Pianostreet calculus group

[rachmaninoff_forever]

Nah.  Initially awkward and uncomfortable, but ultimately all good.

She's probably gonna flame me like my other teachers.  This is NOT good.

All I know is that I will feel very salty.

[j_menz]

She's probably gonna flame me like my other teachers.  This is NOT good.

All I know is that I will feel very salty.

Possibly, but surely that could be done in just one morning. Every morning suggests she's more likely to be actually going to tutor you.

[rachmaninoff_forever]

If y= asinct + bcosct where a, b, and c are constants, then what is the second derivative of that?

I'm stuck where y'' is [ac^2(-sinct)] - [bc^2(-cosct)]

I may be wrong in my execution because it's not any one of the multiple choice answers.

[chopin2015]

If y= asinct + bcosct where a, b, and c are constants, then what is the second derivative of that?

I'm stuck where y'' is [ac^2(-sinct)] - [bc^2(-cosct)]

I may be wrong in my execution because it's not any one of the multiple choice answers.

what are the multiple choice answers? Maybe you should help me!

[rachmaninoff_forever]

what are the multiple choice answers? Maybe you should help me!

ac^2(sint+cost)

-c^2y

-ay

-y

a^2c^2sinct-b^2c^2cosct

[rachmaninoff_forever]

Wait disregard my first answer.  I didn't do product rule on the first derivative. 

Still working on it...

[chopin2015]

ac^2(sint+cost)

[jas_sorian]

If y= asinct + bcosct where a, b, and c are constants, then what is the second derivative of that?

Just a guess:
y'= a((cosct)(c))+b((-sinct)(c))
  = ac(cosct)-bc(sinct)
y''= ac((-sinct)(c))-bc((cosct)(c))
   = -a(c^2)(sinct)-b(c^2)(cosct)
   

[rachmaninoff_forever]

ac^2(sint+cost)

How did you get that?

[chopin2015]

How did you get that?

You mean the work? My dad's friend(software engineer) did it for me. I'm more of a physics gal. Sorry
 Was it the right answer?

[rachmaninoff_forever]

You mean the work? My dad's friend(software engineer) did it for me. I'm more of a physics gal. Sorry
 Was it the right answer?

No, it was -c^2y

[faulty_damper]

So Rach,
How did the meetings with your teacher go?  Were you right or wrong about what you expected?  Was she as scary as you thought?  Did you actually received help?

[rachmaninoff_forever]

So Rach,
How did the meetings with your teacher go?  Were you right or wrong about what you expected?  Was she as scary as you thought?  Did you actually received help?

First she tore me apart.

Then we went over the review worksheet I did...

I GOT EVERYTHING RIGHT!


She felt soooooooooooooooooooooo salty!!!  But then she decided to tear me apart more.  She thinks that I'm trying to fail her class.  We then went over another test that I failed, and it turns out I wrote down the right answers for like five problems but circled the wrong ones.

[faulty_damper]

Umm... so you're teacher did have reasons to be concerned but was wrong about what was wrong.  You clearly need glasses!

(or a magnifying glass.)

[rachmaninoff_forever]

Umm... so you're teacher did have reasons to be concerned but was wrong about what was wrong.  You clearly need glasses!

(or a magnifying glass.)

Well there were a couple problems where I did stupid algebra mistakes. 

Like I remember I added 5x-7x and got 13x.


And I already wear glasses.

[chopin2015]

First she tore me apart.

Then we went over the review worksheet I did...

I GOT EVERYTHING RIGHT!


She felt soooooooooooooooooooooo salty!!!  But then she decided to tear me apart more.  She thinks that I'm trying to fail her class.  We then went over another test that I failed, and it turns out I wrote down the right answers for like five problems but circled the wrong ones.

First, sorry about the answer, but I am glad you figured out.

Also, maybe you should make sure you are getting enough sleep? And it sucks that your teacher isn't cool to note that you wrote good work. Good luck though!

[outin]

She felt soooooooooooooooooooooo salty!!!  But then she decided to tear me apart more.  She thinks that I'm trying to fail her class. 

Now seriously...You do understand that she is concerned for you and trying to help? I am certain she would have much more fun spending her mornings with a cup of coffee and chatting with her colleques instead of spending time with you (even though you are obviously a very charming fellow). I hope you are just joking but if not, time for a reality check 

[chadbrochill17]

Well there were a couple problems where I did stupid algebra mistakes. 

Like I remember I added 5x-7x and got 13x.


And I already wear glasses.

Dude the hardest part of calculus is the algebra. Seriously. Stupid mistakes will screw you up so bad.

[lloyd_cdb]

Dude the hardest part of calculus is the algebra. Seriously. Stupid mistakes will screw you up so bad.

This is true for just about everything after algebra lol.  We take the simple math for granted while focusing intently on remembering the formulas and methods to solve the problems.  This plagued me throughout college.  The major thing I found that helped me was going through the problems a second time when I was done and solving it completely independently.  I'd usually account for at least half my dumb algebra mistakes which could bump my grade up at least 5-10%.  Clearly this is time dependent on tests, but if you spend enough time doing practice problems while studying, you won't be focusing on actually remembering the methods as opposed to knowing it more instinctively. 

[rachmaninoff_forever]

What's the derivative of sin^2(x)?

Note: it's not sin(x)^2
        It's sin^2(x)

Would you just do power and chain rule?  So would it be [2sin(x)][cos(x)]?

EDIT:

I also need the derivative of sin(X)^2

and the derivative of ln^4(15x)

and the derivative of log5(x-7)

I have a test tomorrow and that's what I'm unclear about.  When you have ln raised to something and when you have log of something.

[lloyd_cdb]

What's the derivative of sin^2(x)?

Note: it's not sin(x)^2
        It's sin^2(x)

Would you just do power and chain rule?  So would it be [2sin(x)][cos(x)]?

EDIT:

I also need the derivative of sin(X)^2

and the derivative of ln^4(15x)

and the derivative of log5(x-7)

I have a test tomorrow and that's what I'm unclear about.  When you have ln raised to something and when you have log of something.

 sin^2(x) = [sin(x)]^2 which is NOT the same as sin(x^2).  Your answer for the first question is correct, and is the same answer for the first question of your edit.

ln^4(15x) to my knowledge also means ln(15x)^4 as stated above (I hate typed math), so:

(60/15x)*ln(15x)^3:

You just use the chain rule.

for log5(x-7), remember this is equal to [ln(x-7)]/[ln(5)], so the derivative is:

1/[(x-7)ln(5)]


Basically for ln and log, just use the chain and power rules. And loga(x) = ln(x) / ln(a), so the derivative is 1/[x ln(a)], just remember your derivative rules for ln when applying this.

[rachmaninoff_forever]

THAT TEST WAS FREAKING IMPOSSIBLE!!!

You know how like you get some questions on the test that are just quirky?  Not like you don't know the subject, but they're one of those rare questions that you have to do differently because it goes against what you were taught a little bit.  Kinda like a trick question.

THE WHOLE TEST WAS LIKE THAT!!!

[chopin2015]

Lol, I had a Philosophy test today and I rather enjoyed it. It was on theodicies/problem of evil, my essay question was on the Free Will theodicy. So fun!  So glad all my math classes are out of the way, but I am like 1000 years old.

[lloyd_cdb]

my essay question was on the Free Will theodicy. So fun!

Ewww.... Essays.... 

[lostinidlewonder]

Haha post on a maths forum they will explain it very well for you.... I guess it's fun to post it here though

[faulty_damper]

Philosophy of religion class?

That had to be one of the funnest classes I've ever had.  And I had an essay question asking about my opinion of free will.

1. No, we don't have free will.
2. Yes, we do have free will.

I think I chose the prior, we don't have free will.
That was such a long time ago, with Prof. Hood.  Really fun discussions in class.

But the essay was easy.  Why?  Because we knew a lot about the question.  Essays are hard when you don't know much about the topic.

[lloyd_cdb]

My problem with essays is usually less about the content, but about the format.  Schooling is typically incredibly rigid.  In science and math classes, this is clearly a result of the content.  However, in the 'opinion' classes, the rigidity is a result of the teacher.  My major complaint with my essays in school was that teachers would give an essay topic and say "write me 6 pages".  Why ask a question if you don't give the student the ability to answer it how they think it would be most effective?

Teacher:  Class, write me 6 pages on why I shouldn't fart in class.

Student 1:  Farts come from air we swallow, gases seeping out of our blood stream, as well as digestion from bacteria as well as chemical processes.  The actual composition of farts are variable.  Most of the oxygen we swallow is typically absorbed through the digestive track.  The aspects that makes fart smell is the nitrogen and sulfur composition of the expelled gas.  The average human farts half a liter per day.  Given that the average person farts 14 times per day, the average expulsion consists of 1/28th of a liter.  Our classroom is 20 ft x 10 ft with 7 ft ceilings.  This results in a cubic footage of 1400 ft^3, which comes out to ~400,000 liters.  This gas diffuses to .00000008% of the gas in the room. etc., etc., etc......

Me: Because it stinks, and it's socially regarded as very rude to fart in confined spaces.

Which one of us actually answered the question?  I receive a 60%, Student 1 receives a 95%.  I lose 40% for not writing enough, Student 1 loses 5% because they didn't actually answer the question.  THIS is why I hate essays, and by essays, I really mean the teachers that give page and word limits.

EDIT:  Clearly all my posts are essays.  I do, in fact, actually enjoy writing and being detailed about my opinions.  My point being that I don't hate writing, but hate the school interpretation of my writing.  Call me bitter, /shrug.

[chopin2015]

My English teacher is terrorizing me. He keeps giving me low scores because he doesn't understand what I write about. I want to kick him in the b***s.

[lloyd_cdb]

My English teacher is terrorizing me. He keeps giving me low scores because he doesn't understand what I write about. I want to kick him in the b***s.

I had an economics teacher give me a low grade on a test because I "used techniques we hadn't learned in class".  I didn't realize my grade should go down for being ahead of the class.  I'll dumb my answers down next time...

[chopin2015]

I had an economics teacher give me a low grade on a test because I "used techniques we hadn't learned in class".  I didn't realize my grade should go down for being ahead of the class.  I'll dumb my answers down next time...

lol

[chadbrochill17]

Also, Rach, have you discovered Wolfram Alpha yet?

I mention it not so it does your homework for you, but that it will give you the right answer but also show you the steps. I highly recommend you check it out.

[lloyd_cdb]

I didn't know about Wolfram Alpha.  That's really helpful, thanks for the tip.

[rachmaninoff_forever]

The radius r and area A of a circle re related by the equation A = pi(r)^2.  Write an equation that related dA/dt to dr/dt.

Apparently the answer is dA/dt = 2pi(r)[dr/dt]

I think I kinda get the logic, but could someone go through the work for that?

EDIT:

I actually know the logic, but I don't know WHY.

[rachmaninoff_forever]

When a circular plate of metal is heated in an oven, it's radius increases at the rate of 0.01 cm/sec.  At what rate is the plate's area increasing when the radius is 50cm?

[fftransform]

When a circular plate of metal is heated in an oven, it's radius increases at the rate of 0.01 cm/sec.  At what rate is the plate's area increasing when the radius is 50cm?

Area = (pi)(r^2)
d(Area) = (pi)(2r)(dr) = (pi)(2r)(.01) = (pi)(2)(r)(.01) = (pi)(2)(50)(.01) = (pi)(100)(.01) = pi.


This problem is so straight-forward that I wonder if you have actually tried it on your own at all . . .

[jas_sorian]

The radius r and area A of a circle re related by the equation A = pi(r)^2.  Write an equation that related dA/dt to dr/dt.

Apparently the answer is dA/dt = 2pi(r)[dr/dt]

I think I kinda get the logic, but could someone go through the work for that?

EDIT:

I actually know the logic, but I don't know WHY.

A=pi(r^2)
differentiate both sides with respect to time (treat A and r as a function of time maybe? not sure  )
dA/dt=pi(2)(r)(dr/dt)
dA/dt=2pi(r)(dr/dt)

[lloyd_cdb]

A=pi(r^2)
differentiate both sides with respect to time (treat A and r as a function of time maybe? not sure  )
dA/dt=pi(2)(r)(dr/dt)
dA/dt=2pi(r)(dr/dt)

Exactly.  I assume you were given t= time, and this was the first part of a multi-part question to give you some common sense for solving the next problem.  Most simply, you need to remember than ANY derivative is a measure of the rate of change of any variable in respect to another variable.  So you need to understand that, in respect to t, A changes based on how r changes, and r changes based on how A changes.  In the next part, you are given the rate of change of r in respect to time, which is exactly what dr/dt means, which makes it a simple plug and play question.

[rachmaninoff_forever]

What the heck is...

the dirivative of...

(the inverse of sinx) - (the square root of 1-x^2)

I got (1-x)/(the square root of 1-x^2) but that's not one of the answer choices.

[lloyd_cdb]

What the heck is...

the dirivative of...

(the inverse of sinx) - (the square root of 1-x^2)

I got (1-x)/(the square root of 1-x^2) but that's not one of the answer choices.

to start off, you need to know the derivative of arcsin(x) (inverse sin).

y = arcsin(x) is equivalent to sin(y) = x.  Now you take the derivative with respect to x.
using the chain rule:

cos(y)(dy/dx) = 1
dy/dx = 1/cos(y)

I assume you've learned pythagorean identities, or else you wouldn't be able to figure this out.  The pythagorean identity of cos^2(y) = 1-x^2, so cos(y) = sqrt(1-x^2).  If you haven't done this yet, a) i'd be surprised b) it's simply a^2 + b^2 = c^2, while using soh cah toa.

Hence:

dy/dx = 1/[sqrt(1-x^2)]

I assume you can figure it out from there.

EDIT: after taking 5 seconds to look at my post, this means that the answer IS (1-x)/[sqrt(1-x^2)], so I'm not quite sure why that isn't one of the options.  What are the actual answer choices?  It might just be an expansion of that.

[rachmaninoff_forever]

I am the biggest idiot...

[jas_sorian]

It might just be an expansion of that.

(sqrt(1-x^2))/(1+x)?

[lloyd_cdb]

(sqrt(1-x^2))/(1+x)?

well, the derivative of inverse sin is definitely 1/[sqrt(1-x^2)]. The second part can be written as (1-x^2)^1/2, using chain and power rules you have (-2x/2)(sqrt(1-x^2))^-1/2 = -x/sqrt(1-x^2)

so... I was being stupid and tired last night and didn't subtract the negative (dumb algebra), silly negative signs.  It is the reciprocal of what you wrote:

(1+x)/sqrt(1-x^2)

I am the biggest idiot...

And since we both had done dumb algebra, as we had discussed previously...

I am also an idiot.

[scherzo123]

I'm doing geometry right now, and it's eassyyyyyy.

[rachmaninoff_forever]

I'm doing geometry right now, and it's eassyyyyyy.

Wait till you get to calc...

[rachmaninoff_forever]

Okay so this is how it is...  I don't wanna have to see my Math teacher tomorrow morning, so please answer ths question for me.

A tank of water in the shape of a cone (point down) is leaking wager at a constant rate of 2 cubic feet per hour. The base of the radius of the tank is 5 ft and the height is 14 ft.  At what rate is the depth of the water in the tank changing when the depth of the tower is 6 feet?

I'm stuck with the derivative.  I think I got it, but I don't know.  And I think I know what to plug in, but I still don't know.

[lloyd_cdb]

V = pi/3 * r^2 * h

The question asks for the rate of change of depth in regard to time, while you're given the rate of change of V (dV/dt = -2).  So you need to find dh/dt.

dV/dt = pi/3(r^2*dh/dt)

you can solve for the radius of the cone at h=6, 14/5 = 6/r, r=2.14.

-2 = pi/3(2.14^2)dh/dt

solving for dh/dt:

dh/dt = -0.42 ft/hr

Pretty sure that's right, barring anymore algebra mistakes...

[scherzo123]

Wait till you get to calc...

I'm planning to take calculus AP junior year (high school)! 

[chadbrochill17]

I'm planning to take calculus AP junior year (high school)! 

Is that AB or BC

[rachmaninoff_forever]

Is that AB or BC

Isn't calc 3 an AP course too?

There's only like 10 kids taking that class in my school and I heard they talk about the philosophy of math.

[chopin2015]

Isn't calc 3 an AP course too?

There's only like 10 kids taking that class in my school and I heard they talk about the philosophy of math.

omgosh, really? Is that fun?