1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Liono4ka [1.6K]
2 years ago
14

A tank has the shape of a surface generated by revolving the parabolic segment y = x2 for 0 ≤ x ≤ 3 about the y-axis (measuremen

t in feet). If the tank is full of a fluid weighing 100 pounds per cubic foot, set up an integral for the work required to pump the contents of the tank to a level 5 feet above the top of the tank.
Mathematics
1 answer:
Darina [25.2K]2 years ago
7 0

Answer:

100\pi\int\limits^9_0 {(\sqrt y)^2(14-y)} \, dy ft-lbs.

Step-by-step explanation:

Given:

The shape of the tank is obtained by revolving y=x^2 about y axis in the interval 0\leq x\leq 3.

Density of the fluid in the tank, D=100\ lbs/ft^3

Let the initial height of the fluid be 'y' feet from the bottom.

The bottom of the tank is, y(0)=0^2=0

Now, the height has to be raised to a height 5 feet above the top of the tank.

The height of top of the tank is obtained by plugging in x=3 in the parabolic equation . This gives,

H=3^2=9\ ft

So, the height of top of tank is, y(3)=H=9\ ft

Now, 5 ft above 'H' means H+5=9+5=14

Therefore, the increase in height of the top surface of the fluid in the tank is given as:

\Delta y=(14-y) ft

Now, area of cross section of the tank is given as:

A(y)=\pi r^2\\r\to radius\ of\ the\ cross\ section

Radius is the distance of a point on the parabola from the y axis. This is nothing but the x-coordinate of the point.

We have, y=x^2

So, x=\sqrt y

Therefore, radius, r=\sqrt y

Now, area of cross section is, A(y)=\pi (\sqrt y)^2

Work done in pumping the contents to 5 feet above is given as:

W=D\int\limits^{y(3)}_{y(0)} {A(y)(\Delta y)} \, dy

Plug in all the values. This gives,

W=100\int\limits^9_0 {\pi (\sqrt y)^2(14-y)} \, dy\\\\W=100\pi\int\limits^9_0 { (\sqrt y)^2(14-y)} \, dy\textrm{ ft-lbs}

You might be interested in
What is the slope of the line y = -5 - 3x ?<br> o 3<br> O 5<br> 0 -3<br> 0 -8
nexus9112 [7]

Answer:

we need to see the plane

Step-by-step explanation:

but, its 0 -8

3 0
3 years ago
Anyone know the answer to to this algebra question?
liraira [26]

Answer:

a=1

b= 1/16

c= 1/256

d= 1

e= 4/9

f= 16/81

Step-by-step explanation:

Plug in the values of X on the left side of the table into the function on the right side of the table. Remember that negative exponents mean the number is under a fraction. 4^-0 is like saying one over 4^0.

For the blue table, because the numbers are already in a fraction and in parentheses, you apply the exponent to each number individually.

7 0
3 years ago
A sporting goods store offers 40% discount on all golf clubs. Rocco spent 20% of the money in his savings account on a golf putt
MatroZZZ [7]

Answer:

Rocco doesn't have enough money to buy the golf irons

Step-by-step explanation:

step 1

Find the rest of the money left in the savings account

using proportion

\frac{\$48}{20\%}=\frac{x}{80\%}\\ \\x=48*80/20\\ \\x=\$192

step 2

we know that

The set of golf irons has an original price of $359

Applying 40% discount

100%-40%=60%=60/100=0.60

after the discount the price will be

0.60(\$359)=\$215.4

\$215.4> \$192

therefore

Rocco doesn't have enough money to buy the golf irons

7 0
3 years ago
The diameter of a coin is 26mm. Mathew lined up 56 coins from the left end of his desk to the right end of his desk. What is the
Ne4ueva [31]

Answer:

Your answer is 145.6

Step-by-step explanation:

First multiply 56 and 26 which then you get 1456mm then divide the length value by ten and then you get 145.6.

Hope I helped!

5 0
2 years ago
A book with a base price of $15.75 is marked up by 65%. What is the new price, to the nearest cent?
Vaselesa [24]
15,75 - 100 %

100 % =  100/100 = 1

Then every number multiplied by 1 is 100 % of itself.

If the book was marked up 65% of what is was before, it makes a price of 165% when compared to the original.

165% = 165/ 100 = 1,65

15,75 . 1,65 = 25,9875

25,99 is the nearest option.

a)25,99
4 0
3 years ago
Read 2 more answers
Other questions:
  • Una ciudad tenía 8000 habitantes a final del año 2000. Cada año su población se incrementa en un 0.5 %
    9·1 answer
  • Which number line represents the following statement?<br><br> A number is more than negative five.
    5·2 answers
  • For the figure below the base area and the height has been provided. find the VOLUME
    15·1 answer
  • 75c- 300 - 35 c =25c + 15c + 200
    9·1 answer
  • I already know the answer to the first question just answer the other three, please
    11·1 answer
  • Find the 80th term of the following arithmetic sequence.<br> 16, 23, 30, 37, ......
    9·1 answer
  • Triangle PQR has angles in the ratio of 2:3:5.
    5·1 answer
  • Helpp me pleaseee I need it?
    6·1 answer
  • Let n be equal to 156% of 70. Which of the following proportions is true?
    10·1 answer
  • Write the expanded from of h(3k-12.4)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!