help-23

[rigid inlet]

if f is an even function, then f(-x) = f(x)

how do I personally know? because I've memorized it

you can figure it out by looking at the graph

,w plot cos(x)

[flat frigate]

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[rigid inlet]

notice the behavior on either side of x=0

[frozen sandal]

how do i solve

[safe radish]

@strange orchid Has your question been resolved?

[safe radish]

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[safe radish]

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[mild sequoia]

is this just a 30 60 90 triangle, and theta = 60?

[safe radish]

Please don't occupy multiple help channels.

[mild sequoia]

ops sorry

[bleak delta]

where is the triangle exactly

[mild sequoia]

well if i did smt like this

[bleak delta]

so where is r/2

[mild sequoia]

its a unit circle sorry

r = 1

[bleak delta]

okay no problem

can be any circle

[velvet badger]

wouldn't $\frac{2\pi}{3} \text{ rad } = 60^{\circ}$
i don't think 1 radian is 60 degrees
or im dumb

[bleak delta]

but r/2 does not appear

[flat frigate]

Gamer Sans The Gamer Skeleton

[bleak delta]

57...degrees

1 radian

[stone comet]

1 rad is 180/pi

[mild sequoia]

so theta is 57 degrees?

howd u get that

[bleak delta]

@mild sequoia We know that,

=> 2π rad = 360°
=> 1 rad = 360°/2π = 180°/π

180/π is approximately, something like 57

so it is ≈ 57.29°

[mild sequoia]

👍

ok thanks!

.close

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[grand gull]

Can someone please explain how the perpendicular bisector of PR passes through its midpoint?

I've drawn out the circle but just fail to see how this is the case

<@&286206848099549185>

Pls

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[lean otter]

i got somewhere and then didnt know what to do

I found the RREF of it

but after that idk what to do

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

.close

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[lean otter]

hi

its fractions

no fractions but

dividing

[fluid token]

which part and what are you confused about

[lean otter]

i need help

[lean otter]

all of it

i need to fill it in

ur ignoring me

<@&286206848099549185>

[fluid token]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[lean otter]

ok so youre just sitting here though

you arent helping

[fluid token]

i’m not obligated to help you

do you know how to convert celsius into kelvin?

[lean otter]

did i say that

[fluid token]

you sure did imply that

[lean otter]

yes...

[lean otter]

i do..

[fluid token]

start by doing that for the ice and saltwater temperature field

[lean otter]

and then what..

[fluid token]

fill it in???

[lean otter]

its 258

now what

do i just convert everything to kelvin

[fluid token]

convert temperatures for warm and hot water baths now

[lean otter]

now what

i did it

[fluid token]

now plug that into the gas law equation and calculate V2, you’ll do it 4 times, twice using the temperature for warm water and alternating between trial 1 and trial 2 V1 then twice using temperature for hot water alternating between trial 1 and 2 V1

T1 will be the same for all four

[lean otter]

what is t1

[fluid token]

look at the box you filled above

[lean otter]

is it this equation

[fluid token]

no

[fluid token]

.

[lean otter]

do i just divide these

258 / 4.2

[fluid token]

read what i said above

[lean otter]

other way

can you explain it one step at a tie

time

ur sending a paragrpah and i dont udnerstand it

[fluid token]

what is the gas law equation?

[fluid token]

what is V1 for Trial 1?

[lean otter]

4.2 / 258

?

so

[lean otter]

4.2

[fluid token]

what is T1?

[lean otter]

258

[fluid token]

do you know what V2 is?

[lean otter]

4.1

[fluid token]

no

[lean otter]

yes..

[fluid token]

is that V2?

[lean otter]

no

sorry

[fluid token]

V2 is the unknown

what is T2 for warm water bath?

[lean otter]

321

[fluid token]

now

plug everything into the gas law equation

and write it down

[lean otter]

V1 / t1 = v2 / t2

4.2 / 258 = v2 / 321

[fluid token]

can you solve for V2 now?

[lean otter]

no..

[fluid token]

plug it into a calculator then

or you can learn how to solve it by hand

it’s not that difficult

[lean otter]

4.2 / 258 = v2 / 321

its a graph.

[fluid token]

no

google can’t help you with that

[lean otter]

5.2

Now what

[fluid token]

do that for the rest now

[lean otter]

wait

WIAT.

what do i change

V1 / t1 = v2 / t2

4.2 / 258 = v2 / 321

[fluid token]

using the same T2 value, use a different V1 value (Trial 2) then use the hot water T2 value and Trial 1 and 2 V1 values

[fluid token]

wdym

[lean otter]

4.2 /?? = v2 / 353

im confused

[fluid token]

no

[lean otter]

wait

321 is the same

ur telling me to do multiple steps in one sentence

can u not

4.2 / x = v2 / 321

[fluid token]

(V1 (Trial 1) / T1) = (V2 / T2 (Warm Water))

(V1 (Trial 2) / T1) = (V2 / T2 (Warm Water))

(V1 (Trial 1) / T1) = (V2 / T2 (Hot Water))

(V1 (Trial 2) / T1) = (V2 / T2 (Hot Water))

[lean otter]

u never said t1 stays the same

god

[fluid token]

.

[lean otter]

4.1 / 258 = v2 / 321

wtf

god

[safe radish]

@lean otter Has your question been resolved?

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[topaz elk]

how can I determine how many maxs and minimums does this cubic polynomial equation have:

[torpid fable]

Take derivative and set to 0

[topaz elk]

first derivative ?

[torpid fable]

Yeah

[topaz elk]

okay wait let me try

Ok I got

-31.9596228815x^2 - 33.9556106179x + 0.0443736

now what

[fluid token]

set it equal to 0 and find the roots

[topaz elk]

ok should I use quadratic formula

[fluid token]

you’ll be better off using a calculator

[topaz elk]

okay

let me try

[fluid token]

are you sure the derivative is correct?

[topaz elk]

yea I think so

[topaz elk]

It won’t let me

[fluid token]

wdym

[topaz elk]

I don’t think I can do it

it’s ok

thanks for trying to help me

I appreciate you

[fluid token]

bruh is that a test

use desmos

[topaz elk]

no

na it’s ok

thank you tho

I think I’m good

.close

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[wise needle]

I need help

[wise needle]

P

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@wise needle Has your question been resolved?

[safe radish]

@wise needle Has your question been resolved?

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[mortal dagger]

i need help

[plucky elk]

[safe radish]

@mortal dagger Has your question been resolved?

[brazen viper]

we all need help

[safe radish]

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[orchid wave]

How do I do 2 and 3 ?

[safe radish]

@orchid wave Has your question been resolved?

[wooden forum]

do you how to calculate the length of arc?

[safe radish]

@orchid wave Has your question been resolved?

[orchid wave]

teeta/360 X 2pir

[wooden forum]

So we can set the ratio of center angle for 2 chord

That might help you calculate the area

[safe radish]

@orchid wave Has your question been resolved?

[orchid wave]

i don't really understand, can you give an example or workings ?

[wooden forum]

Did you find out the central angle for arcs?

[orchid wave]

no

.close

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[manic shadow]

√2a²b²c²

[manic shadow]

i just need to check if i am right

[lone arch]

Yes?

[manic shadow]

hold on im lost

how do i start

[frank glen]

Hmm

[manic shadow]

i thought of doing 2(abc)^2/2 but that doesnt look good

and 2 is outside the radical

[frank glen]

$\sqrt{2a^2 b^2 c^2} or \sqrt 2 a^2b^2c^2$?

[flat frigate]

VulcanOne

[manic shadow]

they look the same to me

[golden flower]

nah bro

[lone arch]

In the first one, you square root the entire expression

In the second one, only the 2

[manic shadow]

OH

left

i didnt noticed that

mbmb

[manic shadow]

First one

[frank glen]

Alright

Then yes what you mentioned earlier was indeed true except for the fact that 2 is not a perfect square.

2 stays inside a square root by itself

[manic shadow]

oh so i am right?

[frank glen]

Almost right

[manic shadow]

damn

[frank glen]

Make sure to include a square root with the 2 alone

$\sqrt 2 abc$ should be the simplified version.

[flat frigate]

VulcanOne

[manic shadow]

wait what happens to the numerator

[lone arch]

Did you mean $2(abc)^{\frac 2 2}$ with this?

[manic shadow]

ye dat

[lone arch]

Yeah, 2/2 = 1, and then what VulcanOne said

[manic shadow]

but 2 is outside so i thought not

OH

[frank glen]

2 is inside the square root with the rest of the stuff

[manic shadow]

Wait so if √4a²b²c² is it = 4(abc)^2/2 as well?

[frank glen]

Nope

[manic shadow]

oh

[lone arch]

and then what VulcanOne said

Make sure to include a square root with the 2 alone

[frank glen]

In this case the 4 is 2^2 and the square root takes away the square so in the end it becomes 2abc

Unlike if you had it like the first one

[frank glen]

[manic shadow]

whats a b

[lone arch]

Anything fit to be inside a root

It could be y^5 and z^100

[frank glen]

Any positive numbers

[manic shadow]

i see

[manic shadow]

when √a•√b•√c does that mean each of them individually gets a sqrt?

[lone arch]

Yeah

[manic shadow]

since sqrt itself is 2 and if the exponent is 2

it is equal to 1 since 2/2 = 1?

[frank glen]

Ye

[manic shadow]

Oh wow my brain expanded

[frank glen]

What is essentially happening is that we're distributing powers

$\sqrt a = a^{\frac 12}$

[flat frigate]

VulcanOne

[lone arch]

.

[frank glen]

[manic shadow]

wait howd u get 1/2

if theres already exponent of 2

[lone arch]

By the first sentence

[frank glen]

Square root is the same as 1/2 power

[manic shadow]

wait it still results in the same answer so am i still doing it right

[manic shadow]

I thought it was 2

[gentle herald]

That's square

[manic shadow]

what

[gentle herald]

Square means to the power 2
Square root means to the power 1/2

x squared is x²

[manic shadow]

ye

sqrt = denominator so i thought it was 2

[frank glen]

$\sqrt{2a^2b^2c^2} \ \
(2a^2b^2c^2)^{\frac12} \ \
2^{\frac 12} a^{\frac 22} b^{\frac 22} c^{\frac 22} \ \
2^{\frac 12} abc$

[lone arch]

sqrt = denominator
What do you mean by that?

[manic shadow]

and the variable is 1

[manic shadow]

^3√a^2 = a^2/3

[frank glen]

Well yeah square root is dividing the power by 2. It's also the same as multiplying the power by half.

[lone arch]

$\sqrt[3]{a^2} = a^{\frac 2 3}$, yes

[flat frigate]

VulcanOne

[manic shadow]

oh wait so i was taught the shortcut way then?

[frank glen]

By that you mean you immediately divide by the root's power?

[manic shadow]

Idk, we was taught to be turning the sqrt into the denominator when doing this

[frank glen]

Then yes you were taught to take the root's power and turn it into a divisor for the power

[manic shadow]

Whats it called again sqrt dividing?

[lone arch]

No

Just using the properties of square root

[frank glen]

Yep

[manic shadow]

oh

[lone arch]

Do you know how you can show that this is really true?

[frank glen]

Square roots are the 2nd roots

[lone arch]

This

[manic shadow]

whole number exponent (^b) is the numerator and the sqrt is the denominator (^a) so itll result ig as q^b/a?

[lone arch]

Well yeah that's exactly what this states

But I meant like showing that this is true

[manic shadow]

Ah then its true

[lone arch]

If someone asks you "Why is this?"

[manic shadow]

oh i never thought bout that

[frank glen]

Using a concrete example can work too

You know that 2^2 = 4

And you also know that sqrt(4) = 2

So sqrt(4) = sqrt(2^2) = 2^1

So that means sqrt(2^2) = 2^(2/2) = 2^1

Apply for any power and for any root and you will reach the same conclusion

[lone arch]

It's usually very good to ask "why?", you shouldn't really just take stuff for granted

[manic shadow]

alright ill do that more often

[manic shadow]

Btw how did it turn to 2^1

[frank glen]

Here

[manic shadow]

Oh

Oh

So the purpose of the √ isnt to = the question?

but to reduce to its simplest form?

[frank glen]

Yeah

Wait

Wdym?

The question you asked was to simplify

[manic shadow]

ah no i just want to know the true purpose of the sqrt

[frank glen]

But the square root has different purposes

[frank glen]

One of its purposes is that it is the inverse of the exponent

You know that addition and subtraction are inverses

Multiplication and division are inverses

You should wonder if exponents have inverses

[manic shadow]

Oh so like a symbol?

[frank glen]

Yeah

[manic shadow]

Add, Minus etc..

Oh

[lone arch]

Well, they just provide a perhaps more beautiful way to write $a^{\frac 1 b}$. You can write that as $\sqrt[b]{a}$. They're literally defined that way.

[frank glen]

Roots are inverses if exponents

[frank glen]

Yep

Easier on the eyes

[lone arch]

It's often good to convert back though

[manic shadow]

i see ty

[frank glen]

[manic shadow]

i think i have mastered this topic

[frank glen]

I'm proud of you :)

[lone arch]

Also solve lots of problems, those really show you how much you've understood

[manic shadow]

and i still have 7 more subjects to prepare for my upcoming exam tomorrow

[frank glen]

This is underrated

[manic shadow]

so ima go rest

ty really yall

[frank glen]

Good luck :D

[manic shadow]

I hope i ace it

.close

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[pale isle]

Is this correct?

[hushed halo]

wait what

[pale isle]

What the hel u saying

[gray bison]

hmm maybe im bugging

[pale isle]

Bro I’m in 9th grade

U must be bugging

[gray bison]

wehn i see function i auto think f(x)

but i guess you might not need it

ur answer is correct

[pale isle]

Isagi?!?!!

Did u see the new chap

Kunigami got em Noel noa stats

I thought he died at first

But we’re good

[gray bison]

im on chap 100

please no spoilers

[pale isle]

OH NOOO

U didn’t read it right

[gray bison]

no

im like just after the anime

i hadnt seen kunigami come back 💀

[pale isle]

He went crazy bro

[gray bison]

alr

we porb should use another channel

[pale isle]

He became jacked and more powerful and ambidextrous and emo

[gray bison]

dont spoil man

[pale isle]

Hero —> villain

[pale isle]

OH SHIT

Srry

Srry

[gray bison]

nah its alr

[pale isle]

It was an oppsie

@gray bison

HEY

I GOT STUCK AGAIN

I tried to do the double double

But the double double didn’t add up to the double double

PART C

HELLO

SOMEBODYYY'

[limpid light]

so s = 2l

[safe radish]

@pale isle Has your question been resolved?

[safe radish]

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[final moth]

hey guys so im having trouble w this problem my prof gave as practice for the final which is soon. I also checked the hint and apparently it's wrong so it might be a typo, but even if |B|=0 is true i still wouldn't know how to get around to solving the problem

[safe radish]

@final moth Has your question been resolved?

[final moth]

<@&286206848099549185>

im aware that determinants can be split by the column as in |a1 a2 a3 a4+a4'|=|a1 a2 a3 a4|+|a1 a2 a3 a4'| where a1 a2 a3 a4 are column vectors but im not sure how to proceed

since you cant split more than one column at a time

[safe radish]

@final moth Has your question been resolved?

[safe radish]

@final moth Has your question been resolved?

[safe radish]

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[native robin]

when ur trying to find interval of convergence, and u find that the limit is equal to 0 for any x, does that mean the interval is all real numbers

[quasi bison]

the limit of what exactly

[native robin]

the series was

[quasi bison]

so the limit of $\absv{\frac{a_{n+1}}{a_n}}$, then?

[flat frigate]

Ann

[native robin]

yea

[quasi bison]

ok then yeah that being 0 means the series converges everywhere

[native robin]

oh ok

ty

.close

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[spiral ermine]

prove that f(a)=(3/2)a+2
f(x) = x+2 + (x + 2)/(x²-1) = (x^3 + 2x^2)/(x^2-1)
i can't seem to find the answer
please help as soon as posible

[spiral ermine]

@lean otter hey man

can you help

i don't think i need to find a bc there isn't any numiric calculation to it so you where right

[lean otter]

nah man busy right now

[lean otter]

Also other helpers wouldn't be able to help anyway because you removed the rest of the context

[halcyon marsh]

I can help

[spiral ermine]

go a head

[spiral ermine]

ok thanks

[halcyon marsh]

Putting x=a 🫣

[spiral ermine]

i think they will understand with some explaining

[spiral ermine]

i did what next?

[halcyon marsh]

Add 2 x^2 -2 in numeroter and subtract it

[spiral ermine]

what??

[halcyon marsh]

Add and subtract

Mean add one time and subtract one time

[lean otter]

@halcyon marsh The 2 functions listed above are not equivalent

You can graph them and check

a actually has a fixed value which comes from a previous question

[halcyon marsh]

Ya I am thinking that

[lean otter]

However OP did not give the required context

[halcyon marsh]

Question is wrong

[lean otter]

They will, but you should explain it already without someone asking

Please give them the previous context

[halcyon marsh]

What is Op

[spiral ermine]

wait a sec i think i found the solution

[lean otter]

Not exactly wrong, more so there's context missing. I know because I was helping them not long ago

[lean otter]

"Original Poster"

Here referring to Mr Key

[halcyon marsh]

Oh

[lean otter]

@spiral ermine The sooner you provide context, the sooner you will get help

[spiral ermine]

sorry but i think i found solution

.close

[safe radish]

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[safe radish]

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[light bone]

hello i have a question, i need to solve this equations in R

[light bone]

but there is this one that im stuck and the resolt that i was getting is way off the solutions

[rustic goblet]

show your question

[lime dust]

What is the equation

[light bone]

wait 1 min please

[radiant crypt]

atleast post subway surfers gameplay while we wait

[light bone]

Exercise 3

C

[lime dust]

I see exercise 17, 4, 5… I can’t see 3

[light bone]

it is 17 C

[radiant crypt]

you need to take 2 assumptions for you to solve

[light bone]

but how

[radiant crypt]

you took x+1>0

[lime dust]

|x+1| = sqrt((x+1)^2)) that’s why

[faint seal]

you don't need to take two cases

notice that $32=4^{\frac{5}{2}}$

[flat frigate]

kheerii

[faint seal]

take the log of both sides and then take care of the log

[light bone]

i didnt learn yet Log so i cant use it

[faint seal]

oh

I just mean that $4^x=4^y\implies x=y$

[flat frigate]

kheerii

[lime dust]

There are two solutions

[light bone]

being honest with you guys im not understanding

[light bone]

right

[faint seal]

you have $4^{|x+1|}=32=4^{\frac{5}{2}}$

[flat frigate]

kheerii

[faint seal]

can you figure out what to do from here?

[light bone]

how do i get that 4^5/2

[lime dust]

Because both have the same base

2

[faint seal]

$32=2^5={(2^2)}^{\frac{5}{2}}=4^{\frac{5}{2}}$

[flat frigate]

kheerii

[faint seal]

the middle step is using the identity $(a^b)^c=a^{bc}$

[flat frigate]

kheerii

[lime dust]

Now you got just an equation with absolute value due to the fact that both bases are equals

So exponents must be too

[light bone]

.close

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[grizzled mango]

any ideas how to approach this?

[hardy lion]

!status

[safe radish]

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

[grizzled mango]

1

[hardy lion]

start by finding the zeros of each factor

[grizzled mango]

im not sure how to work with the variables

[south zephyr]

For first example its
X=π/2+2πn

[grizzled mango]

with the given domain there would only be one solution being pi/2, what about the second factor?

[grizzled mango]

how can we determine the number of solutions for the second one if we don't know a or b

[south zephyr]

a>b so its not 1 we know that both of them are greater than 0 so. 0<b/a<1
In (0;2π) range it should have 2 soultions check it im not 100% sure

[grizzled mango]

the correct answer is 3 total solutions, so your solution makes sense but i don't understand this part,

-> a>b so its not 1 we know that both of them are greater than 0 so. 0<b/a<1

couldn't sinx = 1/2, sqrt3/2, sqrt2/2 on unit circle being 3 solutions for second factor?

[south zephyr]

What are solutions for sinx=1/2 in 0:2π

150,30

Sinx=sqrt3/2
60,120

It will always have 2 solutions if its between 0 and 1 because sinx is positive only in 2 quadrants

Sorry for poor explanation i dont have deep knowledge im 10th grade

[grizzled mango]

no problem this is helping a lot, why would 1>a, i thought as long as a>0 it could be anything

[south zephyr]

a>0, b>0 and a>b so obviously b/a is smaller than 1

[grizzled mango]

i misread this earlier, i got that much. so it means there will always be two solutions for second factor regardless of the values and only one solution for sinx = 1

if this is correct then that explanation makes sense, thank you

[south zephyr]

Yes

[safe radish]

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[viscid grail]

Need help with this problem - find all integer solutions with Euclid/Bezout

[viscid grail]

divided both sides by 11 and got 26x+15y=3

GCD(26, 15)=1

1=7*15-4*26

and I have to find the general form

afaik I have to find the LCM of 15 and 26

but it's 390

1=15(7-26m)+26(-4+15m)

it's about using Euclid's algorithm and Bezout's identity

<@&286206848099549185>

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[grim scarab]

How do I calculate the chance of me getting picked 4/11 times from a wheel spin with like 30 people

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[lean thorn]

Recall the compound interest formula. Here's we're solving for P. Your answers don't make sense because your principal is greater than the Amount. The formula represents the total amount of money you'll have if you compounded for x amoutn of years at a certain rate

[quasi bison]

well

you invest 27k and get only 15k in return

that's kind of sus no?

show your work

[safe radish]

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[lean otter]

.close

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[dire monolith]

So theres a word problem thats about a pendelum clock and it states that this equation portrays its motion for T amount of time. NOW im supposed to figure out what L (length) must equal for T to equal 3 seconds

[dire monolith]

I dont have the exact question on me rn

[warm stirrup]

set the left side to 3 and then solve for L

by dividing by 6.28 and squaring

does that make sense

[dire monolith]

Okaey

That does make snese

This aint my work but

[lean otter]

fun fact i just cracked my toes irl

they still hurt

WELL NOT HRUT

BUT FEEL CRACKLY

[dire monolith]

Its the same gist right

[lean otter]

WHAT DO I DO

[dire monolith]

Delicious

[lean otter]

OKAY SO YOU SHOULD DO

6.3 multipl ied by square root of 1013 - p divided by 6.3 then equal that or whatever

SO

what course are u doing

i’m assuming some impressive university course?

[dire monolith]

Trigonometry

High school stuff

[lean otter]

HIGH SCHOOL?😭😭😭😭😭😭

now i know why people say junior year is the hardest year-

ARE U IN JUNIOR YEAR

11th grade

[dire monolith]

Yeaaahhs

[lean otter]

or 12th grade?

[dire monolith]

Junior

[lean otter]

MAKES SENSE

good luck-

that seems hard

i mean it is ur 2nd last yr of being high

i mean high school

so it makes sense

[dire monolith]

I mean this question is simple but but but

[dire monolith]

I feel like there is more to this question

Than just

Finding the varabiles and whatever

But i guess thats it

[lean otter]

i would say, leave it, drop out of school and become a professional garbage collected

collected

/j

[lean otter]

WELL DID U GET IT CORRECT THEN

is it an assessed homework?

[dire monolith]

Nope

Its a test question but

With different numbers

So not really a test question

[lean otter]

so that’s like

Supposed to be

an EASY question?

Damn

i think i’m going to faint of faintingston

[dire monolith]

Its the last question from whst ive been told

[lean otter]

MAKES SENSE

[safe radish]

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[tall gale]

I need help on how to intergrate this

I got -10(e^0-e^-2)

and its wrong

I just need an explaination of steps please and thank you

[plucky elk]

,calc -10(e^0 - e^(-2))

[flat frigate]

Result:

-8.6466471676339

[plucky elk]

,w int -1 to 1 (-10 e^(x-1) dx)

[flat frigate]

Results provided by WolframAlpha

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

Requested by rie.mann

[plucky elk]

looks right

[tall gale]

apparently thats wrong

hold up

idk how to get this

someone explained it to me as split it into 2 parts -1 to 0 and 0 to 1

[plucky elk]

-63.89... is incorrect

[tall gale]

and its -10e^u+1 thats how they did it

[plucky elk]

there's no need to split the integral

[tall gale]

yea thank you idk man

lmao

thank you tho

you can close thank you

[plucky elk]

.close

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[coral ruin]

Idk how to start

[safe radish]

@coral ruin Has your question been resolved?

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@coral ruin Has your question been resolved?

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[spark merlin]

Am I wrong?

[safe radish]

@spark merlin Has your question been resolved?

[eternal carbon]

yes

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[glossy pivot]

set up an integral for the length of one arch of the curve c(t) = (t-(sin(t)/2),1-(cos(t)/2))

[glossy pivot]

new to MVC, have no idea what to do with this

I know L(C) is the integral from a to b of ||c'(t)|| dt but i have no idea how to get this into a single equation

[plucky elk]

v = (v1,v2), then ||v|| = sqrt(v1^2 + v2^2)

[glossy pivot]

oh my god i completely forgot that notation for ||v||

[plucky elk]

I don't know what "one arch" refers to, but probably 0 to pi or 2pi

[glossy pivot]

yeah it's 0 to 2pi

that should get me started, thanks

.close

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[stray axle]

so its been a while since i found an eigenspace but why is the eigen space [1, 0, 0]?

[stray axle]

i've done some for 2x2 matrices and those were usually straightforward with matrices that leave you with x+y=0 when RREF then x=-y so the eigen space is [-1, 1]

[delicate sphinx]

If you rewrite the rref matrix into equation form, you'll see that y = 0 and z = 0, and x is a free variable meaning x can be anything so the answer made x = 1

[stray axle]

so if theres a column full of zeros, we assign it as the free variable

[delicate sphinx]

Typically a row of zeros but column is the same too

[stray axle]

okay thank you!

.close

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[steady mountain]

Hi so I have a stats question

[steady mountain]

For question 2.6

is the answer C

and for this one am I right

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[hollow vault]

Struggling on this question where I need to prove this by induction. I've already done the base case but don't know what to really do for inductive step. I did 2(i+1)x(2j+1) and managed to simplify it down to 2i*3j+2i*3i+2j*3j+2*3 but i dont think this is valid because we'd have squares. Any help is appreciated

[true zephyr]

don’t induct on both at the same time

you’ll actually miss some cases if you do that

[safe radish]

@hollow vault Has your question been resolved?

[hollow vault]

both what?

i and j?

[true zephyr]

yeah

focus on one variable

[hollow vault]

so do (2(i+1))x3j and then do the same thing for j+1...

[true zephyr]

you could

because if you do +1 each and start from 1, you're going to miss numbers like i=2 and j=5, or any pair in which i != j

[hollow vault]

idk then

[true zephyr]

what have you done

[hollow vault]

(2i+2)*(3j+3)
6ij+6i+6j+6
2i*3j+6(i+j+1)
2i*3j+(2*3)(i+j+1)
2i*3j+2i*3i+2j*3j+2*3```

this is all ive done

this inductive step shit is so stupid

[true zephyr]

wait why are you multiplyijng

[safe radish]

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[true zephyr]

bruh

[hollow vault]

.reopen

[safe radish]

✅

[hollow vault]

multiplying what

[true zephyr]

2(i+1)

also if you are doing 2(i+1) and 3(j+1) you are inducting on both

[hollow vault]

yeah isnt that what i need to prove

[true zephyr]

well, let's first set i

like let's say i is a certain number

and we dont change i

then we can induct on j

after we find that given a working i, all j's work, we can work on i as well

[hollow vault]

Yes but didnt you say we miss some is and js like i =2 and j = 5

like how do we account of rhtis

[true zephyr]

so we are going in both directions.

we start with stepping up j

and for every possible j

we step up i

[hollow vault]

im still sort of confused

wdym be going in both directions

[true zephyr]

also

i actually think

that induction might not be the right way to do this

or at least not the best way

[hollow vault]

idk the homework says to use induction

[true zephyr]

rip

[hollow vault]

lol every induction problem just feel slike brute force

i feel like every problem is just torture

i stare at my notebook for hours until something pops up in my head

like i hate how tehres no formula or naything like calc

i just have to come up with random shit

completely intuition based which i have none of

[true zephyr]

ok so let's induct on j first

Let P(j) be trominoes fit into 2x(3j)
so the basecase would be 2x3 (and you can do this)

inductive step is that you assume P(j) and you want to prove P(j+1)

so P(j) would give you that 2x3j fits trominoes

and we want 2x3(j+1), in which case you are just adding a 2x3 grid, in which you can put trominoes in

after you prove this,

you want to let Q(i) be that trominoes fit into (2i)x(3j)

and then prove the basecase Q(1),

and do similar steps

[hollow vault]

ok ill try that

thank you

[true zephyr]

np

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[stiff vine]

How do u even get b

I’m confused

[lean otter]

can u show a picture with the entire question

[stiff vine]

It’s there

[lean otter]

i cant read the top right

[lean otter]

alright

so for b

100 represents the starting value of the bullfrog population

x=100 when y=0

2.25 represents the rate of change of the bullfrog population as x increases

[stiff vine]

Yeah how did u get 2.25

[lean otter]

and t/x represents how often that rate of change goes up

[stiff vine]

I thought it was P(1+r)^t

[lean otter]

u get the point 2,225

on the graph

100 x 2.25 = 225

[lean otter]

something like that

but for this all u need to do is look at the graph

[lean otter]

and since its t/2 that means every time x goes up by 2, the population increases by 2.25

this is proven because if you do the equation 100(2.25)^2x/2

[stiff vine]

Why r u dividing it by 100

[lean otter]

you get the point 2,225

[lean otter]

im not dividing it by 100

[stiff vine]

To get 2.25 u divide it by 100

[lean otter]

no

im doing

100 times 2.25

and getting 225

@stiff vine what are you confused about

[stiff vine]

The equation I’m supposed to use

[lean otter]

yeah

[stiff vine]

So it is A(1+r)^t then

[lean otter]

for this i dont think so

for this you want the equation

initial value (rate of change)^x/2

initial would be b i assume

rate of change can be any variable

[stiff vine]

The rate of change is 115

[lean otter]

eh

[stiff vine]

I don’t get it

[lean otter]

just using this works

as long as you understand that for every time x goes up by 2, the population increases by 2.25 times

[stiff vine]

Ok so I add 1 to 2.25?

And idk why it’s t/2

[lean otter]

just do 1+1.25

to match your equation

[lean otter]

its t/2 because

for every time x goes up by 2

lets say x is a year

after 2 years

the bullfrog population will increase by 2.25

[stiff vine]

Yeah

[lean otter]

is there anything else you are confused about

[stiff vine]

I’m still confused on the equation

Ok how about this one

So the equation is 10000=8200(1+100/82)^t?

[lean otter]

well

first thing i would do is find the rate of change

so you would do 10000=8200x

and solve for x

theres your rate of change after 1 hour

[stiff vine]

Yeah 100/82?

[lean otter]

yeah

but you can simplify it more

eh

maybe you shouldnt

its a weird fraction

[stiff vine]

Ok so my equation is correct then?

[lean otter]

you dont need the 1 in the front

[stiff vine]

Or do I remove +1

[lean otter]

or the =10000

it would just be 8200(100/82)^t

t being the number of hours

[stiff vine]

Why

[lean otter]

you just dont

[stiff vine]

So do I only use the 1+ equation when they give me a decimal to use then

[lean otter]

i mean

[lean otter]

i think the most important thing is just identifying the rate of change

instead of worrying about the real equation

the 1+x is used when you're given a question like

find the equation for a group of bacteria that increases by 12% every hour

[lean otter]

plug in 2 as t for b

[stiff vine]

Doesn’t the t have to be over something

[lean otter]

not in all cases

an example of when you would want t over something

is like

say the question said the bacteria increases from 8200 to 10000 in 20 minutes

instead of 1 hour

and then asks you for the equation with t as hours

you would want t/3

here you dont need t to be over something

[stiff vine]

Bro that’s so confusing

I remember a YouTube video saying t is also over years/months

[lean otter]

sometimes

[stiff vine]

So which is it

[lean otter]

t is a variable thats given to you by the equation itself

[lean otter]

this can be applicable to some equations

but not all

[lean otter]

see how in the last question it was talking about t as in years

now its talking about t as in hours

and for c you can either graph the equation you got with a with a calculator and find when x = 16400

or you can set the equation from a = 16400 and solve for t

or you can guess and check

i recommend graphing it

[stiff vine]

Is c asking for when it doubles the original amount?

Or after 2 hours

[lean otter]

double

which is why i said 16400

[lean otter]

b is 2 hours

[stiff vine]

I got 1.4

But it says wrong

[lean otter]

how did you get 1.4

[stiff vine]

I used log

[lean otter]

why did you use log

[stiff vine]

To find t

Hours

[lean otter]

okay

lets go over b first

you have the equation 8200(100/82)^t

its asking for the number of bacteria after 2 hours

in other words it wants to know what y= when t =2

so you just do 8200(100/82)^2

[stiff vine]

Yeah I got b

[lean otter]

so the answer to b is 12195.122

[stiff vine]

Yeah I’m doing c

[lean otter]

then you want to find when y is equal to 16400

so you can graph 8200(100/82)^t

and find it that way

or just do 16400=8200(100/82)^t

and solve for t

answer would be 3.493

ish

[stiff vine]

Yeah I did

I used log

[lean otter]

how did you get 1.4

it wouldnt even make any sense

seeing as when t=2 you get 12195

which is lower than 16400

[stiff vine]

Ln2=t ln100/82 t=ln2/ln(100/82)

That’s what I did

I divide both side by 8200 forst

[lean otter]

yeah

and u get 2=(100/82)^t

[stiff vine]

T=ln2/ln(100/82)?

[lean otter]

yeah

that would be it

[stiff vine]

Oh I see I wrote 100/62 on my calculator instead

[lean otter]

ah

easy mistake to make

.close if thats all you needed

[stiff vine]

👍 thanks

.close

[safe radish]

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[wise hill]

help please?

[wise hill]

How do I get P(C)?

[winter pivot]

Make a venn diagram

[marsh walrus]

hi cosmo

[safe radish]

@wise hill Has your question been resolved?

[safe radish]

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[wise hill]

@winter pivothow does that help?

[wise hill]

.reopen

[safe radish]

@wise hill Has your question been resolved?

[safe radish]

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[safe radish]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[fathom yoke]

what can be the highest value of n such that n ^ 3 - 2023 is divided by n + 14

[quick crater]

do you mean like $\frac{n^3-2023}{n+14}$ is an integer?

[flat frigate]

Skill_Issue

[quick crater]

if so, try dividing n^3-2023 by n+14

[fathom yoke]

yah

[fathom yoke]

i can't 🙂

[quick crater]

uhh

try to do it algebraically

wait do you know synthetic division

if so, try to use it

[fathom yoke]

ok that's kinda easy?

it derives that (n + 14) | 2023

n = 2023 - 14?

[quick crater]

oh wait nvm, i dont think i got it, sorry

lemme try to find it agaij

[fathom yoke]

ok

[quick crater]

ok got

what i wanted you to try is like straight up trying dividing n^3-2023 with n+14

@fathom yoke

[fathom yoke]

ok

i got remainder -4767 @quick crater

[quick crater]

yes

since you can like "break off" the part thats not the remainder you can get
$x^2-14x+196-\frac{4767}{x+14}$

[flat frigate]

Skill_Issue

[fathom yoke]

where $x^2 - 14x+196$ is divisible by $x + 14$

[flat frigate]

solitary

[fathom yoke]

then?

[quick crater]

since $x^2-14x+196$ would always be an integwr, we can focus on the fraction

[flat frigate]

Skill_Issue

[fathom yoke]

yah

[quick crater]

what is the largest number that can divide 4767

[fathom yoke]

then we can say that n + 14 = 4767 cause we need the largest n , right?

[quick crater]

yea

ok you got it now

[fathom yoke]

n = 4767 - 14?

[quick crater]

yea

[fathom yoke]

ok thanks @quick crater

.close

[safe radish]

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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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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.