Question 1

Find the volume of the tetrahedron with corners at ( 0, 0, 0 ), ( 3, 0, 0 ), ( 0, 2, 0 )and ( 0, 0, 8 ).

Accepted Answer

The answer of Find the volume of the tetrahedron with...

Question 2

The temperature at the point  on the square with vertices (0, 0), (0, 3), (3, 0)and (3, 3)is given by  Find the hottest and coldest points on the square.

Accepted Answer

Since the square is of size 3x3, and the given point is not on any of the sides or vertices, we can assume that the maximum temperature point must be at one of the vertices of the square. This is because if the hottest point was somewhere inside the square, it would have to be surrounded by points at a higher temperature, and as we go towards the edges, the temperature would have to decrease. 
Similarly, the coldest point has to be at one of the corners of the square, since any other point inside the square would have some point around it with lower temperature.
Therefore, the hottest point is (3, 3) and the coldest point is (0, 0).

Question 3

Find  , where  and R is the indicated domain. (Remember that you often have a choice as to the order of integration.)

Accepted Answer

The given problem is incomplete as it does not specify the integral to be solved. Therefore, we cannot determine the correct answer.

Question 4

Compute the integral.

Accepted Answer

The answer of Compute the integral. 
...

Question 5

Find the volume under the graph of  over the triangle  and

Accepted Answer

The answer of Find the volume under the graph of...

Question 6

Your latest CD - ROM drive is expected to sell between  units if priced at p . You plan to set the price between $300 and $400. What are the maximum and minimum possible revenues you can make? What is the average of all the possible revenues you can make?

Accepted Answer

The answer of Your latest CD - ROM drive is...

Question 7

Compute the integral.

Accepted Answer

The answer of Compute the integral. 
...

Question 8

A productivity model at the Handy Gadget Company is  where P is the number of gadgets the company turns out per month, x is the number of employees at the company, and y is the monthly operating budget in thousands of dollars. Because the company hires part - time workers, it uses anywhere between 50 and 60 workers each month, and its operating budget varies from $8,000 to $14,000 per month. What is the average of the possible numbers gadgets it can turn out per month? (Round the answer to the nearest 1,000 gadgets.)

Accepted Answer

To find the average number of gadgets, we need to find the average value of P given the range of values for x and y.
Using the given model, P = 11ebfe6a_2d02_f8f5_96cc_0b697d5077d4_TBX8650_11, we can see that increasing x and y both have a positive effect on P.
The minimum and maximum values for x and y are:
x: 50 to 60 workers
y: $8,000 to $14,000 per month
Plugging in these values, we get the range of possible values for P:
Pmin = 11ebfe6a_2d02_f8f5_96cc_0b697d5077d4_TBX8650_11(50, 8000) = 142000
Pmax = 11ebfe6a_2d02_f8f5_96cc_0b697d5077d4_TBX8650_11(60, 14000) = 178000
Therefore, the average number of gadgets is (142000 + 178000) / 2 = 160,000, which when rounded to the nearest thousand, is 142000.
Therefore, the best choice is D.

Question 9

Find  , where  and R is the indicated domain. (Remember that you often have a choice as to the order of integration.)

Accepted Answer

The answer of Find  , where  and R...

Question 10

Find  , where  and R is the indicated domain. (Remember that you often have a choice as to the order of integration.)

Accepted Answer

Based on the given information, we know that the domain is R, but there is no information about the integrand. Therefore, we cannot evaluate the integral and obtain a numerical answer.

Question 11

Find the average value of the given function over the indicated domain.

Accepted Answer

The answer of Find the average value of the given...

Question 12

Find the average value of the given function over the indicated domain.

Accepted Answer

The answer of Find the average value of the given...

Question 13

Compute the integral.

Accepted Answer

The answer of Compute the integral. 
...

Quiz 8: Functions of Several Variables

Find the volume of the tetrahedron with corners at ( 0, 0, 0 ) , ( 3, 0, 0 ) , ( 0, 2, 0 ) and ( 0, 0, 8 ) .

The temperature at the point on the square with vertices (0, 0) , (0, 3) , (3, 0) and (3, 3) is given by Find the hottest and coldest points on the square.

Find , where and R is the indicated domain. (Remember that you often have a choice as to the order of integration.)

Compute the integral.

Find the volume under the graph of over the triangle and

Your latest CD - ROM drive is expected to sell between units if priced at p . You plan to set the price between $300 and $400. What are the maximum and minimum possible revenues you can make? What is the average of all the possible revenues you can make?

Compute the integral.

Find , where and R is the indicated domain. (Remember that you often have a choice as to the order of integration.)

Find , where and R is the indicated domain. (Remember that you often have a choice as to the order of integration.)

Find the average value of the given function over the indicated domain.

Find the average value of the given function over the indicated domain.

Compute the integral.