help-26

[rain stratus]

Oh

[stuck forum]

Do you see what I'm saying?

[rain stratus]

No

Sorry

[void yew]

How to differentiate b/w different Secant lines btw?

[stuck forum]

What do you mean "differentiate"?

@rain stratus Give me a moment, let me think of an example

[rain stratus]

Ok

Thanks for all the help ;-;

[void yew]

i meant I could mistake the P-Q4 Secant line for P-Q3(Human error)

[stuck forum]

Are you talking about numerically? What do you mean human error?

@void yew at any rate, please open a new help channel. i'm helping mochi here

[void yew]

sry, was asking a question related to his problem, I have another question you can help with me later

[stuck forum]

It's fine, but I need to focus on mochi right now

@rain stratus What do you not understand? Where did I lose you?

[rain stratus]

You said we need to calculate the tangent with a x coordinate of -2

and idk how to do that

[stuck forum]

Okay good. So what do you know about tangent lines

[rain stratus]

They touch one point on the graph

[stuck forum]

Good. And how are they related to the derivative?

[rain stratus]

uhh

when you use limits

[stuck forum]

Okay. keep going

[rain stratus]

the second point approaches the first point

and

they are on top of each other

and that’s the derivative

[stuck forum]

Good!

[rain stratus]

: D

[stuck forum]

So the derivative gives you the slope of the tangent

So if you have y = x^2

[rain stratus]

so for y = -4x^2

[stuck forum]

Okay let's work with that

[rain stratus]

I got the derivative of -8x

[stuck forum]

Right

So that's the derivative at an aribtrary x

we want the value of the derivative at x = -2

[rain stratus]

yea

does that mean

how do we get the one at x = -2

[stuck forum]

the derivative of f(x) = -4x^2 is the one you reported, f'(x) = -8x

We want the value of f'(-2)

[rain stratus]

:0 oh

[stuck forum]

I'm not trying to trick you here

So what's the slope

[rain stratus]

16

[stuck forum]

Great

so the slope (rise/run) is 16

so you want a line that rises by 16 every time it runs by 1

so which plot is that

[rain stratus]

hmmm

I have no idea

Wym by which plot

Like the graph ?

would it be the first one ?

I think it’s the first one

[stuck forum]

Yes that's right

wait no

It's not that one

it doesn't rise enough

[rain stratus]

no?

[stuck forum]

Can you look for any recognizable point in the 1st plot?

Give me two different points in the 1st plot

hint: the x=0 value is easy to read

[rain stratus]

I can’t really recognize any points

Graphs always confuse me ;-;

[stuck forum]

Look at x = 0

Can you read the value of the line at x=0 (we're talking about the first plot here)

[rain stratus]

?????/

ohhh

it goes up in 2’s?

so it’s at 4?

[stuck forum]

yes

(0,4)

and it also looks like it reaches (-1,-4)

Do you agree?

[rain stratus]

yea

[stuck forum]

Okay, so what's the slope for that line

given those two points

[rain stratus]

ye

[stuck forum]

So? what is it?

[rain stratus]

other line???

Im lost

[stuck forum]

Oh, I was just asking for the slope

You said the answer might be the first plot

I asked you to identify two points in that line so we can check the slope

we need to see if it's 16

Does that make sense?

[rain stratus]

ahh

so do you use the formula

For the slope ?

[stuck forum]

Yes

We're just dealing with a regular line here, so yes

[rain stratus]

How do I know which one is y2 and y1 ;-;

[stuck forum]

One point is (0,4)

The other is (-1,-4)

[rain stratus]

yea

Does it matter ?

[stuck forum]

The y values are the second numbers

[rain stratus]

I know but

does it matter which one comes first

[stuck forum]

Oh, it shouldn't as long as you're consistent with the order

[rain stratus]

ok

[stuck forum]

If you choose an order for y, the same should be done for x

[rain stratus]

So I guess for the slope

I got

-4-4/4-(-1)

so 0/5

[stuck forum]

The x values are -1 and 0

[rain stratus]

wait

yea hold on

so it’s 0/-1?

I got -4-4/-1-0

[stuck forum]

Which is

[rain stratus]

um

0?

[stuck forum]

No, not quite

[rain stratus]

No?

[stuck forum]

You should have gotten 8 from that formula

[rain stratus]

????

[stuck forum]

-4-4 = -8

divide by -1 is 8

[rain stratus]

:0 oh

ohhh

yea

I see

[stuck forum]

So it's not the first plot either

[rain stratus]

My bad

[stuck forum]

It's not the last one because the last one doesn't even have a run. It's just a vertical line that always rises

the first one's slope is too small since we calculated it to be 8

the only one that's left is the middle one

[rain stratus]

Yea but how is it the middle one ?

[stuck forum]

Because we ruled out the other two options

You can also calculate it if you want

[rain stratus]

yea

[stuck forum]

the slope I mean

[rain stratus]

ok

I still kinda don’t understand :((

[stuck forum]

It's okay. What do you not understand?

[rain stratus]

like I understand how we got the first part of the answer

But the tangent part I’m not really getting

[stuck forum]

Which part specifically? Choosing the right plot? Or finding the slope of the tangent?

[rain stratus]

both

Somethings not really clicking

[stuck forum]

That's okay

I'm probably not communicating well anyway

Let's try this

[rain stratus]

No it’s not you

It’s just me being slow

[stuck forum]

So do you understand the strategy that we're trying to do here? Like, why we're looking for the derivative?

[stuck forum]

nah, don't say that

[rain stratus]

Yea

[stuck forum]

Okay. Why don't you walk me through it. Maybe we'll see where you're struggling if you explain it to me

[rain stratus]

so I remember we said that the tangent

We can’t use rise / run because it only hits the graph at 1 point

So we use limits to get the derivative

[stuck forum]

Yep

Keep going

[rain stratus]

But it’s the part where it asks to find the tangent when x= -2

[stuck forum]

What about it

[rain stratus]

how we get it

and

how to tell on the graphs

you get what I mean ?

[stuck forum]

We didn't actually look for the tangent line

we only calculated the slope

We calculated the slope by finding the derivative of f(x) at x = -2

Do you agree so far?

Do you want the actual equation for the tangent line? Maybe that will help

[rain stratus]

Yea

[stuck forum]

Okay we can do that

So, what formula can you use to write the equation of a line

[rain stratus]

y = mx + b right

[stuck forum]

That's right!

But we don't know b

So what else can we do?

[rain stratus]

What even is b

[stuck forum]

the y-intercept

[rain stratus]

Ah

[stuck forum]

where the line crosses the y-axis

[rain stratus]

Yea

[stuck forum]

Are you familiar with the point-slope form of a line?

[rain stratus]

no

[stuck forum]

$y - y_0 = m(x - x_0)$

[thorny flame]

TooManyCooks

[stuck forum]

this one

[rain stratus]

no ;-;

[stuck forum]

it's just the formula for the slope

but you fixed one point

here it's (x0,y0)

[rain stratus]

oh

[stuck forum]

you see it?

[rain stratus]

kinda?

[stuck forum]

$m = \frac{y-y_0}{x-x_0}$

[thorny flame]

TooManyCooks

[stuck forum]

How about now?

I just divided both sides by x-x0

[rain stratus]

its still point slope?

[stuck forum]

yes

If I were to give you the slope of a line

and a point ON the line

you can use this formula

[rain stratus]

ohh

[stuck forum]

$y - y_0 = m(x - x_0)$

This one

[thorny flame]

TooManyCooks

[stuck forum]

So, we need two things

the slope, and any point on the line

how do we find the slope?

[rain stratus]

hmm

[stuck forum]

for the tangent line, that is

You talked about this earlier

[rain stratus]

derivative?

[stuck forum]

Yes!

That's right

That gives you the slope

Now we need a point on the line

[rain stratus]

oh

I think I understand?

[stuck forum]

You think? What's your concern

[rain stratus]

you said the derivative gives the slope but we need a point

how do we get the point ??

[stuck forum]

Ah yes, we're getting there

We were asked to find the tangent x = -2

So, the line must pass through the same point as the function y = -4x^2

[rain stratus]

yea

[stuck forum]

That means y = -4(-2)^2 = -4(4) = -16

The key idea here is that we want a point that is on the line AND the function we're interested in

[rain stratus]

hmm

wym by that

[stuck forum]

The tangent line touches the plot at only one point

in other words, at that one point, the function and the tangent line are interescting

[rain stratus]

yea

[stuck forum]

so they must have the same x and y value at that point

[rain stratus]

oh

yea

[stuck forum]

So, to find a point on the line, we can use the point on the function instead

because the line and the function share that one point

Does that make sense?

[rain stratus]

yea

[stuck forum]

Sure?

I can go back if you want

[rain stratus]

no

i get that part

[stuck forum]

Ok good

Just making sure

[rain stratus]

So far I’m understanding

[stuck forum]

So we can use y = -4x^2 to find a point on the line

specifically, we want the point with x = -2

[rain stratus]

yea

[stuck forum]

plug that into the equation and you get y = -4(4) = -16

So the point (-2,-16) is where the tangent line touches the graph of y = -4x^2

[rain stratus]

oooooohhhhhh

bruh

I think I understand it now

[stuck forum]

Great!

So

now we have a slope (thanks to the derivative)

[rain stratus]

yea

[stuck forum]

and we have a point

m = 16, and the point (-2,-16)

Plug that in and we get $y - y_0 = m(x - x_0) \ y - (-16) = (16)(x-(-2))$

[thorny flame]

TooManyCooks

[stuck forum]

or $y + 16 = 16(x+2)$

[thorny flame]

TooManyCooks

[stuck forum]

If you simplify that further you get $y = 16x + 16$

[thorny flame]

TooManyCooks

[stuck forum]

Did I lose you?

[rain stratus]

How does it become y=16x+16?

[stuck forum]

Oh I just simplifed the expression

[rain stratus]

No I’m sorta following somehow

[stuck forum]

Let me know if you're still confused by the 16x+16 part

[rain stratus]

yea

How does it become that

[stuck forum]

Do you agree with this? $y + 16 = 16(x+2)$

[thorny flame]

TooManyCooks

[rain stratus]

Yea

[stuck forum]

Okay

so expand that right side

you get 16x + 32

[rain stratus]

Do you bring the +16 on the left side over

oh

[stuck forum]

yes

32-16

[rain stratus]

oh I see

[stuck forum]

Yep

[rain stratus]

yea

I get it now

[stuck forum]

So the tangent line is y = 16x +16

So, let's go back to the question

we want to find the plot

What can you tell me about the line y = 16x +16

[rain stratus]

that it’s a line

;-; idk man

[stuck forum]

Haha that's fine

So you remember the y = mx + b you talked about earlier?

It's in that form now

[rain stratus]

:0 yea

oh I see

[stuck forum]

m = 16

so m is the slope

[rain stratus]

yes it is

yea

[stuck forum]

16 is the y-intercept

which means what

What does the y-intercept represent

[rain stratus]

the point at which it crosses the Y axis?

[stuck forum]

yes!

[rain stratus]

yess

[stuck forum]

so, of all the plots in the problem

which one crosses y = 16

at x = 0

[rain stratus]

none really

the closest one that looks like it will is the middle one

[stuck forum]

Is it actually?

[rain stratus]

bc the other two already crossed the y axis

but not at 16

[stuck forum]

If you look at the plot, you're only limited to 10

[rain stratus]

I mean

the top one

the bottom one is a vertical line

[stuck forum]

Yeah

[rain stratus]

But there was a fourth too

[stuck forum]

Oh?

[rain stratus]

but it’s definitely not the answer

yea

[stuck forum]

Ok

[rain stratus]

the parabola is too fat

it’s not the one I graphed

[stuck forum]

i see

Then it's gotta be the second one then

[rain stratus]

See

[stuck forum]

yes. it must be the second one since we eliminated everything else

[rain stratus]

yepp

I understand why it’s that answer now tho

[stuck forum]

Good job!

[rain stratus]

it has to intercept the y axis at that point

Because we found the slope using the derivative

and

it gave us the x coordinate

So we have to find where they share the point right ?

[stuck forum]

Yes. The key points are these:

You want a slope, so you need the derivative at that point

You want a point on the line, so you look for where the line and the function intersects

Once you have those two pieces of information, you apply the point-slope formula for the line

simplify and voila

you got the tangent line

Did I lose you?

[rain stratus]

No sorry I’m note taking what you’ve been saying

I’m just writing

[stuck forum]

Oh ok.

[rain stratus]

Ok

I got it all

thanks so much

I just have one more question

These 2 questions are similar so

But they say tangent twice

[stuck forum]

So you just have to find the tangent line's slope

What does that mean?

How can you do that?

[rain stratus]

??

Find the slope

[stuck forum]

yes

how do you do it

for the tangent line

[rain stratus]

Do we use the line formula ?

[stuck forum]

It's a tangent line though

How do you find the slope of the tangent line?

[rain stratus]

uh

do we use the point slope formula ?

idk ;-;

idk ;-;

[stuck forum]

The slope of the tangent line is always the derivative of the function

[rain stratus]

huh

how are we supposed to get the derivative?

[stuck forum]

I thought you knew how

[rain stratus]

do I?

[stuck forum]

You did it earlier

for y = -4x^2

[rain stratus]

do I just do the same thing ?what about x= -3?

[stuck forum]

What do you mean

[rain stratus]

would it be f(x)= 5x - 8 and i substitute the x with -3?

[stuck forum]

What are you talking about? Can you slow down

[rain stratus]

I’m confused

[stuck forum]

By what

[rain stratus]

Everything so far

ok wait no

I get that we need the derivative

[stuck forum]

Where do you want me to go back to

[rain stratus]

but my question is how do we get it

[stuck forum]

How did you find the derivative earlier?

[rain stratus]

because there’s y = 5x - 8

[stuck forum]

Ignore

[rain stratus]

Ok

[stuck forum]

Focus on my question

How did you get the derivative in the previous problem

[rain stratus]

Earlier I did the power rule but I also know the formula for the derivative

[stuck forum]

What rule is that

[rain stratus]

where if you have like for example y=6x^7 you would multiply 6*7 and then put the answer(x)^-1 so it’s 42x^6

[stuck forum]

Okay good

So why can't you do that now?

[rain stratus]

If I do that

[stuck forum]

?

[rain stratus]

then it comes y = 5?

[stuck forum]

Okay

Then that's the answer

[rain stratus]

?

what about the x value that’s there

[stuck forum]

First of all, 5 is the derivative

[rain stratus]

Yea

[stuck forum]

dy/dx = 5

[rain stratus]

yea

[stuck forum]

which means the slope is constant

precisely the case for a line

dy/dx = 5 means the value is 5 FOR ANY x

[rain stratus]

So that’s it ?

man

[stuck forum]

Yes

You shouldn't doubt yourself

you had the right answer all along

[rain stratus]

I hate math

But thank you

[stuck forum]

Let's work on the next problem

[rain stratus]

ok

[stuck forum]

So what's dy/dx

[rain stratus]

if I find the derivative of y = x^2+2x-7

it becomes y’ = 2x + 2?

[stuck forum]

Yes. So what's the slope of the tangent line at x = 3

[rain stratus]

8

[stuck forum]

Good

[rain stratus]

I see

I got 2 more questions that pertain to the tangent

[stuck forum]

Ok

[rain stratus]

and then I’m gonna sleep because my brains all mushy

[stuck forum]

Ah

so they gave you the point already

makes things easier for you

[rain stratus]

yea?

[stuck forum]

I'll wait

[rain stratus]

for??

<_<

[stuck forum]

Oh

I thought you wanted to try it first

[rain stratus]

nah I’m kidding

I will try it

I seem to be stuck

not sure which formula to even use 😭

[stuck forum]

Ok let's take a step back

How do you find the slope of the tangent line

[rain stratus]

do I use the one that says y-y_0= m(x-x_0)?

the derivative

[stuck forum]

Good. What's the derivative

[rain stratus]

bruh

derivative again

[stuck forum]

it gives the slope, and you need the slope here

Since you're only given one point

[rain stratus]

y’=2

[stuck forum]

not quite

[rain stratus]

wait na

2x

mb

[stuck forum]

Good, so the slope at x = 2 is?

[rain stratus]

is 2x?

[stuck forum]

that's dy/dx

but we want to evaluate it at x = 2

[rain stratus]

so it would be

(2, 2x)

?

[stuck forum]

I was looking for a number

dy/dx = 2x

[rain stratus]

uh

[stuck forum]

we want the value at x = 2

[rain stratus]

oh

would it be (2, 4)?

[stuck forum]

Yes, that's right

So m = 4 and you're given the location of the intersection which is (2,7). Now what

[rain stratus]

now I sit here confused

[stuck forum]

Haha we have an equation earlier. You mentioned it actually

[rain stratus]

is that when we use it?

[stuck forum]

You use that to find the equation of a tangent line

so yes

[rain stratus]

Idk what I even got

[stuck forum]

What do you have

[rain stratus]

I erased it but

I got 3/0

but then

there’s the 4

[stuck forum]

This

[rain stratus]

oh I was using something different lol

I got 1

[stuck forum]

You're plugging in m =4, x0 = 2, y0 = 7

x and y should be there in the end

[rain stratus]

???

[stuck forum]

Yes?

[rain stratus]

Oh

jeez I see

wait I still don’t see

I’m confused

I’m still getting 0

don’t we have (2,7) and (2,4)

[stuck forum]

Where are you getting 0

You only have one point

[rain stratus]

o

[stuck forum]

You have a point, and a slope at that point

[rain stratus]

So is it

y-7= 4(x-2) ?

[stuck forum]

Yes

But you need to simplify

[rain stratus]

😭 how

[stuck forum]

You expand. I know you can do it 🙂

[rain stratus]

um

on the right side is it

4x-8?

[stuck forum]

Yes

[rain stratus]

y=4x-1?

[stuck forum]

Yep! Good job

[rain stratus]

that was

ROUGH

[stuck forum]

😅

[rain stratus]

Im running on 1 neuron rn

[stuck forum]

One more

[rain stratus]

one more and I can pass away for a few hours

ok so

now it’s y=x^2 - 2 with the points (3,7)

[stuck forum]

Ok

[rain stratus]

once again

y’=2x

so is does m=4

[stuck forum]

No

[rain stratus]

_> wait

sorry

6

[stuck forum]

X =3

Yes

[rain stratus]

yea

y=6x+11

is what I got

sorry I mean minus

Y=6x-11

[stuck forum]

Yes

Good work

[rain stratus]

I give u my thanks

for being patient with me

and for all the help

[stuck forum]

👍

[rain stratus]

now it’s time

to sleep

goodnight

and thanks again

.close

[topaz sinew]

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[uncut agate]

I don’t know where is my error, I’m trying to solve this exercise: 132x’ + 252y’ = 12(462), find all positive x’ and y’

I find the gcd(132, 252) = 12, so 12|12(462) then the equation has solutions
Divide by 12 I have: 11x’ + 21y’ = 462, where gcd(11,21) = 1
Find the s,t such that 11s + 21t = 1, s = 2; t = -1
Now, I have that 11(2-s) = 21(-1-t), then using Euclid lemma I have, s = -21j - 2, and t = 11j -1
x’ = 462s = 462(-21j -2) = 21k
y’ = 462t = 462(11j - 1) = 11k

But If for example I use k = 2, then my result is 11088 :(

[topaz sinew]

@uncut agate Has your question been resolved?

[uncut agate]

<@&286206848099549185>

[topaz sinew]

@uncut agate Has your question been resolved?

[uncut agate]

<@&286206848099549185> this is the answer, my error is in x’, but 462*2 / 21 = 21(44), then I can factor the 21 :(

[topaz sinew]

@uncut agate Has your question been resolved?

[uncut agate]

.close

[topaz sinew]

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Send your question here to claim the channel.

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

[languid forge]

Suppose I need to solve an equation

[languid forge]

like $\cosh (x) = \cosh (k + x)$ to find x in terms of k, is this possible? And how can I?

[thorny flame]

Realist

[topaz sinew]

@languid forge Has your question been resolved?

[languid forge]

<@&286206848099549185>

I think I can reform the question as $e^{k+x} + e^{-k-x} = e^x + e^{-x}$

[thorny flame]

Realist

[languid forge]

Which is $1 + e^{2x} = e^{k+2x} + e^{-k}$

[thorny flame]

Realist

[sweet shard]

is this supposed to hold for all k?

[languid forge]

some constant k

[sweet shard]

oh so k is fixed

did this come from a problem somewhere

[languid forge]

intuition just tells me to match up e^2x and e^-k

[sweet shard]

or did you make it up

[languid forge]

made up scenario

And that happens to be right

[sweet shard]

you can solver for $e^{2x}$ here

[thorny flame]

riemann

[languid forge]

but how can I be sure that this is a unique solution

[sweet shard]

those are two different problems

which one are you solving first

[languid forge]

oh I got it I see this makes the most sense

[topaz sinew]

@languid forge Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• 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!

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[turbid pecan]

any idea on how to do this?

[topaz sinew]

@turbid pecan Has your question been resolved?

[topaz sinew]

@turbid pecan Has your question been resolved?

[topaz sinew]

@turbid pecan Has your question been resolved?

[topaz sinew]

@turbid pecan Has your question been resolved?

[pallid phoenix]

have done 2 approches but couldn't find out without having AC & AD

But can I assume they r the same?

if that's so we can get theta

[craggy haven]

i don't think so

give yourself a value for AC, either call it 1 or x

[topaz sinew]

@turbid pecan Has your question been resolved?

[surreal idol]

Let AC = x, then can you find BC and AB?

[wild brook]

Do you know the law of sines

?

[turbid pecan]

Yea

[wild brook]

ok

right?

[surreal idol]

you shouldn’t need the law of sines

this is a right-angled triangle

and where does this come from

[wild brook]

I misread, sorry

[surreal idol]

Yes

Let AC = x, then can you find BC and AB?

[wild brook]

AC * BC/2 = BD * AB/2

cancel the 2

AC * BC = AB * BD

[topaz sinew]

Please read #❓how-to-get-help

[topaz sinew]

@turbid pecan Has your question been resolved?

[elder spindle]

hello

can you explain how to divide negative a positive numbers

-5*6

-5 * 6

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[lost marlin]

i dont think u can cancel the (x^2-1) term

[surreal idol]

you canceled out the square on the top

it should still remain, but without the square

first, factor out (x^2 - 1) in the numerator

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[neon iron]

what does s mean

ds/dt = dtheta/dt (r)

i think we r finding dtheta/dt

[flat kindle]

s = rtheta is the formula for circumference

[neon iron]

oh

so where the info of the truck

plug into

[flat kindle]

use this

[neon iron]

-6=1.2(dtheta/dt)?

[flat kindle]

why negative

[neon iron]

because we are losing circumference

no?

but i suppose in the context of the problem it would be pisutive

s.t. dtheta/dt = 5

if

ig*

modeling and related rates r

messing me up

.close

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[rapid herald]

does anyone know how to get part c) the second image

[ashen osprey]

ok

what happens each time you find t2, t3 etc

[rapid herald]

oh wait i just realised how to do it sorry, thanks anyway

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[compact moth]

Can somebody help me with this please?

[pastel juniper]

rationalise the numerator

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[compact moth]

ok thank you I’ll try it :)

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[neon iron]

Can someone explain to me how to solve (x-2/4x-8) with x not equaling to 2?

[neon iron]

solve?

[neon iron]

ye how

That is just an expression

when i solve i just get 2

but the exercise says that i cant get 2

do you mean simplify?

yea

sorry

i mean simplify yes

$$\frac{x-2}{4x-8}$$

[thorny flame]

Replaced by new brandon H

[neon iron]

The top and bottom look similar right?

[neon iron]

yeah

How would you factor the bottom to get something similar to the top

[neon iron]

/4

yeah

so

you

take 4 out

$$\frac{x-2}{4(x-2)}$$

[thorny flame]

Replaced by new brandon H

[neon iron]

wait

im allowed to dot hat?

why not

so just 1/4?

yeah

[neon iron]

idk i thought cuz it was in a parenthesis

that had to be multiplied by something else

so I just get rid of the multiplied by sign between the parenthesis and the 4 and thats totally fine?

?

[neon iron]

cuz its 4(x-2)

so theres a multiplied by

between the 4 and the parenthesis

[idle hazel]

a number attached to a parenthesis is defined as being multiplied

[neon iron]

ah

so i just end up multiplying it by 1

[idle hazel]

if that's what you're asking

[neon iron]

hence keeping it the same

[neon iron]

yeah tysm

[neon iron]

ty as well

i get it now

have a good one

.close

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[acoustic tendon]

i have no idea what these are asking me😭

[acoustic tendon]

at first i went with [5,4) for domain but that was incorrect, i just dont get what theyre telling me to do to "fit" the graph in the rectangle i may be stupid

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[acoustic tendon]

<@&286206848099549185>

[tiny timber]

domain is the possible values for input, range possible values for output. does that make it easier to see what they are asking for?

I see that may not have been the answer to your question, by adjusting domain and range you get a rectangle, the part that is both orange and green. "fit" the graph would mean to cover the graph with said rectangle

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[oak osprey]

Grade 12 physics

Here is the graph

How would one solve this? Thanks!

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[oak osprey]

<@&286206848099549185>

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[oak osprey]

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[hollow dew]

Can someone tell me if I did this problem right? Final answer is 2401 but idk if my answer is right:

[solemn jay]

Im sorry but its wrong

I think it is

[hollow dew]

Wat I do wrong plz

[long dawn]

Everything looks good in finding the value of x, I'm not sure I follow what you did after though

[solemn jay]

same but thats the inside, if says to find the whole frame + poster

[long dawn]

If you know that x~41 is the side length of the smaller square, and that the frame is 4 cm wide, can you find the side length of the full frame?

[atomic skiff]

hint:

[long dawn]

Finding that inside side length helps quite a bit

[solemn jay]

But if u leave it t only inside, its technically wrong

[icy sky]

Guys

[astral temple]

Finding the lengths of the inside edges is definitely the first step here

[icy sky]

49^2=2401

But still, youre estimating too early

[hollow dew]

I add the area of poster (41*41) and the corners (4(16)) and the right, left, top, bottom but idk if that right

[astral temple]

Ye i think we were trying to let cookie figure that one out on his own

[icy sky]

Be more accurate than 41

[long dawn]

That's generally how we help here yeah

[hollow dew]

Ima try this method ig look solid

[atomic skiff]

thereafter trigonometry

to find length

[icy sky]

Yall are overcomplicating this

[atomic skiff]

because this looks like a perfect square, right?

[icy sky]

But sure

[hollow dew]

The problem is idk what I did wrong with my first solution 😢

[icy sky]

You just have to be more accurate than 41

[solemn jay]

be more precise

[hollow dew]

Ok

[solemn jay]

||ngl my chemistry teacher would have killed u if u said accurate rather than precise in this situation infront of him xD||

[icy sky]

Oh right accurate is not the correct term

[solemn jay]

last time he made me write the word precise 20 times 💀 to make sure I knwo the diff

[hollow dew]

I got 2408.2 using mister panda’s method, is right?

[atomic skiff]

alright i think I extracted the answer through my method.

[atomic skiff]

what did you do to get this number?

[hollow dew]

uhhhh

58 + 5.7 + 5.7 to get the diagonal

and then just solving for x

[atomic skiff]

hmm, rounding error

[hollow dew]

oh I prob wasn’t suppose to round the 5.7

[hollow dew]

wat was ur answer

[atomic skiff]

it's a big leap if you are going to round 5.6568 to 5.7. The diagonal length will remain as 58 + sqrt(32) + sqrt(32). Which can be simplified to 58 + 8 * sqrt(2).

so far so good, but from here, i need to recheck my working because i found an error

xd

[hollow dew]

Ok

Ima redo also

Uhhh I got 4804.390186

Uhhhhh

Wait oh

I forgot sum steps

[atomic skiff]

alright, i fixed my error

xD numbers get ugly here

so okok, we agree that the full diagonal length is \ $58 + 2(\sqrt{32})$, or $58 + 8\sqrt{2}$ ?

[thorny flame]

HqppyFeet

[hollow dew]

ye

[atomic skiff]

Nice! What did you do after?

[hollow dew]

x^2+x^2=58+8sqrt(2)

[atomic skiff]

hmm I see what you are trying to do... but there is a simpler way of doing things

(i want to see how far you got through that method, because I didn't do that lol)

(just pasting the question here, tired of scrolling lol)

@hollow dew You with me btw?

[hollow dew]

Oh yeah I was checking some thing srry

[atomic skiff]

dont worry hahah

It is said that this is a square, right?

[hollow dew]

Ye

[atomic skiff]

Yup, so when you cut a square in diagonal, you get two similar triangles--

do we know the angle of these similar triangles?

[hollow dew]

Uhhhh

[astral temple]

You don't need trig for this, you're fine with just the pythagorean theorem and some drawing

[atomic skiff]

hmm?

Yeah ok I see the ways you can find the answer

[astral temple]

$(\sqrt{\frac{58^2}{2}}\cdot (4+4))^2$

[thorny flame]

Joachim

[astral temple]

$\sqrt{\frac{58^2}{2}}$ gets you the internal side lengths, from that just realize you need to add the frame width in both directions and square the side

[thorny flame]

Joachim

[hollow dew]

idk what u mean by this but is 2408.2 close to the answer

[atomic skiff]

It's quite close. I got 2402.2

so whatever you did, it works

I used trig for this, knowing that cutting a perfect square in diagonal will give us two 45 degree angles

Then I used cos(45) = x/(8sqrt(2) + 58) to find the full length, then x^2.

Either way, you eventually get to the answer.

[hollow dew]

Ok thx

I think it was just cuz my rounding so yeah

Thx for the help

I learn very much

I might study some trig after this cuz ur method so convinent lol

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[sacred thorn]

I need to find the missing side (middle question) can anyone help please?

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[runic jungle]

picture is not clear

[sacred thorn]

Sorry I can’t make it any clearer. Sorry for ya time.

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[charred bane]

.close

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[meager apex]

how can i tell how much the graph is being stretched by?

[meager apex]

what was it u said

[acoustic pecan]

you can see the gradient of these is 2 and -2 so |x|->|2x|

[meager apex]

is that from this right here

[acoustic pecan]

its just from the lines generally, from (0,3) they move one away and two down in each direction

[meager apex]

hmmm

but wouldn't you also get -2 here then

[acoustic pecan]

that would be |x|->-|3x|+4

[acoustic pecan]

is should have been more specific here: |x|->-|2x|+3

[meager apex]

ah ok

thank you

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[meager apex]

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[hollow jacinth]

hello im using a textbook and this is my problem. 3 boys 3 girls In how many ways if only the boys must sit together?

but chatgpt grouped the boys as 1 entity while girls are 3. probability and assume its in a row

[empty sail]

but chatgpt grouped the boys as 1 entity while girls are 3
Please do not use chatgpt for math

[hollow jacinth]

gotcha. can you show me how to do the problem? my professor help me in terms of experiments but i got confused

[neon iron]

Do you know the answer?

[hollow jacinth]

i do but i dont know how to solve it

[neon iron]

What's the answer tho?

[hollow jacinth]

my book says 144

[neon iron]

Hmmm

[hollow jacinth]

but im allowed to write it in noncomplete way like 6! if the order didnt matter for boys and girls and if they were put in a row

[neon iron]

Is it the correct statement?

[hollow jacinth]

i believe it is

[neon iron]

"if only boys must sit together"

Aight so

I got it

,rotate

[neon iron]

We want all boys to be together

Right?

[hollow jacinth]

yep

[neon iron]

We don't want them to get scatter during arrangements

Right?

[hollow jacinth]

yep

[neon iron]

So what about

[hollow jacinth]

but the girls ordering doesnt matter so like G, b, b,b, g, g would also work

[neon iron]

What if we assume like this

And arrange them

Like let's say if we get one of the arrgament

G1 Alpha G2 G3

Still All the boys will be together

[hollow jacinth]

can you explain this symbol?

[neon iron]

Alpha

[hollow jacinth]

gotcha continue

[neon iron]

Do you got this?

Basically we considered all the boys together as One

[hollow jacinth]

i get thats how its done but i dont understand why

[neon iron]

You don't understand why we took Alpha?

Why we took all 3 boys as one?

[hollow jacinth]

yeah

[neon iron]

Because we want them to be together

By bounding them into Alpha, we assured that they will always be together

[neon iron]

Where ever the alpha goes it will take all 3 boys too

If alpha comes in middle of arrangement, then all 3 boys will be in mid

And so on

It's like we tied all of those boys together

Such that they all can be together and don't scatter

Getting it?

[hollow jacinth]

yeah that makes sense

[neon iron]

And inside this process of tying them

There will be one more arrangement

Arrangement of tying boys

That will be 3!

Got that?

[hollow jacinth]

wdym by tying boys

[neon iron]

We tied them (alpha) so that they remain together

Together

[hollow jacinth]

so 1 group but 3 boys that can be arranged in any order which is why its 3!

[neon iron]

Yes, the arrangement inside box, arrangement in tying them is also present and that will be 3!

[hollow jacinth]

ok i understand now

[neon iron]

And arrangement of alpha with other 3 girls will be 4!

Clear till now?

[hollow jacinth]

yes i believe so thank you so much!

so the end would be 1(3!)(4!) right?

[neon iron]

Yes

[hollow jacinth]

thank you!

[neon iron]

No worries

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[opal cliff]

ed

[opal cliff]

Hello

I need help with a derivate aplication problem

this is what i have, read traslation:

An airplane flies at an altitude of 5 miles and at a speed of 600 miles per hour toward a point located exactly vertically to an observer (see figure). How quickly is the angle of elevation of THETA changing when the angle is 30, 60, and 75 degrees?

<@&286206848099549185>

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[opal cliff]

heeelp

I still have not anwers

.close

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[hardy stirrup]

Hey could anyone yell me

[hardy stirrup]

Help

[torpid matrix]

YEAH I SURE CAN

[hardy stirrup]

OK SURE!

[lucid junco]

HI

[hardy stirrup]

I NEED TO FIND THE VALUE OF THE RED LINE

[lucid junco]

SORRY WE CANT HELP YOU ONLY YELL AT YOU

[hardy stirrup]

Darn

[gleaming reef]

Ong

I’ve never seen someone so mad to get math help

[hardy stirrup]

Who was mad?

.close

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[cosmic summit]

Hello, i am stuck on this a little bit.

[cosmic summit]

I know that the vector eq of a line is r = r_o + tv

and i think my r_o is <5,14,7>

im not sure how to get r_o and v

[drifting swift]

v is your direction vector, and it is meant to be perpendicular to the two vectors <16,2,11> and <15,11,3>

do you know how to get a vector in R^3 that's perpendicular to two given vectors?

[cosmic summit]

cross product?

[drifting swift]

yes exactly

btw we usually have 0 as a subscript not the letter o

so r_0 not r_o

[cosmic summit]

okay i did cross product now @drifting swift

i got <-115, -117, 146>

is that my v? in that equation

[drifting swift]

yes that's your direction vector

gonna take your arithmetic on faith there

[cosmic summit]

it should be good ill double check

so will i have

r = 5,14,7 + t (-115, -117, 146)

? @drifting swift just to be sure, if my cross product is correct

[drifting swift]

r = (5, 14, 7) + t (-115, -117, 146) yes

[cosmic summit]

okay thank u!

appreciate iot

.close

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[hardy stirrup]

Hey can anyone help me

[hardy stirrup]

.close

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[neon iron]

-2^x = -8
-2 = (1^1/x) (-8^1/x)
putting x = 3 we get -2 , -2w , -2w^2 ?