pseudo notch]

i got -2

it was right

i can do this one too im pretty sure

i got y=5/3x-1

@ripe horizon you there?

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[median remnant]

7x+5<10x−7<7x+8 how would you solve this

[median remnant]

i added the 7 to both sides

i got

7x+12<10x<7x+15

i dont know what to do now

[ripe horizon]

try eliminating the x term on the leftmost and rightmost part

[median remnant]

how would i do that

would i dived by 7 on both sides?

[ripe horizon]

not really

you can subtract 7x tho

thatll remove 7x from 7x+12 and 7x+15

,,(7x+12)-7x<10x-7x<(7x+15)-7x

like that

[median remnant]

ok

[glossy valve]

Renz

[median remnant]

but how would i get the answer after

[ripe horizon]

what does this simplify to

[median remnant]

12<10x<15

[ripe horizon]

the middle is 10x-7x btw

[median remnant]

ok

i think i got it

thank you

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[torn jolt]

how does the given part become 0 + 0?

[umbral dome]

the determinant is 0 if there are linearly dependent rows or columns

[torn jolt]

first and second row are the same albeit with a different scaling factor

same goes for second and third rows of the second det

but how doe that make it 0?

i assum it's referring to this property

oh can you take R1 --> R1 + R3

oh damn it

i'm stupid

it's just

R2 --> R2 - R1

and then first and second rows become the same

so det of that is 0

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[marsh haven]

Bianglala berputar satu putaran dalam waktu … menit.

does anyone know this?

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[weak iron]

please translate into english

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[tulip badge]

what is kernel in linear algebra

[tulip badge]

im learning abt linear mapping and copies

so if someone can explain it in simple or like

explain to me what is mapping and copies and what is kernel

[torn jolt]

The kernel of a linear map, also known as the null space, is the subset of the domain mapped to the zero vector. denoted ker(T)

[tulip badge]

so its a subspace as u r saying

its a subspace but for the T:E->F

[torn jolt]

yea

T: E-->F is indeed a subspace of E

To put in simpler terms, the kernel of a linear map T is the set of all verctors in E that T mapps to the zero vector in F

This means it satisfies all the properties kinda like a closure under addition and sclar multiplication

So when u say that a “subspace for T:E->F”, it means the kernel is a subspace of the domain E of the linear map T.

does that help?

[tulip badge]

ok i got it but

the mapping part

i didnt understand much what is mapping exactly

is it like a span ?

or a subspace

[torn jolt]

i mean

Mapping is a generalconcept

it can be applied alot so

in linear algebra mapping refers to a spcial kind of association

[fast peak]

mapping is a different word for function

[torn jolt]

yea, to put it simpily :/

A linear mapping stretches, shrinks, or slips vectors according to a set of rules

[tulip badge]

the set of rules that r in summing and in multiplying right

[torn jolt]

in linear maps there aretwo key rules

addivity

and homogeneity

which mean to take two vectors and add them together or multiply is by a scalar respectively

does that help?

[tulip badge]

ye

so if those 2 rules

can occur

its a linear map for sure

[torn jolt]

If a mapping follows those two rules, additivity and homogeneity, then it qualifies as a linear map.

These rules are elementary to how linear maps behave and what makes them distinct from other kinds of mappings.

why am i speaking like a college professer lol "those rules are elementary" 🤣

but all jokes aside, those rules are the basics into understanding how linear maps behave

A mapping follows those two specific rules, additivity and homogeneity, if so then it is guaranteed to be a linear map.

well i gtg, i hope i helped

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[clever turret]

how to calculate the domain of the denominator

pls help

[torn jolt]

whats after 2x

?

[clever turret]

+1

[tribal steppe]

it's defined when x>=-2 and 2x+1-sqrt(x+2)>0

[clever turret]

Ok

I try

[clever turret]

????

To square , you don't need to create the system √f(x)>g(x)

I get x>1

Its wrong

😭

[tribal steppe]

you can easily find that 2x+1-sqrt(x+2) always increases, so just solve for 2x+1=sqrt(x+2)

x=1/4

for all x>1/4, 2x+1-sqrt(x+2)>0

that's faster than column inequality

[clever turret]

How

[tribal steppe]

2x+1 grows faster than x+2, and sqrt actually makes x+2 grows slower

[clever turret]

I don't know where wrong

😭

[tribal steppe]

how did you get that

[clever turret]

I didn't square the right....

It should be on the right

(2x+1)^2

[tribal steppe]

yes, solve that and you will get it

[clever turret]

👍

Thank you

x>1/4

👍

[tribal steppe]

👍

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[tawny radish]

anyone can help me with integral question

[fathom swift]

#help-16 message

[tulip oriole]

use u = lnx

[tawny radish]

i mean i get it but what happens to X in denominator

[tulip oriole]

it cancels out with the derivative of lnx which is 1/x

[celest pewter]

$du = \frac 1 x dx$

[glossy valve]

b

[celest pewter]

and again your integral is $\int \ln x (\frac 1 x dx)$

[glossy valve]

b

[tawny radish]

ow thanks i got it now

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[granite holly]

hi

if n is the normal to the plane

wouldnt d always be 0?

and r is any vector in the plane

O is (0,0,0)

this is the line

[glacial pasture]

d isnt necessarily always 0, no
the plane also contains the point (1,2, -2)

and the normal to the plane is perpendicular to (-3, -1, 4)

such a dot product wouldnt return 0 in all cases

[ashen crescent]

d would be the distance from the origin in the direction of the normal

[granite holly]

Ohhh okay ty so its the

positing vector for the normal vector

wait no its the magnitude of the position vector?

[granite holly]

Im confused, isnt r supposed to be vectors within the plane?

[glacial pasture]

its the position vectors of points in the plane

[ashen crescent]

The normal to a plane doesn’t necessarily have to be linked to a position vector, since the normal to a plane is the same everywhere on the plane

[granite holly]

ohh

ok ok i see, thank you

So if i wanted to find d and had both r and n

sorry just n

I could take any point on the plane*, and write it as r

[glacial pasture]

(1 2 -2) and (-3 -1 4) are two vectors in the plane, you can get the normal by a cross product

[granite holly]

and find the dot product to get d

[ashen crescent]

Although, since you know the plane goes through the origin, then d will in fact be 0

[granite holly]

if this is true wouldnt d change based on which point we pick on the plane? for r

[ashen crescent]

Yeah that would get you d

[ashen crescent]

No, because the angle between the position vector and the normal will compensate for the change in magnitude of the position vector

Recall that the dot product is |x| |y| cos theya

[granite holly]

AHhh I get it, didnt relise that would account for it

Tysm

Couldnt I have solved this with just the line formula?

ohh nvm yeah

Ok ty ty

[ashen crescent]

Yeah if you follow azo said here

[granite holly]

Yeah but if we didnt know that it went through the oirigin

just the line would not be enough correct?

[ashen crescent]

Then you would just have to do one more step: compute the dot product of the normal you just found and a point on the plane

[granite holly]

okay understood

thank you very much

[ashen crescent]

In general

You want 3 points on the plane, then find the normal by computing the cross product of 2 vectors given by the 3 points

So for points p1, p2, p3, you make one of the points the tail of the 2 vectors

And the other two points will be the heads

You will have something like
v1 = p2 - p1, v2 = p3 - p1

Then n = v1 x v2

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[granite holly]

ohh yeah

thank you

will close the channel now

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[urban plume]

I solve the difference quotient for both velocity value thingy's (question 5) but I'm not actually sure what I'm solving. Do I just add the two calculated values together and then divide by 2, like normal averages ?

[pseudo cape]

What did you do for 4.?

[urban plume]

I just got a simplified formula (-16x^2+8x+24)

for 5, I plugged both values into the equation, and got -4.16 and -79.04

not sure if that part is right tho @~@

and if it is, what to do after

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[elder monolith]

Supposing I have a circle and a point on the coordinate plane, how can I know the lines for the 2 tangents from that point to the circle?

[wide sundial]

What have you tried

[elder monolith]

uhh

using the dot product

say the point 3,4 is A

and the tangent goes through the circle at M

I have the dot product vecOM.vecMA = 0

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[lyric mantle]

actually guys

[lyric mantle]

i had a question

when do we do direct proportion

and when do we use unitary method

i dont have the exact questions

im just asking in general

like theres specific patterns to questions right

when do u guys usually use direct proportion and when unitary

[regal shuttle]

u use the unitary method if u wanna get the proportionality constant, ie y=kx, u find k

u use direct proportions when information is not given about the exact relation (hence the proportionality constant) but the relation like a is proportional to the square of r is given

[lyric mantle]

oh

wait

so unitary method

is just direct proportion then right

we just use it as a name

@regal shuttle

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[outer dust]

why is it not [2,1]

where did they get the 2 in 2* 1* a

is it not 1* a + -2 *b?

[devout valley]

Sorry what's the "inner product of Example 7.2"?

Assumedly $\ip{u}{v} = 2 u_1 v_1 + 3 u_2 v_2$ right?

[glossy valve]

@devout valley

[outer dust]

oh

okay, that makes sense

gracias

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[trail dome]

im kinda confused..

[trail dome]

i need to make x the subject

[grave elm]

what's this in terms of y?

(kinda weird question tho, infinitely nested square root isnt something that's usually well-defined)

[trail dome]

idk wdym

[grave elm]

You need to make one key realization here

$y=\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x \dots}}}}$

[glossy valve]

MethIsAlwaysRight

[grave elm]

$y=\sqrt{x+\sqrt{x+\sqrt{x \dots}}}$

[glossy valve]

MethIsAlwaysRight

[grave elm]

both of these are true, right?

[trail dome]

yes

[grave elm]

now can't you see this exression hidden in the previous one?

[trail dome]

yeah now i can

so is it just y= square root x+y

[grave elm]

yep

[trail dome]

that makes it easier

[grave elm]

by quite a lot, indeed

[trail dome]

yeah

thank you so much

[grave elm]

you are welcome

[pseudo cape]

This problem is also often given as \begin{problem} Find the value of [\sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}]\end{problem} or \begin{problem} Find the value of [\sqrt{2 + \sqrt{2 + \sqrt{2 + \cdots}}}]\end{problem}

[grave elm]

or something like $1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\dots}}}}$

[glossy valve]

MethIsAlwaysRight

[grave elm]

all use the same strategy

[trail dome]

ohhhhhh alright

thanks so much

im gonna close the channel now

tysm

.close

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[tall glen]

would somebody be able to explain these two problems ? i don't really understand the whole e part

[limber carbon]

whats the question exactly? does it want you to derivate these functions?

[tall glen]

yes it's asking for the derivative

[limber carbon]

derivative of e^x is e^x

[tall glen]

so it's just the same thing ? for the first one i got 15e^3x+2

im not sure if that's right tho

[limber carbon]

nope

when youre derivating it, you should derivate the power of e and multiply it with the result

[tall glen]

im not sure i understand

[limber carbon]

wait wait youre right, exactly

i didnt see the 15

you got it right!

[tall glen]

ok cool thank you! and for the second one you're doing product rule right

[limber carbon]

mmhmm

exactly

dont forget to derivate the power of e

[tall glen]

so 3e^2x * secxtanx + secx * 3e^2x ? or is it 6e^2x

[limber carbon]

it would be 6

you need to derivate the power as well

[tall glen]

i thought deriviative of e you just kept it

[limber carbon]

it only works for e^x since derivative of x is 1

but if it is not just x, like here, you gotta derivate it

[tall glen]

so is this just e^2

6e^2

[limber carbon]

no, you keep the power intact

you only multiply with the derivative

thats it

basically this!

[tall glen]

i dont really understand

[limber carbon]

what part

[tall glen]

i understand the multiplying 3 by the power to get 6 but i dont understand what goes next

by the derivative of the power *

[limber carbon]

youre basically done

[limber carbon]

you got it right here, only needed to do 6

[tall glen]

oh so i had it right the first time with 6e^2x ? and then after that just do number part letter part etc and make it look straight ?

[limber carbon]

i dont understand what you mean by the letter part

[tall glen]

oh that's just how i was told by my professor to organize my final answer, with number part coming first , then letter part then trig part

[limber carbon]

ohhh

yea i suppose so

[tall glen]

thank you i get it now

[limber carbon]

ofc!

[tall glen]

have a great rest of your day

[limber carbon]

you too

[tall glen]

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[warm solstice]

Hey need help with these problems
https://discord.com/channels/268882317391429632/1234562140132741201

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@warm solstice Has your question been resolved?

[warm solstice]

<@&286206848099549185>

[warm solstice]

<@&286206848099549185>

[torn jolt]

Yes?

[warm solstice]

Hey thank you so much I need help with these questions
https://discord.com/channels/268882317391429632/1234562140132741201

I have been working on them I need explaining why they were wrong/right

[full forum]

@warm solstice Has your question been resolved?

[warm solstice]

This is link to the questions

https://discord.com/channels/268882317391429632/1234562140132741201

[warm solstice]

<@&286206848099549185>

[torn jolt]

Hey

[torn jolt]

sorry didn't help you earlier

[warm solstice]

No worries I figured you were busy

[torn jolt]

I am helping three people at once

that's why

[warm solstice]

I understand that is alot

[torn jolt]

Thank you for waiting

Can you show me the questions?

[torn jolt]

Is it this?

[warm solstice]

Yes 🙂

You're busy I understand I was trying to reach someone else who can help I really appreciate you helping me and letting me know

[torn jolt]

<@&286206848099549185> Someone help here

[torn jolt]

I'm very sorry

I can't help you much

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@warm solstice Has your question been resolved?

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[limpid glen]

hello, quick question

[limpid glen]

how does $$e^{\ln 3}$$ for example cancel out the ln?

[glossy valve]

Maladroit

[manic jacinth]

ok

so

what does ln really mean?

[limpid glen]

natural logs?

[manic jacinth]

its basically asking "e to what power is 3?"

right?

[limpid glen]

yea

yupyup

[manic jacinth]

get it now?

e to power of the number that when raised to this number makes it 3

[limpid glen]

i still dont get how its canceled

[limpid glen]

but i get this statement somehow

[manic jacinth]

i get it man

used to have the same problem

[limpid glen]

does it have something to do with

the ln’s base being e asw?

[manic jacinth]

yes

so

think about it

again

ok nvm

so whats the natural log of e?

[limpid glen]

1

[manic jacinth]

basically, e to the what power is e?

yep there we go

[limpid glen]

1

OHHHH

I SEE

$$e^{\ln_{e}} = \ln_{e} e$$

[glossy valve]

Maladroit

[limpid glen]

right right?

[manic jacinth]

uh

ln base e?

or is that supposed to be ln e

[limpid glen]

i mean i just added the base of e

but i mean

ln’s base is usually e right

just for demmo

demo

[manic jacinth]

i mean in e^ln_e

[limpid glen]

yea

[manic jacinth]

how about i explain it this way

[limpid glen]

mhm mhm

[manic jacinth]

ln (x) is asking "e^what power is x"

[limpid glen]

mhm

[manic jacinth]

lets call "what power" y.

so y=ln(x)

[limpid glen]

mhm

[manic jacinth]

so e^y is x

because, again, its asking "e^what power is x"

but wait

if y=ln(x)

[limpid glen]

mhm

[manic jacinth]

and e^y=x

what have we done here to the left side?

we raised e to that number

and so, we raised e to the other side as well

and thus, e^lnx=x

so the e and ln cancel out

[limpid glen]

i see

[manic jacinth]

gtg

hope that helped

[limpid glen]

alralr

im gnna try to digest

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[drowsy axle]

For 18A. Does 9(4 to the power of 1-X) become 36 to the power of 1-X?

[torn jolt]

no, you cannot combine those because they do not have the same base

it has to stay as 9(4^1-x)

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[drowsy axle]

.reopen

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✅

[drowsy axle]

How do I solve the question then?

[manic jacinth]

ok

[manic jacinth]

u know pemdas?

just a reminder just in case

parenthesis, exponents, multiplication/division, addition/subtraction

[drowsy axle]

Yah. I was taught bedmas but they are pretty much the same

[manic jacinth]

well here, we do parenthesis first

so no, we cannot just combine them

[drowsy axle]

What do I do instead tho?

[manic jacinth]

so, look at the other questions, and see the logarithms

thats a big hint

[drowsy axle]

I add log to all of them?

[manic jacinth]

so, we can take log_4 on both sides, right?

[drowsy axle]

Yah. But why base 4?

[manic jacinth]

that makes it 2x+1=log_4(9(4^1-x))

no more exponent on one side makes it easier

[drowsy axle]

Yah. The way I was taught was to do log base 10 and then use power rule to get rid of exponent and then use algebra to solve the rest.

Or not get rid of exponent but move it in front of log

If that makes sense

[manic jacinth]

yes

ik my log properties

actually, change of plan

nvm that changges absolutely nothing

[drowsy axle]

I’m just letting you know because the way you were telling me before in not really sure how to do and I want to do everything in a similar way

@manic jacinth this is what I did and I got it wrong. Ik it was because I combined the 9 and 4

But I’m not really sure what to do instead

[manic jacinth]

divide by 9 on both sides, then take log 4

see where that gets you

ping me btw

[drowsy axle]

Oh, so would It be 4/9 to the power of 2x+1?

[manic jacinth]

no (4^2x+1)/9

[drowsy axle]

Alr

[drowsy axle]

I have an online class starting now so I can’t fix it. But is it ok if I dm you later?

[manic jacinth]

you can ping me

you know what sure

[drowsy axle]

Alr ty for the help. I’ll be sure to ping you when I get a chance to fix it

[manic jacinth]

just i'm probably gonna be asleep

timezones you know

[drowsy axle]

Yah

Alr i gtg now but I’ll ping you later

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@drowsy axle Has your question been resolved?

[drowsy axle]

@manic jacinth I still got it wrong

@manic jacinth

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@drowsy axle Has your question been resolved?

[drowsy axle]

Nvm I figured it out. Thanks for the help tho

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[wide sundial]

i must be missing somthing simple here

[wide sundial]

it says the otherwise f(t) would be infinite

but about about the negatives

couldn't t be negative then 1 - a_i t would be 1+ a_1 * positive side of t

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[timber wadi]

I don't know how to get the rejection regionT_T

[timber wadi]

plz help

[barren onyx]

define the null and alternative hypothesis, choose a significance level α, select a suitable test statistic, calculate critical values based on distribution

what kind of question is that anyway

you are too vague

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[plain fox]

the integral of this would be $$\int_{-1} ^9 (x^3+1) dx$$?

[glossy valve]

JustToPro

[plain fox]

find the area enclosed by the curve y = x^3 + 1 , line x = 2 and x axis

[inland moth]

-1 to 9?

[plain fox]

yeah the curve crosses / intersect the x axis at -1

or should i be 0?

[inland moth]

-1 is good

but why 9

[plain fox]

because area enclosed by curve and x = 2

so i thought its point of intersection should be the top limit

[inland moth]

you should only be integrating from -1 to 2

[plain fox]

oh

so only x axis counts as bounds?

[inland moth]

you're integrating with respect to x yeah?

[plain fox]

yes

[inland moth]

then consider your lower and upper limits on the x axis

[plain fox]

oh so if i were to integrate with respect to y

it would be 0 to 9 ?

[inland moth]

yeah

[plain fox]

oh ok

so $$\int_{-1} ^2 (x^3+1) dx$$?

[glossy valve]

JustToPro

[inland moth]

yeah

[plain fox]

ok ty for the help

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[hushed spruce]

is there a formula to the find nth term or is this done by intuition?

[inland moth]

just pattern recognition

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[amber totem]

The numbers 1 to 10 are arranged in a line (uniformly at random). What is the probability that the first number is odd and the last number is even?

[rapid rain]

how many ways can you arrange 1 to 10 in a line in total?

[amber totem]

1023?

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@amber totem Has your question been resolved?

[rapid rain]

i don't understand how you got that

how many ways are there to arrange 10 elements in a line?

[amber totem]

the nCr

[rapid rain]

and r = ?

[rapid rain]

it's not that unfortunately

Say you want to arrange 10 elements in a line

how many choices do you have for the 1st number (on the left)?

[amber totem]

9 choices

[rapid rain]

you have 10 numbers...

[amber totem]

yeah if u take one number out of it then 9 choices are left to match with that one number

[rapid rain]

Why would you take 1 number out of it?

Why would a number not be allowed to be in first position?

[amber totem]

well then it would have 10 choices

[rapid rain]

yes

how many choices for the 2nd number after that?

[amber totem]

either 10 or 9 choices

so 10! ?

[rapid rain]

yes 10! in total

10 times 9 times...

[amber totem]

yes i got that

but how do i work with the answer

[rapid rain]

well now that we have the amount of ways we can arrange 1 to 10 in a line

[amber totem]

yupp

[rapid rain]

so out of all those ways

how many of those ways have the first number even and the last number odd?

(this is the exact same type of reasoning as we did above)

[amber totem]

so if it is arranged in order since there are 5 even and 5 odd so 5!?

[rapid rain]

why would it be arranged in order?

and why 5!?

[amber totem]

because 1,3,5,7,9?

and 2,4,6,8,10?

[amber totem]

thats my mistake . its at random

[rapid rain]

so you're fixing the positions of ALL even numbers andd all odd numbers?

[amber totem]

hmm no

[rapid rain]

ok

Suppose you have such an arrangement

How many choices for the first number?

[amber totem]

10

[rapid rain]

nuh uh

don't forget our condition

[amber totem]

ok so first number to be even there are 5 even numbers

[rapid rain]

yeah opposite sorry 1st number odd last number even

[amber totem]

and for last to be odd there are 5 odd numbers

ok so

[rapid rain]

doesn't change anything

[amber totem]

it can start from 1,3,5,7,9

any of those numbers

[rapid rain]

yes

so 5 choices for first number, 5 choices for last number

[amber totem]

yes

[rapid rain]

suppose you've chosen both of them

how many choices for 2nd number?

[amber totem]

4

or 8

because it can be any number

as long as first and last is odd n even respectfully

[rapid rain]

yes 8

how many choices for 3rd number?

[amber totem]

7,6,5….

it goes on

[rapid rain]

yep

so how many choices in total?

[amber totem]

1+8+7+6+5+4+3+2+1

[rapid rain]

oof why addition?

[amber totem]

because total

😭💀

[rapid rain]

no

you add choices when they're DISJOINT

[amber totem]

then multiply?

[rapid rain]

here the choices are IN A ROW

so we multiply

[amber totem]

ok so 1 to 10 multiply each number?

1x8x7x6x5x4x3x2x1

[rapid rain]

weird, I don't remember there being 1 choice for first number

and last number

[amber totem]

umm

omg

sorry

5x8x7x6x5x4x3x2x5

[amber totem]

so what about the 5 in middle?

[rapid rain]

?

well it's just a 5

doesn't hold anything to it

so there are 5^2 * 8! choices in total

[rapid rain]

so I think from here you should get the answer to your original question

[amber totem]

wait thats it

so 1008000 is the final answer??

[amber totem]

but the question is probability

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[hybrid mist]

Hello

[hybrid mist]

Circumference is (2)(pi)(r)

[ancient folio]

Whats the question then? Checking ur answer?

[hybrid mist]

yes

the question is a and b

I checked them and it was wrong

[ancient folio]

Show your work

[hybrid mist]

deadass have no clue

where do I go form here

I don't have r

I only have r of earth

not the radius of topic of cancer

<@&286206848099549185>

[ancient folio]

Bruh

Wrong triangle

Make the right triangle upside down

[ancient folio]

23.5 deg is the angle on the down side bruh

[hybrid mist]

yea yea mb

oh wait

I'm so dumb

[ancient folio]

Look at the earth model

[hybrid mist]

its the radius

but doesn't the upper line also the radius

cuz it goes to the edge of the circle

[ancient folio]

Oh right

Mb

Yeah

Use trigonometry to find the radius of the Cancer thing

[hybrid mist]

so we js use sin

[ancient folio]

Then 2 pi × r

Thats it

[hybrid mist]

for r

[ancient folio]

Not sure I dont have my calculator here but I assume u knkw how to deal with it

[hybrid mist]

yea

how do u find the distance

of 2 points

we are not expected to use the distance formula btw

is it js the radius * 2

cuz it the diamete

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[vague fulcrum]

How to do 4

[vague fulcrum]

This mich done

THIS IS 3 SET PROBLEM

[reef viper]

!status

[full forum]

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

[vague fulcrum]

2

4 c

[reef viper]

All of 4c?

[vague fulcrum]

Also can u check my notations if they r correct or not

[vague fulcrum]

Yes quite cobfused

[reef viper]

[ \frac{{\text{pupils who do both jogging and cycling }}}{{\text{Total number of pupils}}} \times 100% ]

[glossy valve]

Gaza

[reef viper]

You can find that set from your Venn diagram if you’ve done it nicely

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[vestal verge]

Solve with u sub?

[craggy tapir]

seems like so

[vestal verge]

Yeah but how

[hot herald]

have you done integeration with sub before

[slate violet]

Honestly you might as well expand everything and integrate term by term

I don't see a nice way to use u-sub here

[vestal verge]

Yes

[slate violet]

Hopefully you have copied the question correctly

Oh wait

[vestal verge]

I did

[slate violet]

Yeah it's just u = 1 - x

[torn jolt]

Expanding a 5th root is pain tho

[slate violet]

true okay yeah u-sub was the way to go

[torn jolt]

U can just put the other expression in terms of u

Shouldn’t be too hard

And then expand the binomial

And distribute the u^5

[vestal verge]

If u is 1-x then what

[slate violet]

Yeah the key here is to transform the x + 1 into a function of u

Cause it's much easier to expand a power of 2 than a power of 5

[vestal verge]

That makes x+1 = -u+2

Right?

[slate violet]

Then find dx

[vestal verge]

du/dx is -1

[slate violet]

Yes

[vestal verge]

So we need to multiply it by -1

And then we get

(-u+2)^2 (u)^5 du

[torn jolt]

Where is the negative

[slate violet]

Yes you missed a negative

Anyways

[vestal verge]

The negative became du

[torn jolt]

No

That’s not how that works

[vestal verge]

Why

-1 is du/dx

[slate violet]

du = -dx
So -du = dx

[vestal verge]

what

[torn jolt]

ok

du/dx =- 1

Right

[vestal verge]

Yep

[torn jolt]

We want to isolate dx

So how do you do that

[vestal verge]

Wdym

[torn jolt]

Treat it as a fraction

du/dx = -1

And solve for dx

[vestal verge]

we do du/dx *dx and we get du

[torn jolt]

But du/dx = -1

[vestal verge]

Yeah

-dx =du

[torn jolt]

So you need to multiply both sides of the equation

Right

-dx =du

[vestal verge]

Yeah the other guy said the opposite

[torn jolt]

So dx = - du

[vestal verge]

He said -du=dx

[torn jolt]

Yes

[vestal verge]

How

[torn jolt]

Algebra

[vestal verge]

Why

[torn jolt]

Not even algebra

Arithmetic

[vestal verge]

Why do we need to

We have du

That’s it

[torn jolt]

Take du = -dx and multiply both sides by -1

[vestal verge]

Yeah but why

du=-dx

We are done

We found du

[slate violet]

You need to replace dx with du

[vestal verge]

I just did

[torn jolt]

no

[vestal verge]

We take out the -1*dx and replace it with du

[slate violet]

Well there isn't a -dx in the original integral
Unless you do -1 * (-dx)

[torn jolt]

there wasn’t a -1 dx in your original expression

[vestal verge]

I just said I multiplied the integral by -1

I did that in the very beginning

[slate violet]

If you did that

Then you should be integrating (-1) * (-u+2)^2 (u)^5 du

[vestal verge]

What??

The -1 went into the dx to make du

The -1 is gone

It’s just a negative integral

[torn jolt]

yes

That doesn’t mean it’s gone

You make the integral negative

[vestal verge]

Yeah

I did

Now what

[torn jolt]

Now what is your new integral

Do you know your bounds

[vestal verge]

It’s not bounded

It’s indefinite

[slate violet]

Yeah there are no bounds

[vestal verge]

So what’s next

[torn jolt]

Oh ok

[vestal verge]

This is where we are