Aria

1.) Find the volume V of the region between the plane z = x and the surface z = x2, and the planes y = 0, and y = 42

Not quite sure what I'm doing wrong...could you help?

1. Calculate all four second-order partial derivatives of f(x,y)=(6x+13y)^2

2. Calculate all four second-order partial derivatives of f(x,y)=6xe^y

3. Calculate all four second-order partial derivatives of f(x,y)=(17x+16y)e^y

Calculate all four second-order partial derivatives of f(x,y)=32sin(x/y)

Thank you so much!

Not quite sure what I'm doing wrong...could you help?

1. Calculate all four second-order partial derivatives of f(x,y)=(6x+13y)^2

2. Calculate all four second-order partial derivatives of f(x,y)=6xe^y

3. Calculate all four second-order partial derivatives of f(x,y)=(17x+16y)e^y

Calculate all four second-order partial derivatives of f(x,y)=32sin(x/y)

Thank you so much!

Partial derivatives seem to make sense to me pretty well, but we have online homework and these ones I just can't seem to get right! Not sure if I'm doing something wrong or if the online system is just being picky...would someone mind trying to figure these out? Thanks a million!

1. f(x,y)=13x^2 y^3 + 5xy^2 - 6x^2

Find fy(x,y)

2. find dz/dy | (3,1.5) if z=e^(x+y) * siny

3. find d/dv (v+at)

First of all, I'd like to say that I do NOT think I am "fat." I know quite a few people with eating disorders and I have been very conscious to make sure that I don't fall into that type of mindset. However, I do have some fat (belly, arms, thighs) that I would like to get rid of. My body measurements are 34-28-34, and I am about 5'6" and weigh around 135 lbs. In high school I used to be consistently 121 lbs. I feel that a 25 or 26 waist would be healthiest for me. I am nineteen years old, and I think that a lot of this fat gain has been since I started college. I never party or drink so the fat gain can't be blamed on that, but I go to college at a school where seven out of the eight months I am there are snowy, so it is very difficult for me to get outside and be active, and the gym is much too expensive for me to afford. I've tried to eat the healthiest I can, but it's very difficult with dorm food, especially because of the limited amount of whole grains and fruits and vegetables available. Because I am an engineering major and have a very intense amount of homework each day, I can't set aside hours to work out each day. I am tired a lot even when I get eight hours of sleep, and I think that this could be partially because my body isn't very healthy. Do you have any advice for me to get my body a bit healthier under college-life conditions?

First of all, I'd like to say that I do NOT think I am "fat." I know quite a few people with eating disorders and I have been very conscious to make sure that I don't fall into that type of mindset. However, I do have some fat (belly, arms, thighs) that I would like to get rid of. My body measurements are 34-28-34, and I am about 5'6" and weigh around 135 lbs. In high school I used to be consistently 121 lbs. I feel that a 25 or 26 waist would be healthiest for me. I am nineteen years old, and I think that a lot of this fat gain has been since I started college. I never party or drink so the fat gain can't be blamed on that, but I go to college at a school where seven out of the eight months I am there are snowy, so it is very difficult for me to get outside and be active, and the gym is much too expensive for me to afford. I've tried to eat the healthiest I can, but it's very difficult with dorm food, especially because of the limited amount of whole grains and fruits and vegetables available. Because I am an engineering major and have a very intense amount of homework each day, I can't set aside hours to work out each day. I am tired a lot even when I get eight hours of sleep, and I think that this could be partially because my body isn't very healthy. Do you have any advice for me to get my body a bit healthier under college-life conditions?

A 69.5kg football player is gliding across very smooth ice at 2.10m/s . He throws a 0.430kg football straight forward.

a.) What is the player's speed afterward if the ball is thrown at 12.0m/s relative to the ground?

b.) What is the player's speed afterward if the ball is thrown at 12.0m/s relative to the player?

Solve exactly for the variable.

1+x+x^2+x^3+...=5

By recognizing the series in as a Taylor series evaluated at a particular value of x , find the sum of the following convergent series.

1-0.1+(0.1^2)-(0.1^3)+...

By recognizing the series in as a Taylor series evaluated at a particular value of x , find the sum of the following convergent series.

1+1/4+(1/4)^2+(1/4)^3+...+(1/4)^n+...

By recognizing the given series as a Taylor series evaluated at a particular value of x, find the sum of the following convergent series.

1+(8/1!)+(64/2!)+(512/3!)+...+(8^n/n!)+...

Find the first four terms of the Taylor series for 1/x about 1

Find the first four terms of the Taylor series for sin(x) about a= -pi/4

A fuel tank is in the shape of a cylinder that is oriented vertically. The tank is 10 feet high, with a radius of 5 feet. The weight density of the fuel is 50 lb/ft^3. Assume that the tank is half full to start.

(a.) What is the pressure at the bottom of the tank? All answers are in lb/ft^2.

50

250

500

750

750 pi

(b.) What is the weight of a slice of fluid that is (delta h) ft thick.

25 pi * delta h

250 pi * delta h

750 pi * delta h

1250 pi * delta h

(c.) To pump a slice of fluid from the tank, what is the distance that it must be raised? Assume that the bottom of the tank is at an elevation of zero, that is, h = 0 at the bottom. All answers are in units of feet.

5

10

10 - h

10 - h/2

(d.) Find the work required to pump all of the fuel from the tank (over the top).

15,625 pi

23,725 pi

46,875 pi

62,500 pi

A fuel tank is in the shape of a cylinder that is oriented vertically. The tank is 10 feet high, with a radius of 5 feet. The weight density of the fuel is 50 lb/ft^3. Assume that the tank is half full to start.

(a.) What is the pressure at the bottom of the tank? All answers are in lb/ft^2.

50

250

500

750

750 pi

(b.) What is the weight of a slice of fluid that is (delta h) ft thick.

25 pi * delta h

250 pi * delta h

750 pi * delta h

1250 pi * delta h

(c.) To pump a slice of fluid from the tank, what is the distance that it must be raised? Assume that the bottom of the tank is at an elevation of zero, that is, h = 0 at the bottom. All answers are in units of feet.

5

10

10 - h

10 - h/2

(d.) Find the work required to pump all of the fuel from the tank (over the top).

15,625 pi

23,725 pi

46,875 pi

62,500 pi

A fuel tank is in the shape of a cylinder that is oriented vertically. The tank is 10 feet high, with a radius of 5 feet. The weight density of the fuel is 50 lb/ft^3. Assume that the tank is half full to start.

(a.) What is the pressure at the bottom of the tank? All answers are in lb/ft^2.

50

250

500

750

750 pi

(b.) What is the weight of a slice of fluid that is (delta h) ft thick.

25 pi * delta h

250 pi * delta h

750 pi * delta h

1250 pi * delta h

(c.) To pump a slice of fluid from the tank, what is the distance that it must be raised? Assume that the bottom of the tank is at an elevation of zero, that is, h = 0 at the bottom. All answers are in units of feet.

5

10

10 - h

10 - h/2

(d.) Find the work required to pump all of the fuel from the tank (over the top).

15,625 pi

23,725 pi

46,875 pi

62,500 pi

A fuel tank is in the shape of a cylinder that is oriented vertically. The tank is 10 feet high, with a radius of 5 feet. The weight density of the fuel is 50 lb/ft^3. Assume that the tank is half full to start.

(a.) What is the pressure at the bottom of the tank? All answers are in lb/ft^2.

50

250

500

750

750 pi

(b.) What is the weight of a slice of fluid that is (delta h) ft thick.

25 pi * delta h

250 pi * delta h

750 pi * delta h

1250 pi * delta h

(c.) To pump a slice of fluid from the tank, what is the distance that it must be raised? Assume that the bottom of the tank is at an elevation of zero, that is, h = 0 at the bottom. All answers are in units of feet.

5

10

10 - h

10 - h/2

(d.) Find the work required to pump all of the fuel from the tank (over the top).

15,625 pi

23,725 pi

46,875 pi

62,500 pi

Consider a rod of length of 3 meters, which has a density of 2 + cos(x) grams/meter. The rod is positioned along the x-axis with the left end at the origin.

(a.) Where is the rod most dense?

At the left end

In the middle

At the right end

At multiple points on the rod

It is of uniform density

(b.) Where is the rod least dense?

At the left end

In the middle

At the right end

At multiple points on the rod

It is of uniform density

(c.) What is the total mass of the rod

5.86 gm

6.00 gm

6.14 gm

6.28 gm

6.42 gm

(e.) Where is the center of mass of the rod? Give answer a distance from the origin

x = 0.0

x = .6

x = 1.2

x = 1.5

x = 1.8

x = 2.1

x = 2.4

x = 3.0