help-0

[alpine sable]

oh yeah

[gray isle]

and then try applying this to your original question

[alpine sable]

so c / (abc) + a / (abc)?

[gray isle]

yes

[alpine sable]

but how

the only thing i can actually see

is the x+3 under 8 and under 5

[gray isle]

if it's too overwhelming to combine 3 fractions at once, start with the first two

[alpine sable]

alright

hi, i think i need a little break, i did a lot of math so my brain is kind of not working so il go take a little rest

and then come back

[gray isle]

the example with 1/(ab) + 1/(bc)
is very similar to what you have

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[tardy torrent]

Anyone know what I'm doing wrong here on this homework problem?

[lone heart]

@tardy torrent Has your question been resolved?

[lone heart]

@tardy torrent Has your question been resolved?

[solar pebble]

c is the Temperature difference

[tardy torrent]

?

[solar pebble]

@tardy torrent is that the full question?

the second line is half a sentence

[tardy torrent]

I'll send the full pic of the question in a second, just got in. Eating food.

[tardy torrent]

@solar pebble

Tried a diff answer still wrong

[solar pebble]

@tardy torrent Remember that e^0 = 1

[solar pebble]

replace C for -60

[tardy torrent]

What

I do have C= - 60 top

[solar pebble]

You've not written it in the answer box

[tardy torrent]

So it should be what

-60e^kt + 140

[solar pebble]

yep

unless I've not seen something else

[tardy torrent]

that was right

xetrov can i hire you per hour to help me with this calculus homework

[solar pebble]

no

[tardy torrent]

.close

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[alpine sable]

got this far:

[remote sapphire]

2 ^ 3 = x^2/x

x^2 = 8x

[alpine sable]

can you break it down

more

like show each line of working

dont skip

[remote sapphire]

okay you know that we can bring the constant in front of log to be the power of the term within the log?

rule 3

so when i bring the 2 up, it is essentially squaring (x/sqrt(2))

if you know how to square this, you will get x^2/2

log_base power = evaluation

[lone heart]

@alpine sable Has your question been resolved?

[solar pebble]

there's 2 log x but one log rt x

[alpine sable]

ye

[solar pebble]

you can't simplify it like that

[alpine sable]

oh

so would it just be that i need to put the whole thing in brackets

and put 2 outside

[solar pebble]

$\log_2 x^2$

[ocean seal]

Xetrov

[alpine sable]

how and why idgi

[solar pebble]

that's your first term

[alpine sable]

$\2\log_2 x^2 - \log_2\sqrt{x} =3$

[ocean seal]

şaka şaka
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[solar pebble]

get rid of the 2

$\log_2 x^2 - \log_2\sqrt{x} =3$

[ocean seal]

Xetrov

[alpine sable]

im trying to show u what orginal equation was incase u read it wrong

but original question had 2 in front

of first term on left

[solar pebble]

Now it doesn't, its popped onto the x^2

[alpine sable]

ohhhh

u chaneged it from 2 log base 2 of x to log base 2 of x^2

[solar pebble]

yep

[alpine sable]

so now i can change it to a fraction right

[raw shard]

yes

[raw shard]

simplify

[alpine sable]

?

[raw shard]

yes

now simplify the left side

[alpine sable]

?

[devout summit]

You replaced x²/√x by x/√x in the left hand side

x²=(√x)⁴. So, x²/√x=(√x)³=8

[lone heart]

@alpine sable Has your question been resolved?

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[remote iron]

This is newtons law of cooling, I am aware.

but I am still so brain dead.

[lone heart]

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[sonic valley]

Here is a better picture, the last question, I wrote sin Nd cos 100° instead of 80, ignore that

What do I write sin and cos 80° as?

[charred flint]

are you asking how to simplify sin80?

[sonic valley]

Yes

[charred flint]

oh it doesn't really have a nice answer I'm pretty sure

just leaving it as is would be fine, unless you want like 3 decimal places

[sonic valley]

Like how I did the one above, but the one above was included in a table my teacher gave me

[charred flint]

yeah 30,45, and 60 are well known and you can use them

[sonic valley]

How do I do that?

My teacher didn't explain well, so am sort of stuck

[charred flint]

what are you trying to do?

[lone heart]

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[sonic valley]

Uhh, this

[sonic valley]

The way I solved the first question but I only managed to solve that one because 60° was given in the table

I don't know what to do if a degree is not given

[charred flint]

what's the question with the 80 degrees in it?

[sonic valley]

Find the coordinates of the point on a unit circle corresponding to angle of 5pi/9

[charred flint]

oh just saying (cos(100),sin(100)) is enough

[sonic valley]

Oh

Alright lol, thanks

.close

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[sonic cipher]

How to solve this problem using matrix multiplication

[charred flint]

you can get it from the adjacency matrix M

M respresents 1 step, M^4 represents 4 steps

[sonic cipher]

Ohhh okay. So if I want to get the total amount of paths of length 4, I would do M^4 and add all values in the matrix.

[charred flint]

correct

[sonic cipher]

I didnt think of using the adjacency matrix. Thank you so much!

.close

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[humble ferry]

Is anyone able to give me a hint about where to start with this? Ive got no idea where to even begin

[modest zodiac]

Write $x = \sum_{j=1}^n \lambda_j \cdot v_j $ and $y = \sum_{i=1}^n \mu_j \cdot v_j$ for families of real numbers $\lambda_j$, $\mu_j$

[ocean seal]

polikuj2

[modest zodiac]

Then expand everything, and I believe that it'll work

[humble ferry]

Ive said that (x.v)(y.v)=(x.y)+(x.v)+(y.v)+abs(v)^2, can i even do that?

[modest zodiac]

That feels wrong

Have you tried my method ?

[humble ferry]

i havent because i dont know how to do it that way, i know that dot products are distributive like v.x+v.y=v.(x+y) but i dont know if that means you can like multiply out

[modest zodiac]

I don't see a general formula for dot product that will solve your problem instantly

[ocean seal]

polikuj2

[humble ferry]

ive just found something in my book called the expansion theorem that looks like it could be vaugley useful ill maybe try with that, because im not conviced that what i wrote makes any sense at all

[modest zodiac]

(with the 2 being outside the norm, my bad)

I don't think that's useful

Since $v_i$ are a basis, the vectors $x$ is some linear combination of the $v_i$, right ?

[ocean seal]

polikuj2

[modest zodiac]

So you can express the x in terms of just the $v_i$ and some real coefficients. Using what I wrote earlier about the $v_i \cdot v_j$ should suffice to conclude

[ocean seal]

polikuj2

[humble ferry]

Unless im misunderstanding what the expansion theorem is saying, isnt that basically what that says?

[modest zodiac]

Is https://en.wikipedia.org/wiki/Binomial_theorem what you call the expansion theorem ? Is there something else I don't know about ?

[humble ferry]

thats what i was referring to

[modest zodiac]

Oh

Yeah, that looks like it's it

But "it's a special case of this theorem in the book" feels like cheating, what I'm giving you is a way of deriving it from basic properties of the dot product

[humble ferry]

Ok ill go give it a shot and come back to you if i get lost, i think i might have an idea of what to do

[lone heart]

@humble ferry Has your question been resolved?

[humble ferry]

So thats what ive worked out but thats wrong, im not sure why

and i just tried using the theorem from the book because im not sure how to do it the other way

[modest zodiac]

That looks right to me

What's the problem ?.

[humble ferry]

theres a vi term dotted with everything at the front which isnt in the answer given in the question

[modest zodiac]

The ugly term $(x \cdot v_i) (t \cdot v_i)/|| v_i||^2$ is a scalar, not a vector

[ocean seal]

polikuj2

[modest zodiac]

So you can't write the last line

The one before that is right tho

[humble ferry]

yeah true so isnt that just going to be some scalar times Vi dotted with another scalar time Vi, giving abs(Vi)^2 but the question doesnt state that its orthonormal so its not going to be 1 and that still means i have a problem does it not

[modest zodiac]

Ok, I see the problem

[humble ferry]

if thats more clear of what i mean

[modest zodiac]

There are two terms of $||v_i||^2$ in the denominator

[ocean seal]

polikuj2

[humble ferry]

oh yeah

[modest zodiac]

So there is a $||v_i||^4$ that cancels out

[ocean seal]

polikuj2

[humble ferry]

forgetting how multiplication works lol thank you

[modest zodiac]

Just be careful when going line 3 -> line 4 ; it would be wrong if the v_i were not orthogonal

The general formula is $\sum_{i,j} \frac{(x \cdot v_i) (x \cdot v_j)}{||v_i||^2 ||v_j||^2} v_i \cdot v_j$

[ocean seal]

polikuj2

[humble ferry]

Ah ok, well i think thats me got that then, it wasnt as bad as i thought other than me forgetting how to multiply, thank you!

.close

[lone heart]

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[visual heath]

Hello

[visual heath]

@charred flint So for the second one I have the code

input(n)
for i = 1 to n by 1 do
    j = n
    while j > 0 do {
        print ‘‘*’’
        j = floor(j/2)
}
next i

I understand the while loop iterates 2^j=1 as you've said earlier. Then the for loop will iterate (n-1) so that we have a summation

$\sum_{n=1}^{k} (n-1)*2^n$

[charred flint]

why is it n-1?

this problem looks like log(1)+log(2)+...+log(n)

[ocean seal]

A Kid Named Galois

[visual heath]

Oh I was thinking since it says 1 to n by 1

[charred flint]

oh idk what "by 1" means either

[visual heath]

n is an integer >0, does that explain it?

[charred flint]

like are you doing the inside for i=1,2,3,...n?

anyways using log(a)+log(b)=log(ab) you get that it's log(n!), which is ~nlogn by stirlings approximation

[visual heath]

Yes

[visual heath]

Oh it just clicked. Essentially you have the log(n) for the while loop (you halve it until it hits 1). Then the for loop, since we have, 1,2,..,n is the summing of the log() part

Thank you

.close

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[chrome depot]

Iscosceles trapezoid, whose base lengths are 2 and 3 cm and angle is 60 degrees, rotates around shorter base. Calculate area and volume of that shape.
I got that the height of trapezoid is H=sqrt(3) / 2, and s (side) of trapezoid has length of 1
I also somewhat understand how it looks like, but I am not sure about area and volume formulae

[chrome depot]

<@&286206848099549185>

anyone?

[modest zodiac]

The volume is the integral over the angle of rotation of the area of the trapezoid

[chrome depot]

I am sorry, but I know nothing about integrals

This is not even needed to solve it since we didnt learn them yet

[modest zodiac]

I'm not sure I understand then

Are we talking about the 3D object created by the trapezoid rotating ?

[chrome depot]

Yes

As far as I can google, it seems to be something like this:

[raw shard]

this sure looks like something an integral would do

just saying lol

[chrome depot]

They claim that the area of this object is: 2*r*PI*a + 2*r*s*PI

where a is the longer base of the trapezoid

and s is its side

[modest zodiac]

I think that the volume is 2pi times the area of the trapezoid

times the height of the trapezoid

[lone heart]

@chrome depot Has your question been resolved?

[lone heart]

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[frosty jackal]

Hi, so i have this on my homework and i cant figure it out

[frosty jackal]

coppy it to #help-1

go to #help-1

oh ummm

ok

im getting undifined

it wants me to find thoes as ints

ok

ah

now i see

thanks

:)

a = 4/3b+-1/3c

ok

i gtg soon though

i have a call in 10

Thanks tho

[vivid ginkgo]

e

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[prime mist]

is this true or false?

[prime mist]

I know that element null is subset of every set

[charred flint]

false, even if it seems a bit strange

[prime mist]

oh

thanks, I think I understand what you mean

[alpine sable]

Can someone help me with this?

[charred flint]

@alpine sable repost that in an available help channel above like #help-13

[lone heart]

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[whole wadi]

On the line y = -3x - 4, the point P is in the fourth quadrant. The distance between P and origin is 8 units of length. Determine the x-coordinate of P. Answer exactly.

[lethal ore]

Understood the problem?

[whole wadi]

I don't know how to solve it, no

[lethal ore]

No I mean I'm not asking about the solution

[lethal ore]

Once you understand the problem, then I can help you about further concepts

[whole wadi]

The distance formula?

I think that's good

[lethal ore]

No. I mean do you know what's happening in the question?

[whole wadi]

I have an idea of what the question is asking

is saying*

[lethal ore]

The fourth quadrant thing and all

[whole wadi]

Yeah

[lethal ore]

That's perfect

[whole wadi]

Distance is 8 l.u. from point P.

[lethal ore]

Can you forget this graph for few mins?

[whole wadi]

Sure

[lethal ore]

It's gonna confuse you

There's a point in 4th quadrant which is 8 unit from the origin

So can you imagine a quarter of a circle in the fourth quadrant whose radius is 8 units? @whole wadi

[whole wadi]

Yes

Channel is busy

[vague iris]

Ohh sorry

[lethal ore]

Great. Now the given line is across the xy-coordinate

If you've any app/software you can plot both the function
x^2+y^2=64
And y=-3x-4
@whole wadi

[whole wadi]

I don't think I am allowed to use this on the exam, I have a TI-82

[lethal ore]

So it means both the functions intersect at two points and you've to solve both the functions to get the corresponding values of x and y
Now imagine what this means?
Those x and y solutions are coordinates of intersection
I'll leave the final part to you. Which pair of solutions you need to chose so that the point P is in the fourth quadrant

[lethal ore]

It's for your own imagination purpose and also these kinda apps/softwares are fun to operate/play with

[whole wadi]

So it means both the functions intersect at two points and you've to solve both the functions to get the corresponding values of x and y
We're only interested in the point of the fourth quadrant, though?

Is there the algebraic way of solving it as well?

[lethal ore]

Yea

Now tell me what are the values of x and y in the fourth quadrant

[whole wadi]

(1.298, -7.894)

[lethal ore]

Yes but no

I mean you've to solve both of those functions manually
And arrive at the values of x and y

[whole wadi]

I don't get it, we've our point at the fourth quadrant. What more do we need?

🤔

[lethal ore]

It's not about the destination. It's about the journey

In your exam you've to write the steps for your answer
As we talked earlier the procedure would be
solving for x and y using those two functions and checking which of the coalition coordinates lie in the fourth quadrant

[whole wadi]

To write the steps I have to solve the question algebraically, I imagine?

[lethal ore]

Yes

You've to solve x^2+y^2=64 and y=-3x-4

[whole wadi]

x^2 + (-3x-4)^2 = 64

10x^2 + 24x + 17 = 64

[lethal ore]

Go on

[whole wadi]

x^2 + 2.4x + 1.7 = 6.4
x^2 + 2.4x + 1.7 - 6.4 = 0
x^2 + 2.4x - 4.7 = 0

[lethal ore]

You lost me. What's with all those commas?

[glass lichen]

they're decimals

[whole wadi]

x = -1,2 ± √((2,4/2)² + 4,7)

[lethal ore]

Yep

[whole wadi]

x = -1.2 ± √(6.14)

[lethal ore]

But one small suggestion. Even though you arrive at the right answer, just try to avoide decimals in future
Not saying it's wrong but instead its not preferred

[whole wadi]

x = -1.2 ± 2,47...

The correct answer contains decimals, so I don't know

As in the x-coordinate

[lethal ore]

Oh then you're doing well

[whole wadi]

x₁ = 1.27

[lethal ore]

So you've two values for x now, right?

[whole wadi]

x₂ = -3,74

[lethal ore]

Wait. How you wrote that 1 as sub script? You got special type of keyboard?

[whole wadi]

Yeah

cmd + ctrl + space

[lethal ore]

Oh you're on Mac I guess

Do you know the shortcut for windows?

Nvm. I'll look it up on Google

Leave it. So you've two values for x and when you substitute these two values in the functions, you'll have two values of y

[whole wadi]

x^2+y^2=64 and y=-3x-4
y(1.27) = -3(1.27) - 4

[ocean seal]

Result:

-7.81

[whole wadi]

-7.81 = -3(1.27)-4

y = -3(-3.74) - 4

,calc -3(-3.74) - 4

[ocean seal]

Result:

7.22

[whole wadi]

-3(-3.74) - 4 = 7.22 = y(-3.74)

[lethal ore]

(x1, y1) and (x2, y2)
Check the signs and submit the pair of (x, y) which are in the fourth quadrant
And you're done 🙂

[whole wadi]

It seems like I'm off a bit

I should've maybe not rounded off

1.2979992 is the correct answer for the fourth quadrant

And I wrote 1.27

[lethal ore]

I guess you might've mess up some small details while calculation

,w solve x^2+y^2=64 and y=-3x-4

[ocean seal]

Results provided by WolframAlpha

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

Requested by bakasta#8464

[lethal ore]

Give me a minute

I guess I screwed up somewhere

[whole wadi]

x^2+y^2=64 and y=-3x-4
x^2 + (-3x-4)^2 = 64
10x^2 + 24x + 17 = 64
x^2 + 2.4x + 1.7 = 6.4
x^2 + 2.4x + 1.7 - 6.4 = 0
x^2 + 2.4x - 4.7 = 0
x = -1,2 ± √((2,4/2)² + 4,7)
x = -1.2 ± √(6.14)
x = -1.2 ± 2,47...

I think it's here that I needed to include more decimals?

[lethal ore]

Nope. I'm good

Ukw

Forget the decimals

[whole wadi]

If I needed more decimals it would be 2.47790...

[lethal ore]

Here look this

[lethal ore]

Yea this one

Yea. You've the formula

Solve this using the formula

No

Don't

What happened?

You're going good

[whole wadi]

LOL

$$10x^2 + 24x - 47 = 0$$

[ocean seal]

Theophania

[whole wadi]

From here?

[lethal ore]

Yep

[whole wadi]

I think I need to get rid of 10

i.e. dividing by 10 on both sides

[lethal ore]

Not necessary

How're a=10, b=24 and c=-47

,w solve 10x^2 + 24x - 47 = 0

[ocean seal]

Results provided by WolframAlpha

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Requested by bakasta#8464

[whole wadi]

🤔

[lethal ore]

You'll end up with these values of x as solutions for sure
Now you convert values of x1 and x2 into decimals and then find the value of y1 and y2

You've 10x^2 + 24x - 47 = 0
How're a=10, b=24 and c=-47

[whole wadi]

x = (-24±√((24²)-(4*10*-47)))/(2*10)

[lethal ore]

Good

If typing all these things is tedious then you can solve it on a piece of paper and share the pic

[whole wadi]

x = (-24±√(576-(-7))/2*10)

[lethal ore]

Way more convenient for you

[whole wadi]

x = (-24±√(583)/(20))

I will solve this with my calc now

Can I split it into -24/20 and ±√(583)/(20)?

[lethal ore]

Nooo
Check the -4ac part
(-4)(10)(-47)

[whole wadi]

Yep one sec

x = (-24±√((24²)-(4*10*-47)))/(2*10)
x = (-24±√((24²)-(-1880)))/(2*10)

[lethal ore]

Yep

[whole wadi]

x = (-24±√(2456)/(2*10))

Can I split it into -24/20 and ±√(2456)/(20)?

[lethal ore]

Yes you can

All perfect up until this point

[whole wadi]

x = -1,2 ± √(2456)/(20)
x = -1,2 ± (49,558/20)

x = -1,2 ± 2,4779

x₂ = 1,2779
x₁ = −3,6779

Hmm still not the same

[lethal ore]

Now get y1 and y2

What the hell man?
Why are we getting that error? 😭

[whole wadi]

The bolded part here #help-0 message

Let's try

[ocean seal]

The following error occured while calculating:
Error: Unexpected operator , (char 7)

[whole wadi]

,w -1.2+2.477902338672773

[ocean seal]

Results provided by WolframAlpha

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Requested by Theophania#1704

[whole wadi]

Wtf 😂

[lethal ore]

There's something that we're missing
This is math. There has to be a reason

[bleak ridge]

Wots the problem?

Its just not working out like desmos says it should?

[whole wadi]

Yeah

My friend also wrote x = 1.2979992 and was correct

[lethal ore]

😭😭😭😭😭😭😭😭

[bleak ridge]

It looks like your uhh

c value is wrong

In the polynomial thing

[whole wadi]

x^2 + (-3x-4)^2 = 64
10x^2 + 24x + 17 = 64
x^2 + 2.4x + 1.7 = 6.4
x^2 + 2.4x + 1.7 - 6.4 = 0
x^2 + 2.4x - 4.7 = 0
x = -1,2 ± √((2,4/2)² + 4,7)
x = -1.2 ± √(6.14)
x = -1.2 ± 2,47...

[lethal ore]

Here. Check the line 2
It should be 16, not 17

So ignorant of me 😭

[whole wadi]

Yeah that's true

Let's see

$$10x^2 + 24x - 48 = 0$$

[bleak ridge]

Also why factor out 10 and get the nasty decimals

[ocean seal]

Theophania

[lethal ore]

Nooooooo

Yessssss

[whole wadi]

Hahaha

Okay let's try out the formula now

[lethal ore]

Divider everything by 2

[whole wadi]

$$5x^2 + 12x - 24 = 0$$

[ocean seal]

Theophania

[whole wadi]

We don't use this formula here in Sweden, for the record, we usually get rid of the 'a' coefficient

[bleak ridge]

Oh

Reasonable

[whole wadi]

We call it 'pq-formeln'

[finite spindle]

here in norway we use the quadratic equation , why is it different??!

[bleak ridge]

Because sweden

[whole wadi]

So x = -12/(2*5)±√(12²+4(5*-24))/(2*5)

[elfin fiber]

is this channel free rn?

[bleak ridge]

[finite spindle]

(no)

[elfin fiber]

oki

[whole wadi]

There should be a - in the numerator

So x = -12/(2*5)±√(144+480)/(2*5)

[elfin fiber]

where do i ask for help

bro

[whole wadi]

x = -1.2±√(624)/(2*5)

x = -1.2±(24,979/10)

x = -1.2±2,4979

[bleak ridge]

#help-10

[elfin fiber]

oki

[whole wadi]

x₁ = 1,297999199359359

Finally?

Yeah, this will do

[lethal ore]

You know there are many ways to teach a destination
Ways really don't matte
It's just that I didn't know you were Denton Sweden 😝

[lethal ore]

This one's good as well

[whole wadi]

Okay thanks I think this answer will do for the x-coordinate

.close

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[charred flint]

the trick is saying this equals x, then trying to move things over to the x side

[lone heart]

@unique sun Has your question been resolved?

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[fiery berry]

ok

18

sorry I am a little confused

why did you need help

is this it

2026

ig

is this it?

ok

um to close a ticket type !close

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[south horizon]

Second Quarter
DLP 1
Directions: A. Find the quotient. Differentiate the quotient as terminating or repeating
decimal by putting a check (/) under the corresponding column.
Equation Quotient Terminating Repeating
Ex. 5 ÷ 15 =
0.33̅ √

1. 3 ÷ 15 =
2. 4 ÷ 45 =
3. 9 ÷ 12 =
4. 8 ÷ 12 =
5. 2 ÷ 4 =
   B. Give the equivalent value in decimal form.

1
5

2
3

1
4

B. Write the following decimals to fraction.

1. 0.66̅
2. 0.8
   Attachment URL: https://drive.google.com/file/d/1SUQBq4jQHZks2M2DNa7d4Ii2dn3tEnsp/view

[south horizon]

<@&286206848099549185>

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@south horizon Has your question been resolved?

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[strange blade]

can anyone help me determine if this series is convergent or divergent? I know it would generally decrease in value as n->infinity. The divergence test is inconclusive. I thought about an integral test, but I honestly have no idea how to take the integral of this. Maybe it is something simple i’m forgetting?

[chrome salmon]

It's a geometric series

With common ratio 1/pi

If you know the radius of convergence of geometric series

[strange blade]

i’m confused. i thought so too, but the format my prof gave me in order for geometric to be applicable is a*r^(n-1)

[south horizon]

nope

[alpine sable]

1/(pi^n) = ...?

[strange blade]

idk maybe i’m stupid. or maybe prof is. thank you.

.close

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[alpine sable]

neither

[chrome salmon]

Yes thats for sequence but what about series

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[south horizon]

Second Quarter
DLP 1
Directions: A. Find the quotient. Differentiate the quotient as terminating or repeating
decimal by putting a check (/) under the corresponding column.
Equation Quotient Terminating Repeating
Ex. 5 ÷ 15 =
0.33̅ √

1. 3 ÷ 15 =
2. 4 ÷ 45 =
3. 9 ÷ 12 =
4. 8 ÷ 12 =
5. 2 ÷ 4 =
   B. Give the equivalent value in decimal form.

1
5

2
3

1
4

B. Write the following decimals to fraction.

1. 0.66̅
2. 0.8
   Attachment URL: https://drive.google.com/file/d/1SUQBq4jQHZks2M2DNa7d4Ii2dn3tEnsp/view

[south horizon]

wHA-

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[lone heart]

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[tribal wasp]

we can work like this for a contradiction if then statement yeah? because when you do contradiction, you're taking the negation of the original statement to be fact. So you can work from a = 2k+1 towards a^2 and disprove the 'fact' right?

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[alpine sable]

Please help me, I don't understand how this works.

[lone heart]

@alpine sable Has your question been resolved?

[chrome salmon]

First find the minimum and maximum value the sequence of multiple of 6 can takd

We want a_1 > 8 and divisible by 6 so a_1=12

In the same way we want last element of sequence a_n<70 and divisible by 6 which will therefore be a_n=66

So a_1=12 , a_n=66 , d=6

Can you find value of n from this

[alpine sable]

kay hold on

same formula on the image?

[chrome salmon]

Yes

[alpine sable]

is it 10?

[chrome salmon]

I wont answer that but go ahed and find the sum

[alpine sable]

okay

390?

[alpine sable]

my issue here is that the first term is 16 but theres no 16

and also why 16

[tough hatch]

wdym by 'theres no 16'?

[alpine sable]

nvm that

why i6 though?

16*

[tough hatch]

16 is the least multiple of 4 that is less than or equal to 15 and greater than or equal to 45
44 is the greatest multiple of 4 that is less than or equal to 15 and greater than equal to 45

[alpine sable]

OHHHH

I SEE

thanks man

[tough hatch]

less than or equal to 15 and greater than or equal to 45
literally what "between 15 and 45" means

[alpine sable]

I don't really understand English well but thank you :D

.close

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[pastel vessel]

Hello, please help me with this laplace transform question. Here is my attempt to solve the problem. I am not sure if its right or wrong.

[lone heart]

@pastel vessel Has your question been resolved?

[lone heart]

@pastel vessel Has your question been resolved?

[south horizon]

NO

WHY DOES EVERYTIME I POST A QUESTION NO ONE HELPS ME WITH IT

[stuck ether]

ping the helpers?

[south horizon]

even if i ping them tho

[pastel vessel]

<@&286206848099549185>

[south horizon]

there is still none

[fair crater]

I would suggest reading #❓how-to-get-help

There is a very clear reason why no one bothers to reply

[pastel vessel]

I followed the instructions but still no one replied

[fair crater]

• While asking questions, make sure to mention all relevant details, including what you have tried and what you're stuck at. Do not expect others to simply solve your questions for you.

3rd point at #❓how-to-get-help

[pastel vessel]

Well in that problem I'm having a hard time performing second translation or time-shifting property.

[fair crater]

Well uhh, f(t)=...
seems fine, but writing immediately after that
$f(t)=t^{50}$ is not fine.

Write down specifically
$$\mathcal{L}{f(t)}= ?$$
Write down the translation theorem. It should be fine to literally just combine the two results.

[ocean seal]

ShatteredSunlight

[lone heart]

@pastel vessel Has your question been resolved?

[pastel vessel]

Oh, so after writing it specifically, the answer would be correct already?

[fair crater]

I'm pretty sure this example is designed for that, yes

It's for you to build up confidence in Laplace transforms

[pastel vessel]

Thank you very much!

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[golden ridge]

What would be the equation for the volume of each slab?

[golden ridge]

I think these are the slabs for part a

[bleak ridge]

Wouldnt it be more like this?

Cause its parallel to the triangular face

[golden ridge]

oh

thanks lol

would part b be like this?

[bleak ridge]

Ye I think so

[golden ridge]

ok cool thx

.close

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[golden ridge]

.reopen

[lone heart]

✅

[golden ridge]

Oh no why do I have two different answers 😭

Im pretty sure part a is correct

[bleak ridge]

Part a looks correct

[golden ridge]

yea

But i must have done something wrong in part b

[bleak ridge]

Well the depth of the slice is like a linear line

Its slope being 2/3

[golden ridge]

oh

this may be stupid but how do we know its 2/3 and not 3/2?

[bleak ridge]

I mean it could be 3/2

But in that case youd have to divide by y and nastiness would occur

[golden ridge]

ok

[bleak ridge]

I chose 2/3 cause its horizontal/vertical

[golden ridge]

ok

[bleak ridge]

And you wanna multiply by vertical to cancel out vertical and get horizontal cause its easier

Rather than dividing by vertical or y

[golden ridge]

ok thanks

[bleak ridge]

Np

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[whole wadi]

In 2006, 3.31 million tonnes of milk were weighed at Swedish dairies. In 2016, the weighting had dropped to 2.66 million tonnes of milk. In what year can we expect less than 2.50 million tonnes of milk to be weighed for the first time, if the percentage decrease is the same every year?

[whole wadi]

The answer is 2019, but I don't understand how

Are we looking at a exponential function in the form of y = C*a^x?

[lone heart]

@whole wadi Has your question been resolved?

[empty ridge]

Hi @whole wadi. Why do you think the exponencial function apply in this case?

[whole wadi]

It's a pure guess.

[empty ridge]

It shouldn't be.
What does it means by "the percentage decrease be the same every year"? Can you express this mathematically?

[whole wadi]

1-p, where p is percentage decrease in decimal and 1≥p>0

@empty ridge

[empty ridge]

I mean, if the quantity of milk is M today, what would be the quantity of milk next year?

@whole wadi

[whole wadi]

I’m not sure…

[whole wadi]

I’m not sure how you mean we should solve it.

[empty ridge]

@whole wadi
You should think about this idea:
If there is 3.31 M tonnes of milk in 2006, and in 2016 there is only 2.66 M.
AND, the percentage decrease is the same every year... What is going on?
My first question is: what is the yearly percentage decrease in milk? Can you determine this?

[whole wadi]

.close

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[ionic elk]

Hey

How do I do this ?

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[bright remnant]

would a cubic graph have an inverse?

[wary stream]

Yes

[bright remnant]

how do I get the intercept of the graph 2+x-x^3 and its vertexes

Im left with x(x^2+1)-2(x+1)

[wary stream]

I think it's more ideal to use rational root theorem to find the intercepts of that cubic

[bright remnant]

??

[gray isle]

there aren't nice zeroes for that

[bright remnant]

I have no idea how do get any of these values

[gray isle]

you'd probably need to resort to something like cubic formula
or methods of approximation if that's what the question intends

[bright remnant]

its just a mixed pratice excersize on functions

[wary stream]

Looks like there are two complex roots

[gray isle]

the turning points can be obtained by considering the first derivative

[bright remnant]

no calculus

you aren't expected to know how to do calculus im pretty sure

[gray isle]

then it'll be very tedious algebra

[bright remnant]

whatever

im going to use calculus idrc anymore

[bright remnant]

how do I find the inverse?

[lone heart]

@bright remnant Has your question been resolved?

[lone heart]

@bright remnant Has your question been resolved?

[red mirage]

How much work is done by the engine when exerting a force of 12 kN over a distance of 160 ft ?

can someone explain the formula to me for this question ^

[bleak ridge]

Well work = force * distance yes?

[red mirage]

yes

[bleak ridge]

So where do you get stuck

[red mirage]

idk know how to do it

[bleak ridge]

You just multiply

Just remember the kilo

[red mirage]

12 x 160 = 1920 ?

[bleak ridge]

Yes

So 1920 kilojoules

[red mirage]

i have an answer sheet and it says the answer is 585 kj

im not sure how my teacher got 585 from 12 x 160

[bleak ridge]

Oh whoops

You didn't have the feet before

You gotta concert it to meters

[red mirage]

how would i do that

[bleak ridge]

Just look up the conversion factor

[red mirage]

im gonna fail 😫

im 10/10 so lost right now

[bleak ridge]

1 foot is 0.3048 meters

So how many meters is 160 feet

[red mirage]

48.768?

[bleak ridge]

Yes

[red mirage]

ahh so its 12x48.768 = 585 kj

[bleak ridge]

Yes

[red mirage]

how did you know you had to convert it ?

[bleak ridge]

Cause when you have Newtons the only thing that goes with it is meters

Newton's have a unit of kg m/s^2

And joules are kg m^2/s^2

Not kg m ft/s^2

[red mirage]

so if i see a question with kN over Ft i should assume that its actually in meters not ft

?

[bleak ridge]

Ye anything with metric units needs metric units for the formulas

[red mirage]

so for this question would i just multiply to get the answer becasue its asking for the mass?

If a force of 12 kN is exerted on an object with a resulting acceleration of 25 m/s2, what is the mass of the object?

i guess its alreeady in m/s formula

[bleak ridge]

You'd divide

Cause f=ma

12=m*25

m=12/25

[red mirage]

youve taught me more then my teacher

What height must a 120 lb weight be lifted to produce 900 ft-lb of work?

so how would this one be done?

[bleak ridge]

So this has all American units

So it's all the same and you don't have to convert

Just plug it into w=fd

Sorry

Work = force distance

[red mirage]

900 divided by 120

thats correct thank you

[bleak ridge]

Np

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@bright remnant Has your question been resolved?

[sonic wyvern]

how would i skip a digit each time

i need the previous term + 2 in the denominator

not sure how to get that

[wanton jasper]

7+2n?

[sonic wyvern]

thank u im stupid

[wanton jasper]

np

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[rich lichen]

Hey all

Im self studying common core's mathematics

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[rich lichen]

Im trying to gain better education than the one offered in my country, south africa

[rich lichen]

What books can I use for Number and Quantity?

Vectors, matrix, etc

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[slim spire]

There is a channel book recommandation

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@rich lichen Has your question been resolved?

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[cinder fox]

Anyone know which mc this would be?

[lone heart]

@cinder fox Has your question been resolved?

[alpine sable]

what is this?

ok I guess it's supposed to have nothing to do with the multiple choice question?

[cinder fox]

It’s the evaluation of the logarithm

[alpine sable]

or it does and expression should probably say equation instead

[cinder fox]

Ig so ya

[alpine sable]

anyway, what is your confusion?

[cinder fox]

It does cuz it’s asking what values for x, make this expression equal 2

I’m not sure how to answer the question

Ik that d isnt the right choice tho

[alpine sable]

2log_3(3x) - log_3(x^2) is an expression, 2log_3(3x) - log_3(x^2) = 2 is an equation

that's why the language was confusing me but I know what they wanted to write now

how do you know d is not the right answer?

[cinder fox]

I tried it

Cuz my friend was like “that seems like it makes the most sense”, but i only get two attempts to get it right so

That was wasted when it was incorrect

[alpine sable]

oh ok lol

what do you know about logarithms?

[cinder fox]

Pretty much nothing cuz

I been usin ma calculator

[alpine sable]

ok let's try this

definition: $\log_3 x$ is the unique real number $y$ such that $3^y=x$

[ocean seal]

Botnuke

[cinder fox]

I-

What is this

[alpine sable]

if log_3(x) is written somewhere then that's what it means

so for example

what is log_3(27)?

it's the unique real number y such that 3^y = 27

which is?

[cinder fox]

12.9?

[alpine sable]

what the

how did you get that?

[cinder fox]

Log 3 (27)

Told u i just my calculator

[alpine sable]

well this isn't a question that you can use a calculator for

unlucky

[cinder fox]

Yoikes

[alpine sable]

(the homework problem I mean)

so again: if y is a real number satisfying 3^y = 27 then y = ?

think about it for a few seconds

I will explain if you cannot come up with an answer

[cinder fox]

Sorry

9

[alpine sable]

nope, if y = 9 then 3^y = 19683, which is not 27

I think you can come up with the right answer though

[cinder fox]

WAIT SHIT

Sorry it’s not multiplication

y= 5.2

[alpine sable]

nope, if y = 5.2 then 3^y is something bigger than 27

ok the answer is, y must be 3

y = 3 then 3^y = 3*3*3 = 27

[cinder fox]

Tf

OH WAIT

oml no cuz i legit coulda got that

Ig I wasn’t payin attn

[alpine sable]

it's alright

[cinder fox]

So what does that mean in terms of the mc ?

[alpine sable]

I will get to how this applies to the homework problem but what is mc?

[cinder fox]

Multiple choice

[alpine sable]

oh

So to remind ourselves: $\log_3 x$ is the unique real number $y$ such that $3^y=x$.

[ocean seal]

Botnuke

[alpine sable]

$\log_3 x$ is a function

[ocean seal]

Botnuke

[alpine sable]

it takes in $x$ and outputs a $y$

[ocean seal]

Botnuke

[alpine sable]

according that rule (which isn't "an expression to compute" but it doesn't need to be)

but as a more familiar example, a function like $f(x) = \sqrt{x}$ may give some trouble

[ocean seal]

Botnuke

[cinder fox]

Here’s the thing i dont get

Theres only x’s in this expression

Is there smth im missin

[alpine sable]

well...

I could say $f(x) = \log_3 x$, lol

[ocean seal]

Botnuke

[alpine sable]

$\sqrt{x}$ is the unique positive real number $y$ such that $y^2=x$

[ocean seal]

Botnuke

[alpine sable]

same thing now?

but anyway, this only has meaning in the real numbers for x >= 0

when you define there should be a domain and range defined as well, but that seems like it's going to be too much

so we'll just discuss what inputs are "meaningful" instead

let's say I want to try to evaluate $\log_3 -4$

[ocean seal]

Botnuke

[alpine sable]

according to our definition, $\log_3 -4$ is the unique real number $y$ such that $3^y=-4$

[ocean seal]

Botnuke

[alpine sable]

any trouble here?

this might be too hard of a question. The answer is that there is no such y because 3^y > 0 for any real number y

[cinder fox]

Right so the mc would be B right?

[alpine sable]

yes

[cinder fox]

Ty!

[alpine sable]

log_3(x) is meaningless if x <= 0

[lone heart]

@cinder fox Has your question been resolved?

[finite mesa]

What did I do wrong?

The interval of convergence should include 1 and -1

If you plug in 1 for x it will be AST

and it’s decreasing and limit is 0

If you plug in -1 for x u will get 1/sqrt(x+3) which converges to 0

[slim spire]

What is AST?

Alterning series test something like that?

[finite mesa]

Yeah

Alternating series test

Either way I tried changing the interval to () instead of []

That didn’t help

Idk what I did wrong in that case

And it won’t tell me if one part is correct and the other is wrong

[slim spire]

Why dont you use the (-1)^n in your ratio test?

[finite mesa]

Cuz ratio test takes absolute value

And I do |x| at the end

[slim spire]

I dont even recall ratio test lmao wait Im going to google it

$$\frac{1}{R}=\lim_{n\to\infty}\left|\frac{(-1)^{n+1}\sqrt{n+3}}{(-1)^n\sqrt{n+4}}\right|=1$$

[finite mesa]

What about x

[ocean seal]

SkyTwX

[finite mesa]

x^(n+1) / x^n too

[slim spire]

Idk what your formula is

[finite mesa]

an+1/an absolute value

x is being raised to the n

[slim spire]

For the ratio test to find the radius of convergence

[finite mesa]

For radius of convergence it should just be halfway between the 2 bounds

[slim spire]

Yeah thats what I wrote then

[finite mesa]

-1 and 1

R should be 1

[lone heart]

Channel closed

Closed by @cinder fox

Use .reopen if this was a mistake.

[finite mesa]

But it’s not

.repoen

[slim spire]

I have R=1 here

[finite mesa]

.reopen

[lone heart]

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[finite mesa]

I’m using ratio test to find interval of convergence

[finite mesa]

The ratio test usually tells if the series will converge but there is an x inside

[slim spire]

Check the bounds more carefully

What happens when x=(-1) ?

[finite mesa]

When x = -1 it will be (-1)^n * (-1)^n = 1^n = 1

Oh wait

[slim spire]

It becomes:

[finite mesa]

Ok I got it now

I shouldn’t have taken limit of that

Should have used comparison test

Thanks

[ocean seal]

SkyTwX

[slim spire]

👍👍

[woven geyser]

hi

[slim spire]

Hi

[woven geyser]

i'm trying to upload a screenshot of the question but it isn't working

[slim spire]

Just write it

[lone heart]

@finite mesa Has your question been resolved?

[lone heart]

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[idle dawn]

Evaluate without a calculator: cot(10)cot(50)cot(70)

[idle dawn]

In have tried to write it as cos(10)cos(50)cos(70)/sin(10)sin(50)sin(70) then multiply up and down by 2sin 10 but this hasn’t worked

Any pointers?

(This should be able to be done w/o the use of the product formulas for sin and cos)

[chrome salmon]

Yk formula for sinA×sinB

[idle dawn]

^

Otherwise I would use that

[chrome salmon]

I see

But what were you trying to do with 2sin(10)

[idle dawn]

Use double angle formula to potentially cancel a lot of things

[lone heart]

@idle dawn Has your question been resolved?

[idle dawn]

<@&286206848099549185>

[arctic laurel]

Hey im really confused how this question should be done without a calculator, i can derive it but solving for x is a bit weird.

[slim spire]

Not readable @arctic laurel

[glass lichen]

not your channel

[arctic laurel]

o sorry so which channel do i got to

[glass lichen]

The one you claim...

#❓how-to-get-help

[arctic laurel]

ooo

[lone heart]

@idle dawn Has your question been resolved?

[thorn kindle]

ok. cot(10)cot(50)cot(70)

[rough hull]

can anyone help me

[thorn kindle]

not in this channel

[rough hull]

please

[thorn kindle]

go to a free channel haha

[rough hull]

can u help me

[thorn kindle]

go to a free channel first

ok so cos(10)cos(50)cos(70)/sin(10)sin(50)sin(70)

all you really need to do is evaluate cos and sin at the points 10, 50, 70

[idle dawn]

w/o a calc unforutnately

[thorn kindle]

which is why we use identities

the "easy" values of cos and sin are at 0, 30, 45, 60, 90

unfortunately none of these values are really expressible as a sum or difference of the easy values

there are product identities

that hopefully you will not have to memorize

but here they are

i think this turns out nicely

[idle dawn]

i see, ill give it a try

thanks

.close

[lone heart]

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[hallow harness]

<@&286206848099549185>

[frozen python]

where is your question?

[wintry helm]

damn, @frozen python never expected to find you here

[frozen python]

my warframe homie

[wintry helm]

yeah 😄 , long time no see

[frozen python]

yeah i'd recognise that name anywhere

it is a small world

[wintry helm]

it really is dude

is there a chill-chat?

[lone heart]

@hallow harness Has your question been resolved?

[lone heart]

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[alpine sable]

Help I still don’t get this.

[alpine sable]

I know that I have to like move the variable to be by itself

[vast bobcat]

the error is in the second line

[alpine sable]

?

[vast bobcat]

when you do 3(h+2) it should be 3h+6, not 3h+2

[alpine sable]

Wdym second line?

[vast bobcat]

the second line is 3h+2 = 2h + 2+ 5

[alpine sable]

I meant like, how do I solve it?

The teacher said I have to do reverse bodmas.

Or not use regular Borja’s.

Bodmas.

I’m confused.

[vast bobcat]

so the question is 3(h+2) = 2(h+1) + 5
so now you have 3h + 6 = 2h + 2 + 5
3h + 6 = 2h + 7
h = 1

[alpine sable]

Ok.

Wait.

Wait

3h+6=2h+7

Wait what

@vast bobcat

Wait oh ok.

Thanks.

[vast bobcat]

no problem

[alpine sable]

But I meant like

The questions above

Not the final one.

I got help from a teacher but still don’t understand.

eh

poor child

I’m 13 bro.

Of course I’m dumb.

no no

dont say that

What.

7th graders are dumb.

lmao

They’re not adults or senior high schoolers.

Wait.

[alpine sable]

what do u not understand here

lemme help

How does it become a negative and a positive.

The numbers switch.

So they can add or subtract each other.

So it becomes -15-4=5m+6m

Yet it becomes 11=-11 after.

yo kid

?