I want to find the volume of the solid enclosed by the paraboloidz=2+x2+(y−2)2&nbsp;and the planes&nbsp;z=1,x=−1y=0,and&nbsp;y=4

Imaghine that the volume of the surface given by the equation&nbsp;2+x2+(y−2)2=z&nbsp;that is above the xy plane and the given rectangle is being cut off by the plane&nbsp;z=1. So:∫−11∫042+x2+(y−2)2&nbsp;dy&nbsp;&nbsp;dx&nbsp;−∫−11∫04&nbsp;dx&nbsp;&nbsp;dy&nbsp;∫−11∫042+x2+(y−2)2&nbsp;dx&nbsp;&nbsp;dy&nbsp;−8=883−8=643

Answered: "I want to find the volume of the..."

High School

babeeb0oL

Answered question

2021-10-29

I want to find the volume of the solid enclosed by the paraboloid
$z = 2 + x^{2} + {(y - 2)}^{2}$ and the planes $z = 1, x = - 1 y = 0, a n d y = 4$

Answer & Explanation

irwchh

Skilled2021-10-30Added 102 answers

Imaghine that the volume of the surface given by the equation $2 + x^{2} + {(y - 2)}^{2} = z$ that is above the xy plane and the given rectangle is being cut off by the plane $z = 1$ . So:
$\int_{- 1}^{1} \int_{0}^{4} 2 + x^{2} + {(y - 2)}^{2} d y d x - \int_{- 1}^{1} \int_{0}^{4} d x d y$
$\int_{- 1}^{1} \int_{0}^{4} 2 + x^{2} + {(y - 2)}^{2} d x d y - 8 = \frac{88}{3} - 8 = \frac{64}{3}$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High School

At the beginning of an environmental study, ad forest covered an area of $1500 k m^{2}$ .Since then, this area has decreased by 4.25% each year.Let t be the number of years since the start of the study.Let y be the area that the forest covers in $k m^{2}$ .
Write an exponential function showing relationship between y and t.
Some friends tell you that they paid $25,000 down on a new house and are to pay $525 per month for 30 years. If interest is 7.8% compounded monthly, what was the selling price of the house? How much interest will they pay in 30 years?
t e^-4t sin3t
Find all whole number solutions of the congruence equation.
3x ≡ 8 mod 11
Use a direct proof to show that the product of two rational numbers is rational.
Y=2(x-) (x+1)
what is vertex
axis of symmetry
x-intercept(s)
y-intercept
Stairs- Each step of a set of stairs has a tread depth of 11.5 inches and a riser height of 6.5 inches. What is the slope of the set of stairs?
A ball of mass 5 kg is attached to a string of length 10 cm, forming a pendulum. If the string is raised horizontally as shown and released from point A, then what is the v
assume that the random variable Xand Y have the joint pdf f(x,y)=1/2x^3
5=20 mod 4 true or false answer
5x−4y=
- $- 12$ −12
Pets Plus and Pet Planet are having a sale on the same aquarium. At Pets Plus the aquarium is on sale for 30% off the original price and at Pet Planet it is discounted by 25%.

Store Original Price
of Aquarium ($)
Pets Plus 118
Pet Planet 110

If the sales tax rate is 8%, which store has the lower sale price?

, 1 of 1.Select ChoicePets PlusPet Planet has the lower sale price.
Part B
Fill in the blank question.
How much will you save by buying the aquarium at the store with the lower sale price? Round to the nearest cent.

$
Prove that if x is and irrational number and x>0 then route over x is also irrational
A small object has charge Q. Charge q is removed from it and placed on a second small object. The two objects are placed 1 m apart. For the force that each object exerts on the other to be a maximum. q should be: A. 2Q B. Q C. Q/2 D. Q/4 E. 0

Didn't find what you were looking for?

Store	Original Price of Aquarium ($)
Pets Plus	118
Pet Planet	110