help-27

[mild basin]

For g(f(x)) can't remember if brackets stay after squaring it

Oh, I forgot about D and R

gotta keep originals

The original domain and range from f(x) and g(x), right?

Domain is Inside function and End function

Range is End function

<@&286206848099549185> I have that correct for composite functions?

For higher composite, f(g(h(x)) would I need inside domain of g and h functions as well as the end function? or just inner most function h and end function?

.close

[devout snow]

Channel closed

Closed by @mild basin

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[light quail]

after ive found my g(x) and f(x), how do i get f'(x) and g'(x)?

[wooden wraith]

differentiate them

[light quail]

how

[wooden wraith]

What are g(x) and f(x)?

[light quail]

(x+3) and (x-4)^-1

[wooden wraith]

Oh, okay, you're using the product rule then?

[light quail]

i suppose, another helper helped me get those. idk why (x-4) has the ^-1

[wooden wraith]

Okay, let's back up a second

What formula are you looking at?

in order to find dy/dx

[light quail]

the other guy gave me this

[wooden wraith]

Okay, this works

So, see you're taking the derivative of f(x)/g(x)

So, in your problem

f(x) = x+3

g(x) = x-4

That's all, no negative exponent

in order for it to fit the form f(x)/g(x)

[light quail]

ok

[wooden wraith]

Do you agree with that so far?

[light quail]

yes

[wooden wraith]

so then, if f(x) = x+3

What is f'(x) ?

[light quail]

im not sure

[wooden wraith]

hm

I think you should review your basic derivative identities.

Otherwise problems like this one involving the product/quotient/chain rules are going to be basically impossible

[light quail]

wait is it -6?

i plug in 3 for x

because we looking for the thing at that point

[wooden wraith]

No, that's just the value of your original function at x=3

That's why they give you the point (3,-6)

The derivative of a linear function is just its slope

so for f(x) = x+3

f'(x) = 1

[light quail]

how did you calculate that

[wooden wraith]

The power rule and sum rule

I really think you should go back and review derivatives of basic functions

You should honestly be very comfortable with this step if you're working with the quotient rule

[light quail]

but how did you get 1 from x+3?

[wooden wraith]

power rule and sum rule

f(x) = x+3 = x^1 + 3
f'(x) = 1x^0 + 0 = 1

[light quail]

why the ^1 part of x^1 + 3

[wooden wraith]

x^1 is the same as x

[light quail]

what does x^0 mean

[wooden wraith]

anything to a zero power is equal to 1

[light quail]

how did you get f'(x) = 1x^0 + 0 = 1

[wooden wraith]

Using the power rule, the derivative of x^1 is 1x^0

Using the constant rule, the derivative of 3 is 0

And using the sum rule, we can add them together

so the derivative of x^1 + 3 is 1x^0 + 0

which is equal to 1

[light quail]

so every x always has an imaginary x^1? and when they get brought down to x^0, they become 1x?

that part is confusing me

[wooden wraith]

x^1 is kind of an unusual case. The general rule is written in that picture

d/dx x^n = nx^(n-1)

so for example

d/dx x^4 = 4x^3

d/dx x^8 = 8x^7

d/dx x^1 = 1x^0

but x^0 just happens to be equal to 1

so that last one just simplifies to 1

[light quail]

g(x) for x-4 is x^1 - 4 (?)

[wooden wraith]

yes, those are equivalent

[light quail]

how do i get derivative from this

[wooden wraith]

Do the same thing I did above

What would be the derivative of x^1 ?

What would be the derivative of -4 ?

Then add them together

[light quail]

should i know -4 derivative off hand?

[wooden wraith]

The derivative of any constant is 0

That's the "constant rule" on the image I sent

[light quail]

-4 is a constant?

[wooden wraith]

Yes, anything without a variable is constant

[light quail]

1x^+0 = 1?

[wooden wraith]

yep!

so f'(x) and g'(x) are both 1

[light quail]

did you know it was gonna be that this whole time

are they always 1?

[wooden wraith]

Yeah, I mean that's why I was telling you I think you should review the basics more. Your original problem requires the quotient rule. But by the time you get there, this stuff with the power rule should kinda be a piece of cake.

No, it's not always 1

[light quail]

so this is next

?

[wooden wraith]

yeah

[light quail]

bottom will be (x-4)(x-4)

?

[wooden wraith]

yep

[light quail]

and what does this tell me

[wooden wraith]

So, your original problem is to find the equation of a tangent line at the point (3,-6)

The quotient rule will give you the derivative of your function. And plugging in x=3 to that derivative will give you the slope of your tangent line

[light quail]

and then

[wooden wraith]

And then you have the slope of the line, and a point it passes thru (3,-6)

So you can find the equation of the line

[light quail]

like this?

[wooden wraith]

Did you put this into mathway or something?

[light quail]

symbolab

[wooden wraith]

Honestly, I have to tell you, you're really struggling with the very basics here. And by using things like symbolab I don't think you're doing yourself any favors

[wooden wraith]

This already is the derivative. That's the whole point of the quotient rule. Don't differentiate it again

$\frac{dy}{dx} = \frac{(x-4)-(x-3)}{(x-4)^2}$

oh the bot's dead

[wooden wraith]

what you have here in the parentheses is already the derivative of your function

[light quail]

then how do i turn that into the tangent line equation?

[wooden wraith]

Plug in x=3 and you'll get the slope of the line

[light quail]

into x+3/x-4 ?

[wooden wraith]

No, into the derivative

[wooden wraith]

what you've got in the parentheses here

[light quail]

i got 0

[wooden wraith]

Hm, not quite

[wooden wraith]

You're still differentiating again

get rid of the d/dx

[light quail]

-7?

is dy/dx different from d/dx

[wooden wraith]

dy/dx is d/dx (y)

the derivative of y

if you just put d/dx in front of something, it means the derivative of that thing

but yeah -7 is good

That's the slope of your tangent line

[light quail]

so y= -7x-6

[wooden wraith]

Not quite, because -6 is not the y-intercept

It's (3,-6) not (0,-6)

You could use the point-slope form

[light quail]

it wants y=

[wooden wraith]

Well you can start with the point slope form, and then rearrange it

Do you know what I mean by point slope?

[light quail]

y+6=-7(x-3) ?

[wooden wraith]

without the x after the -7

yeah, then just subtract 6 to get the y by itself and you're good

[light quail]

y=-13(x-3) ?

[wooden wraith]

no

y = -7(x-3) - 6

It should accept it like that, but you could distribute -7 and combine like terms

[light quail]

ya

that was right

[wooden wraith]

🎉 👍

[light quail]

is there an easier way to do all of that?

[wooden wraith]

Review your basic derivative rules

There isn't really a simpler way to do it, but I'm afraid you struggled because you're not clear on the basics

[light quail]

what are my g(x) and f(x) here?

[wooden wraith]

This is a totally different kind of function

It is not of the form f(x)/g(x)

You'll need the chain rule here

[light quail]

how you know

[wooden wraith]

I'm afraid I can't help you anymore except to emphasize: You really need to review the basics or the rest of this class is going to be very rough for you

[light quail]

o

[wooden wraith]

I'm sorry, i hope that doesn't come across as rude. It really is important that you're very comfortable with things like the power rule and sum rule first, before you tackle things like this

[dim perch]

you can ask yourself if you physically see two functions f and g being divided, or is a function inside another function

might help you decide what kind of rule you're going for

[light quail]

alright well thank you for telling me everything you did. ill have to learn more online

[dim perch]

good plan

always good to do supplementary studying and strengthen your foundations

it just makes everything so much easier when you know why things are happening, and you dont get hung up on simpler parts of the concepts

[light quail]

do you know of anywhere like this but uses voice chat?

[dim perch]

the math discord?

[light quail]

ya or where other math help is

[dim perch]

mm im not sure

this is probably the most popular ppl go to

its hard to find ppl who are willing to dedicate even typing helpful hints out, much less volunteer voice, streaming the work in a call, etc.

or a large group at least

but i wish ya the best of luck in your future studies

perhaps you can find other ppl who are doing similar material in a class/online and get into calls w em so you guys can help each other out :0

[light quail]

yep ty

i feel in voice chat you can find the flaw in someones logic much easier when you hear them explain their issue

.close

[devout snow]

Channel closed

Closed by @light quail

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[sinful zinc]

Just a quick question, what does this mean: solving in terms of sin

[sinful zinc]

Do I need to include sin

I don’t quite get it

[magic pine]

,rccw

[magic pine]

yes

they want you to write it with only sin(x) in there, no cos, sec, or anything of the sort

[sinful zinc]

How is that possible

Cosx to sinx?

Cosx doesn’t equal sinx

[magic pine]

you can have square roots and constants and stuff

just no other trig functions

[sinful zinc]

Oh

I see

So the first one is good

[winter patrol]

make your fraction lines sufficiently long

[sinful zinc]

Yeah good idea

But is the first one good?

[winter patrol]

if the fraction lines are long enough and there's no ambiguity in your expression, then it will be good

[sinful zinc]

Hmmmm

Is sin^2x considered okay

[pseudo basin]

yes, sin^2(x) is okay for your purposes.

but you should still write your fraction lines properly

[sinful zinc]

Ah yeah I see

Thank you all

.close

[devout snow]

Channel closed

Closed by @sinful zinc

Use .reopen if this was a mistake.

[sinful zinc]

.reopen

[devout snow]

✅

[sinful zinc]

Ok for b) is it possible to just multiple Cosx by Cosx and

Is sinx/tanx acceptable?

If not would I multiply cosx by cosx then use an identity

[pseudo basin]

sqrt(1-sin^2(x)) might be what they are looking for. though that is dodgy

[sinful zinc]

Indeed, I don’t think there is any other solution

[devout snow]

@sinful zinc Has your question been resolved?

Channel closed

Closed by @sinful zinc

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[restive river]

How do u differentiate with only constants i don’t rlly get it

[restive river]

i just end up getting b+1/a+1

[winter patrol]

i just end up getting b+1/a+1
can you show your work

[woven radish]

MathIsAlwaysRight

[restive river]

ohhh

i didn't know that rule

[polar chasm]

A is a constant

[restive river]

.close

[devout snow]

Channel closed

Closed by @manic crag

Use .reopen if this was a mistake.

[restive river]

tyvm

[polar chasm]

As you can see, no matter what a is, the slope (dy/dx) stays 0

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[eager crystal]

How do you calculate arctan of -1?

[eager crystal]

I mean it’s obvious that if both sin and cos values are the same

It would be 1

[green kelp]

Yeah, at -π/4

[eager crystal]

Because same value over same value would result in 1

So

I think it would be

Either

(-,+)

Or (+,-)

Therefore

Either 145 degrees

Or

270+45

Which is

315 degrees

So are the answers 145 and 315?

Degrees?

[topaz axle]

↖ ↘

[eager crystal]

What does it mean

Up and down?

[pseudo basin]

you mean not 145 but 135

and arctan outputs values between -90° and +90° anyway so it's -45° you want

[eager crystal]

Oooh

I forgot

Opps

So yeah

It would be on the right half pf the circle

Since -90 to 90

Yup

Much appreciated

🙂

.close

[devout snow]

Channel closed

Closed by @eager crystal

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[restive river]

Cosx+1 =2cos²x/2
How?

[dark dawn]

how what

[warm mesa]

Do you know the formula for cos(2x)?

[restive river]

yes

[quaint citrus]

$\cos(x) + 1 = \frac{2\cos^2(x)}{2}$ ?

[woven radish]

Stephen

[warm mesa]

$cos(2x) = cos^2(x) - sin^2(x)$

[woven radish]

hanzo

[winter patrol]

what are you being asked to do with this equation

[warm mesa]

Now instead of 2x suppose we take x

So x gets replaced by x/2 on R.H.s

[restive river]

x/2

yes

[warm mesa]

Now convert the sin²(x/2) on R.H.s to cos²

Using sin² = 1 - cos²

Then try to rearrange

[warm mesa]

You will get this

[quaint citrus]

@restive river is this ur original problem?

[restive river]

no

[warm mesa]

He just wanted to ask how its derived

[restive river]

am let me check it again

[warm mesa]

$cos^2(x/2) - sin^2(x/2) = cos^2(x/2) - (1 - cos^2(x/2))$
so R.H.S finally it becomes 2cos^2(x/2) -1 $

[woven radish]

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

[warm mesa]

Idk the compile error, its correct

[restive river]

yessssssssssssssssssssss

thanks a lot ^^

[warm mesa]

👍

[restive river]

.close

[devout snow]

Channel closed

Closed by @wraith panther

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[restive river]

I need help plz

It's due in tmmr

Please help me

[mighty sparrow]

$tan(39)=46/a$

[woven radish]

Singularity2024

[restive river]

What's a?

[mighty sparrow]

Rearrange doing trig

On the angle with the green angle

A is the adjacent which is the side shared with the triangle with the orange angle

A =DB

[restive river]

What do I do after I find a

And also how do I rearrange to find a

[mighty sparrow]

Do tan(57)=a/AB

[restive river]

How do I find a

[mighty sparrow]

Just normally trganomatry

[restive river]

K

Forget it

This is too hard

Thx for trying to help me anyways

[mighty sparrow]

Try and think of each side as 2 right Rangel triangles that share a side and call that side A then just do trig to find A and then on the second triangle you can do it again to find AB

[restive river]

I got 46 is AB

@mighty sparrow

[mighty sparrow]

Yeah that’s right

[restive river]

Now what do I do

[mighty sparrow]

That’s the answer isn’t it

[restive river]

No I have to find AD

Not ab

[mighty sparrow]

Now do trig one more time with Ab and the angle 51

$Cos(51)=46/AD$

[woven radish]

Singularity2024

[restive river]

Do I rearrange to find AD

[mighty sparrow]

Yeayh

[restive river]

Oh

Thank you it was right

I have one more question if you don't mind helping

[mighty sparrow]

Top down look from shape to find OC just use Pythagoras

Part a tho is just (23^2+23^2)^0.5

[restive river]

Ok

[mighty sparrow]

This is for part B

[restive river]

Part a I got 32.5 cm

Do I rearrange to find oc for part b

What does the number below oc say?

I got oc is 83.7

I do t know if that right

[mighty sparrow]

Yeah that’s right

[restive river]

I'm confused on what to do next

[mighty sparrow]

That’s the answer

[restive river]

What is?

[mighty sparrow]

83.7

[restive river]

Oh

Are you sure

[mighty sparrow]

Yeah

[restive river]

Ok

Oh

Thank you so much for helping me

I rlly aplreciate

[mighty sparrow]

No problem

[devout snow]

@restive river Has your question been resolved?

[restive river]

Yes

[devout snow]

Channel closed

Closed by @astral nexus

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[mossy remnant]

does this solution make sense?

[mossy remnant]

question is at the top of the picture

[devout snow]

@mossy remnant Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[mild basin]

Trying to visualize this, we say that the range cannot include 3 because

e^x approaches the limit of 0 when we plug in a negative value

but never reaches 0?

1/e^9999999999 for example

[quaint citrus]

It approaches but never reaches u mean?

[mild basin]

ya

never makes it to 0

just really really really close

[quaint citrus]

Yep it never reaches, only gets infinitesimally close

[mild basin]

depending on how big you wanna make that negative x value

so without the +3 the range would be (0, Inf)

not including 0

[quaint citrus]

That’s correct

[mild basin]

there is no exponent that can make a base 0 exactly

this is why we can't have log0(x)? or am I reading that wrong

or would it be log(x) = 0 (cannot happen)

ln(x) = 0 (cannot happen)

[quaint citrus]

well for log(x) = 0, consider the case when x = 1

[mild basin]

oh right

[quaint citrus]

Same for ln(x)

[mild basin]

so the 0 is the exponent in that case

but for log0(x)

0 is the base

[quaint citrus]

Yea u can’t do log_0(x)

[mild basin]

ln(0) = x

what about this

can't do it either

ln to the power of something gives 0 for output

impossible

can we determine what x is from log(x)? or it needs to be log(x) = something?

log_a(b) = c
a^c = b

[quaint citrus]

Log(x) by itself doesn’t let u determine what x is

[mild basin]

OK

thanks!

.close

[devout snow]

Channel closed

Closed by @mild basin

Use .reopen if this was a mistake.

[quaint citrus]

$\log_e{0} = x \therefore e^x = 0$, but that can’t happen as you mentioned

[woven radish]

Stephen

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[smoky gyro]

For part B do we do 600-100

[smoky gyro]

Because

[topaz beacon]

Yes

[smoky gyro]

👍

Do you know how we would do part C

cross wind coming from the south

I suppose you’re supposed to draw a diagram right

[topaz beacon]

Draw your vectors

[smoky gyro]

I’m not too sure if I drew the crosswind vector right but crosswind is wind coming perpendicular from the side of the plane right?

[devout snow]

@smoky gyro Has your question been resolved?

[smoky gyro]

.close

[devout snow]

Channel closed

Closed by @smoky gyro

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[high gulch]

I’m so confused

[supple knot]

!show

[devout snow]

Show your work, and if possible, explain where you are stuck.

@high gulch Has your question been resolved?

[high gulch]

Oh crap sorry I meant to send another one here

Number 73

@supple knot

Nvm I got it

[devout snow]

Channel closed

Closed by @high gulch

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[bleak rain]

How to change the variable from t to cos o in this equation

[devout snow]

Please don't occupy multiple help channels.

[bleak rain]

I am not sure how to do a change of variables

[magic thicket]

Chain rule ?

Since it's y(t) so y(cos o)

[bleak rain]

So y'' is (-sinoy')'? Or does o depend on t also

[magic thicket]

Right so that gets a bit painful, but yes

[bleak rain]

Is it not (o'-sinoy')'?

[magic thicket]

o' = 1 since it's d/do

[bleak rain]

So wait what are we doing when changing variables exatly

We no longer derive with respect to t?

[magic thicket]

dy/dt = dy/do do/dt = -sino y'(cos o)

Literally the chain rule

[bleak rain]

So do/dt is 1?

[magic thicket]

Bruh

o = cos t

[bleak rain]

O=arccos(t)

[magic thicket]

Oh t in [-1, 1]

I guess it avoid adding trig to it in a way. Now you have fractions and square roots instead

[bleak rain]

I think i got it now, thanks a lot

.close

[devout snow]

Channel closed

Closed by @bleak rain

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[restive river]

hello

[restive river]

so

2 log 6^(x+5) +log6^9=2

wee can combine the logs and we get

2 log ^9x+45=2

so can we minus 2 on both sides??

[sick fulcrum]

what is this

$2 \log_6 (x+5) + \log_6 (9) = 2$?

[restive river]

correct

[sick fulcrum]

why not divide

[restive river]

ok we can do that to

so we get...

[sick fulcrum]

isnt it much easier lol

[restive river]

so then\

we are just left with

9x+45

well

log6 ^9x+45

I think

[shy dirge]

you cant do this

[restive river]

oh

[shy dirge]

you have to use the power of number rule

bring the 2 inside

then use sum rule

[shy dirge]

Use this rule

and bring the 2 inside...

[restive river]

so

log 6 ^2x+10

[shy dirge]

No...

$log_6{(x+5)^2}$

[woven radish]

Man-ish

[shy dirge]

you hve to bring it as an exponent

[restive river]

ohh

[shy dirge]

Now, use sum rule

combine both the logs

[restive river]

question

do I have to expand this before I combine them?

[shy dirge]

yes

[restive river]

ok

so

log 6 ^x^2+10x+25 (9)=2

[upper schooner]

[shy dirge]

$log_6 (x^2+10x+25) (9)=2$

[woven radish]

Man-ish

[shy dirge]

thats right

[restive river]

yes

[shy dirge]

whats your idea? how can we proceed?

[restive river]

So now times the 9 in to the whole thing.

then

minus it by 2

[sick fulcrum]

im so shocked this hasnt been finished yet

[restive river]

to get it equal to zero

[shy dirge]

nah nah

no dont do that

[sick fulcrum]

did you not divide it by 2 like I suggested?

[shy dirge]

wait

[restive river]

ok

[restive river]

So move 2 as the exponet

and put the equation on the other side

then we have to factor it

[shy dirge]

So, $6^2 = (9)(x^2 + 25 + 10x)$ ?

[woven radish]

Man-ish

[restive river]

yesss

[shy dirge]

Now divide both the sides by 9

[weak cove]

Why did you introduce a quadratic?

[shy dirge]

i thought it would be easier....

i used to do it by that way

so...

[arctic field]

[weak cove]

Probably would be much simpler to use this rule to simplify $$ log(a)+log(b)=log(ab) $$

[woven radish]

AustinU

[weak cove]

and then to divide both sides by 2

[restive river]

so

times it by 9

[weak cove]

That is a true property of logarithms, but it just unnecessarily complicates this question

[weak cove]

if by "it" you mean x+5 , and keeping it inside of a log base 6, then yes

[shy dirge]

hmm.. okay

[restive river]

SO...

what am i doing??

[weak cove]

,, 2\log_6{(x+5)}+\log_6{9}=2

[woven radish]

AustinU

[restive river]

right

[weak cove]

use this property of logs

to combine the logs

[restive river]

We combined them

[weak cove]

and then tell me what the new equation is

[restive river]

So it would be

log6 ^(x+5)^2(9)= 2

[weak cove]

First divide this by 2

and then you can subtract the log_6(9)/2 to the other side of the equation it is a constant and this will allow you to solve for x.

[weak cove]

using this

[restive river]

So then what are we left with?

[weak cove]

well you tell me

[restive river]

Im not sure

[weak cove]

Which part of those steps are you getting stuck at

feel free to send a picture of your work

[restive river]

Im pretty sleepy. I think im going to give my homework a little break. And work back on it tomorrow

[devout snow]

@restive river Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

Channel closed

Closed due to the original message being deleted

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[gentle mantle]

how is this wrong?

[gentle mantle]

the work i used is on the right

[devout snow]

@gentle mantle Has your question been resolved?

[gentle mantle]

<@&286206848099549185>

[quaint citrus]

Maybe they want the 30-0.5x instead for the integral

How many tries u have

@gentle mantle

[gentle mantle]

Hi sorry

[gentle mantle]

abotu 10\

[gentle mantle]

nope

.close

[devout snow]

Channel closed

Closed by @gentle mantle

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[restive river]

test

[restive river]

Wanted to check my work

[proud perch]

I mean I don't see how else you could do this asides from assuming that it's normal

[restive river]

yea

we do

[proud perch]

Then whats the problem

[restive river]

im checking my work...?

is this correct?

for part i)

[proud perch]

Looks good

Wait

You need to find the t value at (1 - α/2)

Νot at α/2

[restive river]

i did

[proud perch]

Doesn't look like it

https://www.statisticshowto.com/tables/t-distribution-table/

[restive river]

nono

are you talking about ii)?

[proud perch]

For a 95% CI with two tails you want the t value corresponding to 0.025 and 24 degrees of freedom

[restive river]

which part are you talking about

[proud perch]

Your t value for part i

[restive river]

t value?

[proud perch]

Yes, you need the t distribution to estimate the population mean

[restive river]

huh?

we know the sample mean

and pop std deviation

why do we need t score

[distant harbor]

You don't need t score, pop stdv is known

[restive river]

does my answer look right

[proud perch]

Your z score should be 1.96

For the 95% interval

[restive river]

bro what are you talking about

alpha over 2 is the relevant z score

and z (a/2) is the probability of that z score

[proud perch]

Yes, I agree. α = 1 - .95 = 0.05, so α/2 = 0.025

What is the z score there

[devout snow]

@restive river Has your question been resolved?

[restive river]

the z score is 0.025

[proud perch]

Try using a calculator. The area between -z and z should be 0.95

[restive river]

ahhh nvm

the z score is one s.t.

[proud perch]

,w int_(-z)^z exp(-x^2/2)/sqrt(2pi) = 0.95

[woven radish]

Results provided by WolframAlpha

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

Requested by Mr. Gamer#6658

[proud perch]

?

[restive river]

ahhh

the z score needed isnt 0.025

but the z score is

P(z < Z) = 0.025

which is z score of 1.96

oops that was silly of me

[proud perch]

Yeah

The z score is the point on the x axis

[restive river]

i did P(0.025 < Z) = ?

OOPS!

[proud perch]

The 0.025 is the desired area in the left or right tail.

[restive river]

i dont like looking at the pdf

look at the cdf

but yea i got it wrong thanks

[proud perch]

Haha

I could not stand to read that table back in stats

I set everything up as an integral

[restive river]

lol

fair enough

what do i do on number two

i know this is wrong but where did i go wrong lol

[proud perch]

$ε = z \times \frac{\sigma}{\sqrt{n}}$

[woven radish]

Mr. Gamer

[proud perch]

Where we want the z score such that the area to the left is 0.05

,w int_(-inf)^z exp(-x^2/2)/sqrt(2pi) = 0.05

[woven radish]

Results provided by WolframAlpha

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

Requested by Mr. Gamer#6658

[restive river]

Ty

Im not supposed to use integration

[proud perch]

Lol good luck with those tables then

[restive river]

will do lol

[proud perch]

My bad, we actually want the area to the right to be 0.05. z score here should be +1.64

@restive river

Which makes sense right? Epsilon should be positive so x - eps is less than x

[restive river]

so we want the area to be the right to be .95 though

isnt it a lower bound?

heres how i did it

$\epsilon = -(z_{\alpha}) * \frac{\sigma}{\sqrt{n}}$

[woven radish]

! matthewzz

[restive river]

where alpha is the amount of probability you want above the the lower limit

so

$\epsilon = -(1.64) * \frac{34.03}{5}$

[woven radish]

! matthewzz

[restive river]

$\epsilon = -11.16$

[woven radish]

! matthewzz

[restive river]

this is right? @proud perch

[proud perch]

Does it make intuitive sense for the lower bound of the estimate to be greater than the sample mean itself?

[restive river]

it isnt

oh shit

yea it is

LOL

sadlkbfsldkbg

[proud perch]

It will be, because you will then be subtracting a negative quantity

[restive river]

yee

wait but

if its the lower limit

dont we want .95 of the probability to be above

so we take the z score of .95 and invert it

[proud perch]

We want P(x-ε <= μ), meaning this has a right tail

The right tail being P(x-ε >= μ) = 0.05

@restive river

[restive river]

oh yea

i was confused on this

can you explain

[proud perch]

Explain what

[restive river]

P(x <= μ + ε) should be 0.95

right

?

[proud perch]

Yep

[restive river]

so why does it switch again?

[proud perch]

But there's a reason why we write "x-ε <= μ"

[restive river]

wait

[proud perch]

Avoid doing algebra inside the P(), it obscures the relation

[restive river]

ill start from the top

P(u <= x - e) = 0.95

thats by the question right

[proud perch]

Other way around

The question states P(x - ε <= μ) = 0.95

[restive river]

ok yea

we set e s.t. the true mean is usually larger than our sample mean

thats how id state that in words

then what

[proud perch]

Not quite

[restive river]

wait

now?

[proud perch]

We want a lower bound for μ, which is x - e; let's call this L.
We desire that there is a 95% chance that L is less than μ

[restive river]

yes

now whats the algebraic manipulation

[proud perch]

How do I explain this

[restive river]

do we do 1 -

[proud perch]

"x-e" is your variable.

[restive river]

to flip the signs

[proud perch]

If that makes sense.

[restive river]

do we do 1-(left = right)

and then manipulate the inequality to solve for x

instead of mu

[proud perch]

P(L <= μ) = 0.95
We define:
L = x - ε, because we desire the lower bound to be less than the sample mean. (This means ε>0)
Now the only issue is solving for a suitable ε, which we can do by taking the z score and multiplying it by the standard error.

No need for algebra inside the P(), that is just messy and unnecessary. I'd actually argue that it obscures the relation.

Treat "x-e" as a single quantity

[restive river]

im confused

[proud perch]

?

Let me put it this way. If you desired:
P(X <= 1)
Do you have a left tail, or a right tail?

[restive river]

left

[proud perch]

Correct. So if you have P(L <= μ), is that a left tail or a right tail?

[restive river]

left

[restive river]

this z score is 1.96 right?

[proud perch]

So what would the diagram look like? What region under the curve do you shade in?

[proud perch]

No, 1.96 gives the 95% CI for a TWO TAILED test.

What we desire is a z such that the area under the pdf from -inf to z is equal to 0.95

Let us see:

,w int_(-inf)^z exp(-x^2/2)/sqrt(2pi) = 0.95

[restive river]

oh shit

wait

i think i get it

[woven radish]

Results provided by WolframAlpha

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

Requested by Mr. Gamer#6658

[restive river]

itd be something like this

we want the area in white

to be .95

[proud perch]

The opposite.

[restive river]

huh??

if mu is 0

dont we want xbar - epsilon to be the lower limit of the probability

[proud perch]

We desire an L such that we are 95% sure that L is less than or equal to μ

[restive river]

ohhh

so something like this

?

where this is the distrubution of x

and mu is somewhere in the white

[proud perch]

Yes, now you're getting it

[restive river]

we want to be 95% sure that x is less than the limit point

is the limit point

xbar + epsilon?

[proud perch]

Again, think of L as your variable.

[restive river]

ohhh

so if this is the distribution of xbar - epislon

that point is mu

and we want L <= mu

[proud perch]

Yes, exactly

[restive river]

hmm okay thats a little tricky to think about at first

so is that point up there

where it changees

[proud perch]

The important thing to remember is that "x-e" is a single quantity, our lower bound L

[restive river]

x\bar?

yes yes

i understand

[restive river]

?

[proud perch]

The shaded region represents where L<=μ, the white region represents where L>=μ

[restive river]

hmm

can you try to label the graph with x, e, mu, and x-e

ik

[proud perch]

Well we can't really label x and e on this graph

Because our horizontal axis IS "x-e"

This is the pdf of "x-e"

[restive river]

mu would be somewhere in the white correct?

[proud perch]

The entire horizontal axis is the distribution of L

[restive river]

ahhh ok

is the mean of the distribution

xbar - epsilon

[proud perch]

The mean is unknown

Thats the whole point

Because if we knew the mean of this distribution, we would know μ

[restive river]

whatd u get the answer as?

[proud perch]

For the whole problem?

Your confidence interval is:
(x - ε, inf)
Where ε = Z_(0.95) × σ/sqrt(n)

And Z_(0.95) = +1.64

[restive river]

wait i got it

no need for another x-e graph

lol

[proud perch]

Lmao

[restive river]

This good?

[proud perch]

Yes

Now state the CI in the form (L, inf)

[restive river]

yee

[proud perch]

Where L is x-e

[restive river]

yep

for this it'd just be taking the difference then solve

right?

[restive river]

.close

[devout snow]

Channel closed

Closed by @rain fulcrum

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[restive river]

where am i going wrong

doing it manually

im 99% sure that 0.67 is the answer

since i used the formula on the review sheet our prof gave us

but im not sure where im going wrong manually

[restive river]

oops got it

.clsoe

.close

[devout snow]

Channel closed

Closed by @rain fulcrum

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[full charm]

Can somebody clarify for me what repeating variables in dimensional analysis is and what it does in terms of buckinghams palace?

[devout snow]

@full charm Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[eager crystal]

Can someone please help me with this problem

How do you solve a

[restive river]

just put 7.8 in x

[eager crystal]

So

We get 4.8?

And

4.8pi/10

So

[restive river]

2 + 5cos (π/10)(4.8)

then solve

[eager crystal]

Cos(4.8pi/10)

Right?

[restive river]

yes

and then calculator

if ur allowed to

[eager crystal]

Oooh

I was wondering

If i was allowed to use the calculator pr not

Would you use it?

I just don’t know the direction

[pastel pasture]

It might be possible without a calculator

[eager crystal]

Do most people use a calculator on that type of question?

It’s high school math for context

[pastel pasture]

nope I don't think it is

[pastel pasture]

Yeah I'd assume

[eager crystal]

Alright thanks

Lemme use it and check the answer

One sec

Ok this is so weird

My calculator and google calculator give me different values

Even when i put the same input

Oooooh

Mvm it took it as an angle value

Cool

Now i know how to use my calculator lool

Thank you everyone that was really helpful

.close

[devout snow]

Channel closed

Closed by @eager crystal

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[waxen lynx]

how does the numerator become 4?

[quaint citrus]

I didn’t expand the whole thing, but notice how e^-x times e^x = 1

[upper schooner]

And you basically have $(e^{x} \pm e^{-x})^{2} = e^{2x} \pm 2 + e^{-2x}$

[woven radish]

@upper schooner

[waxen lynx]

o

sorry last question

how did ln(2)*2^4x *4

Become 2^4x+2

[quaint citrus]

Exponent properties

[woven radish]

Stephen

[waxen lynx]

o

okok ty

[quaint citrus]

Np

[devout snow]

@waxen lynx Has your question been resolved?

Channel closed

Closed by @waxen lynx

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[restive river]

i need help im in 6th grade and im 11

[manic sedge]

<@&268886789983436800> he is 11

[wanton thunder]

If you are 11 you should not be on discord.

[elfin lark]

already taken care of

.close

[devout snow]

Channel closed

Closed by @elfin lark

Use .reopen if this was a mistake.

[manic sedge]

@inland jacinth dm me

Oh

I will miss him

[devout snow]

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[worthy vault]

would this be a c e
as the only way for f`(x) < 0 for all x would be for f(x) to be -ax where a any can be any real number grater than 0

[worthy vault]

so f(x) is linear

[lofty glacier]

@worthy vault f(x) cant be linear

[worthy vault]

huh XD

if f(x) is linear the derivative is constant meaning that we can easily conclude to f`(x) < 0

[lofty glacier]

but what is f(x) = x

then its derivative will be 1

which is not <0

[worthy vault]

yeah

did u not read

[worthy vault]

.

-ax where a is any real number greater than 0

meaning

-5x

for example

which is -5 constnat

for which f`(x) < 0 is true

[lofty glacier]

okok i didnt read the aboce part my bad

[worthy vault]

is this not just only d
since a is not always running faster
and at points (0,0) and (14, 100) they have the exact same speed
and it can be b or c since they finished at the same time meaning runner be finished at the same time as runner a

[devout snow]

@worthy vault Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[restive river]

hi

[restive river]

can sm1 help me pls lol

do i need to work out the angle from the arc length?

[true geode]

Yes

There is a formula for that

Do you know about radians ?

[restive river]

nah

havent been taught that yet

[true geode]

Arc lenth = x/360 × 2Pi r

[restive river]

ohh ok

where do radians come into play with this

[true geode]

Its not nessisary

Just makes life easier

If you haven't studied them yet then dw

[restive river]

do i divide it by 2Pi r, and then multiply it by 360 to get the angle

[true geode]

Yes

[restive river]

then do angle/360 x pixr^2

[true geode]

No
What

Not pi r²

[restive river]

to work out area of sector

[true geode]

Yes
But the question doesn't ask that

[restive river]

oh.

lmfao

misread it

mb

the previous questions were all abt area of sectors so got mixed up

how do i work out to the nearest degree lol

sorry

i got 6.187944187

[true geode]

Are you sure ?

It would be around 60 degrees not 6 degrees

[restive river]

10.8/(2pix10^2)x360

oh

i squared it.

fucks sake

ye

ok i got 61.879...

62

thanks a lot

!close

.close

[devout snow]

Channel closed

Closed by @pastel plank

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[dapper quail]

I need help understanding logs, how can I learn to do them in my head? Kinda like exponents

[hybrid snow]

I mean, they're inverse exponents basically

Like if 2^x = 8, then x = log_2(8)

[devout snow]

@dapper quail Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[devout snow]

Channel closed

Closed by @lethal osprey

Use .reopen if this was a mistake.

Available help channel!

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>.
• Type the command .close to free the channel when you're done.
• 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.

[stone stump]

if B is some matrix, can you say what the eigenvalues of p(B) are where p is any polynomial

[inland vault]

Not sure what p(B) means. We haven't learned about the relationship between polynomials and eigenvalues. Our prof told us that the iteration is convergent iff the spectral radius of T is less than 1, but he left the proof as an exercise. Maybe it could be relevant here?

[devout snow]

@inland vault Has your question been resolved?

[devout snow]

@inland vault Has your question been resolved?

[inland vault]

Got an idea. Symmetric positive definite implies that 1) all the diagonal elements of A are positive and, 2) all the eigenvalues of A are real and positive.
If 1-A similar to positive definite matrix implies that the diagonal elements of 1-A are positive then we could conclude that the diagonal elements of A must be smaller than 1. Then maybe we can use the fact that the eigenvalues of A are smaller than the norms of A to bound the spectral radius of A from above with some norm of A to less than 1
nvm, didnt work

[devout snow]

@inland vault Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.