1. ## 4 Hard Questions!! Help Please!!

Can you please show work? You do not need to answer all the problems even if you know just one your help is appreciated

1) A storage tank in the shape of a right circular cone has a height of 6 meters and a base of radius 2 meters. The cone is inverted and fluid is pumped in at a rate of .002m^3-minute (2 liters/min). At what rate is the level of the fluid rising when the tank is filled to a height of 3meters? Use V= (pie X r squared X h)/3 and R = (H)/3

2) Verify the mean-value theorem for
a) f(x) = x^3 - 3x^2 - 13x + 15 on (-3,1)
(b) f(x) = cos 2x - 2 cos^2 x on ((-pie/2),(pie/4))

3) Locate and classify all critical points, points of inflection, intervals where the Function increases/decreases and where the Function is concave up/down for
a) f(x) = x^4 - 4x^2 + 4x^3 + 1
b) f(x) = (1+ squareroot(x) + cuberoot(x))^9
c) f(x) = x/(ln x)^2
d) f(x) = e^x + e^-2x
e) f(x) = e^(x^3 - x)

4) Using differentials, approximate the numerical value of
a) cuberoot(130)
b) ln (3), you know ln (e) = 1
c) log (8), you know log (10) = 1

2. Originally Posted by alulla
I would ask you the same question ...

3. Originally Posted by alulla
Can you please show work? You do not need to answer all the problems even if you know just one your help is appreciated

1) A storage tank in the shape of a right circular cone has a height of 6 meters and a base of radius 2 meters. The cone is inverted and fluid is pumped in at a rate of .002m^3-minute (2 liters/min). At what rate is the level of the fluid rising when the tank is filled to a height of 3meters? Use V= (pie X r squared X h)/3 and R = (H)/3

2) Verify the mean-value theorem for
a) f(x) = x^3 - 3x^2 - 13x + 15 on (-3,1)
(b) f(x) = cos 2x - 2 cos^2 x on ((-pie/2),(pie/4))

3) Locate and classify all critical points, points of inflection, intervals where the Function increases/decreases and where the Function is concave up/down for
a) f(x) = x^4 - 4x^2 + 4x^3 + 1
b) f(x) = (1+ squareroot(x) + cuberoot(x))^9
c) f(x) = x/(ln x)^2
d) f(x) = e^x + e^-2x
e) f(x) = e^(x^3 - x)

4) Using differentials, approximate the numerical value of
a) cuberoot(130)
b) ln (3), you know ln (e) = 1
c) log (8), you know log (10) = 1
Correct me please if I am wrong.
You are asking us to do these problems in detail for you.
You then are absolved of any necessary to do any work on your part.
You plan to use the reply as if it were your own.
If this is wrong, what is right?

4. Originally Posted by Plato
Correct me please if I am wrong.
You are asking us to do these problems in detail for you.
You then are absolved of any necessary to do any work on your part.
You plan to use the reply as if it were your own.
If this is wrong, what is right?
You are wrong. I know you won't believe me but I have an important test tomorrow and my professor gave us review sheets. This isn't being collected or even looked at. I just need to see how other people are solving it so I can see what I am doing wrong. If you want I can post my work:

Here:

For number 1) I have almost no work. I only drew the Cone out

/\
/ \
/ \
/ \
/ \ the height is 6 and the radius is 2 as you know..but what do I do from there? The only thing I thought of doing was r = h/3 = .002...h = .006...which makes no sense whatsoever.

number 2a) I know I have to use the formula f(b) - f(a)/b-a so
0-0/-4 which is 0/-4....but what do I do with that??? I'm so confused

number 3) I know to find the critical points i have to do f'(x) = 0 and for points of inflection i have to f"(x) = 0 and for increases and decreases and concave up and concave down I just have to plug them in to see + or -...but when I do 3a I get stuck at 4x^3 + 12x^2 - 8x = 0 (the derivative) and then I get that down to 4x(x^2 + 3x - 2)..but how does that factor??

I've tried with great effort to try to do these problems, but the fact remains I just don't understand how to do it. If anyone could help it would be greatly appreciated. I know you probably won't believe me but this is for my own help...I myself don't cheat if someone cheats they are only cheating themselves..whats the point?

5. If you are having a test on these questions, then you have seen similar questions before.
Therefore, you have done similar questions before.
So show us some effort on your part.
If you cannot do any of these, then why should you not fail?

6. Originally Posted by Plato
If you are having a test on these questions, then you have seen similar questions before.
Therefore, you have done similar questions before.
So show us some effort on your part.
If you cannot do any of these, then why should you not fail?
To be honest I deserve to fail ...I have known about this test since Thursday and have made almost 0 effort to study. This weekend I hung out with my cousins in another state..and was looking forward to having a 2 hour study session with a tutor my college provides on Monday. Unfortunately the tutor cancelled, and now I am stuck . So I am looking towards the great Internet for help hoping for someone to help me. I am a High School student taking a College Class for Extra Credit..I was shocked to see the pace at which the professors taught. I'm very sorry if you don't believe me though =(.

7. Originally Posted by alulla
To be honest I deserve to fail ...I have known about this test since Thursday and have made almost 0 effort to study. This weekend I hung out with my cousins in another state..and was looking forward to having a 2 hour study session with a tutor my college provides on Monday. Unfortunately the tutor cancelled, and now I am stuck . So I am looking towards the great Internet for help hoping for someone to help me. I am a High School student taking a College Class for Extra Credit..I was shocked to see the pace at which the professors taught. I'm very sorry if you don't believe me though =(.
Thank you for being honest with yourself. That is a rare happening.
Good luck. Learn from this.

8. Originally Posted by Plato
Thank you for being honest with yourself. That is a rare happening.
Good luck. Learn from this.
Okay thank you. Is there anyone else who would care to help me a little?

9. ## Hints.

Originally Posted by alulla
Can you please show work? You do not need to answer all the problems even if you know just one your help is appreciated

1) A storage tank in the shape of a right circular cone has a height of 6 meters and a base of radius 2 meters. The cone is inverted and fluid is pumped in at a rate of .002m^3-minute (2 liters/min). At what rate is the level of the fluid rising when the tank is filled to a height of 3meters? Use V= (pie X r squared X h)/3 and R = (H)/3

2) Verify the mean-value theorem for
a) f(x) = x^3 - 3x^2 - 13x + 15 on (-3,1)
(b) f(x) = cos 2x - 2 cos^2 x on ((-pie/2),(pie/4))

3) Locate and classify all critical points, points of inflection, intervals where the Function increases/decreases and where the Function is concave up/down for
a) f(x) = x^4 - 4x^2 + 4x^3 + 1
b) f(x) = (1+ squareroot(x) + cuberoot(x))^9
c) f(x) = x/(ln x)^2
d) f(x) = e^x + e^-2x
e) f(x) = e^(x^3 - x)

4) Using differentials, approximate the numerical value of
a) cuberoot(130)
b) ln (3), you know ln (e) = 1
c) log (8), you know log (10) = 1
//

I just thought I could give hints for the problem you posted. you are supposed to find the rate at which the level of the fluid is increasing inside the container. Level corresponds to 'h' which means, you gotta find a value of dh/dt. This gives you the rate at which the height of the liquid changes in the container.

V = [pi * r^2* h] /3

You have already got the important substitution to be made. r = h/3
So, V = [pi * (h^2/9) *h ]/3
= [pi * h^3]/ 27

Now, we've expressed the volume entirely as a function of the height. You can follow this up and do the steps given below.

i) By elementary differentiation, find an expression for dv/dt.
ii) This value dv/dt is given in the question as 0.002 m^3/min.
iii) Plug-in other values such as pi and h as given in the question.
iv) Simplify the equation to find the value for dh/dt.

This is quite easy. Hope it helped your preps.

2) a) You were right in your step where you found that [f(b)-f(a)]/b-a = 0. Now, you gotta find a c belonging to [-3,1] such that it f '(c)= 0. f'(x) = 3x^2-6x-13 .

Just solve this equation for the value '0'. i.e 3c^2 - 6c -13 = 0. Basic theory on quadratic equations would help you with the rest of the problem.

b) the 'b' part would be simple as it involves similar steps as to that of 2.a.

MAX

10. Thank you max!!

With your help I think I got the solution

dH/dT= (dV/dT) * (9/pie) * (1/3) * (1/h^2)

dH/dT=~2.12

11. Hmm.. I got something a little different. v = pi r^2 h / 3 = pi h^3 / 27
dV / dH = pi (h^2) / 9
so when h = 3
dV / dH = 9 pi / 9 = pi
So we have dV / dT = dV / dh x dh / dt
0.002m^3/min = pi m^3 / m x dh / dt
giving dh / dt = (0.002 / pi) m / min