Question 1

Is the function   a probability density function on the interval   ?

Accepted Answer

A)  Yes. 
B)  No, because the integral of the probability is not 1. 
C)  No, because the function can be negative in the range. 
A)  Yes. 
B)  No, because the integral of the probability is not 1. 
C)  No, because the function can be negative in the range.

Question 2

Given the pdf for a particular exam   , identify the cut-off for students scoring in the top 30%. [Hint: If the solution is difficult to obtain analytically, set up the expression to be solved and substitute the various choices below.]

Accepted Answer

A)  70 
B)  73 
C)  76 
D)  17.6 
A)  70 
B)  73 
C)  76 
D)  17.6

Question 3

Compute the volume of a solid formed by revolving the region bounded by

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by   about x = 13.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

Find the length of the line segment described by the function of   from   . Round your answer to three decimal places.

Accepted Answer

A)  55.07 
B)  55.12 
C)  55.17 
D)  55.22 
A)  55.07 
B)  55.12 
C)  55.17 
D)  55.22

Question 6

A football (American) has a circular cross section with radius approximately   for   . Compute the volume of the football.

Accepted Answer

A)  238.9 inches3 
B)  165.9 inches3 
C)  119.4 inches3 
D)  82.9 inches3 
A)  238.9 inches3 
B)  165.9 inches3 
C)  119.4 inches3 
D)  82.9 inches3

Question 7

What is the minimum speed a ball must be thrown upward if it is to reach a height of 11 feet?

Accepted Answer

A)  11 ft/s 
B)    ft/s 
C)    ft/s 
D)  0 ft/s 
A)  11 ft/s 
B)    ft/s 
C)    ft/s 
D)  0 ft/s

Question 8

Find the value of c which will make the function   a pdf on the interval   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Identify the graph and the area bounded by the curves   on the interval   .

Accepted Answer

A)      
B)      
C)      
D)      
A)      
B)      
C)      
D)

Question 10

Set up the integral for the surface area of the surface of revolution and approximate the integral with a numerical method. Round answers to two decimal places.   revolved about the x-axis

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

In a baseball game a base-runner can attempt to advance when a fielder catches a hit ball before it reaches the ground, so long as the runner doesn't leave base before the fielder catches the ball. The fielder then attempts to throw the ball to the base ahead of the runner. If a base-runner can run from 3rd base to home plate in 4.0 sec, how fast must the centerfielder's throw leave his hand if he makes the catch then immediately throws the ball 350 ft from home plate? Assume the base-runner leaves his base at the same instant the centerfielder throws the ball, and that the ball reaches the catcher standing over home plate at the same height from which it was thrown and at the same time the runner would reach the plate. [Hint: This is basically a problem of determining how much initial vertical velocity the ball needs to stay in the air long enough to reach the plate.]

Accepted Answer

A)  88 ft/sec 
B)  64 ft/sec 
C)  108 ft/sec 
D)  152 ft/sec 
A)  88 ft/sec 
B)  64 ft/sec 
C)  108 ft/sec 
D)  152 ft/sec

Question 12

A 2-person tent has a rectangular base   and rises to a single point 5' up. Compute the volume of the tent.   6 ft 7 ft

Accepted Answer

A)  65 ft3 
B)  53 ft3 
C)  105 ft3 
D)  210 ft3 
A)  65 ft3 
B)  53 ft3 
C)  105 ft3 
D)  210 ft3

Question 13

Identify the graph and area of the region bounded by the curves   . Use only one integral. The figures below are not necessarily to scale.

Accepted Answer

A)      
B)      
C)      
D)      
A)      
B)      
C)      
D)

Question 14

Compute the volume of the solid formed by revolving the region bounded by   and   about the x-axis.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Find the area between the following curves on the given interval.

Accepted Answer

A)    
B)      
C)    
D)    
A)    
B)      
C)    
D)

Question 16

A person 6' tall wants to buy a jump rope. If , when the rope is at its lowest point, his hands will be 2' apart and 3' above the ground, and if the rope will take on the shape of a parabola just barely hitting the ground, how long must the rope be? [Consider the form of the rope to be described by the equation   , with the origin being a spot on the ground underneath the jumper.]

Accepted Answer

A)  6.75 feet 
B)  6.50 feet 
C)  6.25 feet 
D)  6.00 feet 
A)  6.75 feet 
B)  6.50 feet 
C)  6.25 feet 
D)  6.00 feet

Question 17

Probability density functions can be weighted so that different properties of the distribution can be enhanced or diminished. For instance, if a set of test scores is to be used in comparing the highest performers in a class, one might want to use a pdf,   , in which the probability of finding a certain score, f(x), is multiplied by that score:   . A mean found using the weighted pdf might be called a score-weighted mean. Find the score-weighted mean for an exam for which the probability of finding a score   is given by the function   . You will need to construct the weighted pdf then use it to find the mean score.

Accepted Answer

A)  66.7 
B)  60.0 
C)  50.0 
D)  75.0 
A)  66.7 
B)  60.0 
C)  50.0 
D)  75.0

Question 18

A projectile passes overhead, and you attempt to shoot it down with a cannon. When it passes overhead it is traveling horizontally at 100 m/s at an elevation of 1500 m. Your cannon launches shells at 200 m/s, and in this instance you fire just as the projectile passes overhead and at an angle of 60o. In this scenario the horizontal velocities of the two projectiles are the same. At what elevation will the cannon shell and the other projectile collide?

Accepted Answer

A)  They won't collide before the cannon shell hits the ground. 
B)  1457.6 m 
C)  1224.4 m 
D)  1132.5 m 
A)  They won't collide before the cannon shell hits the ground. 
B)  1457.6 m 
C)  1224.4 m 
D)  1132.5 m

Question 19

A given sample of a particular polymer will have molecules with a range of molecular weights, MW. If the molecular weight pdf is   , what fraction of the molecules will have a molecular weight less than 500?

Accepted Answer

A)  0.118 
B)  0.882 
C)  0.221 
D)  0.000 
A)  0.118 
B)  0.882 
C)  0.221 
D)  0.000

Question 20

Show that the volume of a solid formed by revolving the region bounded by x = y2 and x = r about x = r is   .

Accepted Answer

@#IMG-DLM& Use the method of disks integ

Is the function a probability density function on the interval ?

Given the pdf for a particular exam , identify the cut-off for students scoring in the top 30%. [Hint: If the solution is difficult to obtain analytically, set up the expression to be solved and substitute the various choices below.]

Compute the volume of a solid formed by revolving the region bounded by

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about x = 13.

Find the length of the line segment described by the function of from . Round your answer to three decimal places.

A football (American) has a circular cross section with radius approximately for . Compute the volume of the football.

What is the minimum speed a ball must be thrown upward if it is to reach a height of 11 feet?

Find the value of c which will make the function a pdf on the interval .

Identify the graph and the area bounded by the curves on the interval .

Set up the integral for the surface area of the surface of revolution and approximate the integral with a numerical method. Round answers to two decimal places. revolved about the x-axis

A 2-person tent has a rectangular base and rises to a single point 5' up. Compute the volume of the tent. 6 ft 7 ft

Identify the graph and area of the region bounded by the curves . Use only one integral. The figures below are not necessarily to scale.

Compute the volume of the solid formed by revolving the region bounded by and about the x-axis.

Find the area between the following curves on the given interval.

Show that the volume of a solid formed by revolving the region bounded by x = y² and x = r about x = r is .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 6: Applications of the Definite Integral

Is the function a probability density function on the interval ?

Given the pdf for a particular exam , identify the cut-off for students scoring in the top 30%. [Hint: If the solution is difficult to obtain analytically, set up the expression to be solved and substitute the various choices below.]

Compute the volume of a solid formed by revolving the region bounded by

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about x = 13.

Find the length of the line segment described by the function of from . Round your answer to three decimal places.

A football (American) has a circular cross section with radius approximately for . Compute the volume of the football.

What is the minimum speed a ball must be thrown upward if it is to reach a height of 11 feet?

Find the value of c which will make the function a pdf on the interval .

Identify the graph and the area bounded by the curves on the interval .

Set up the integral for the surface area of the surface of revolution and approximate the integral with a numerical method. Round answers to two decimal places. revolved about the x-axis

A 2-person tent has a rectangular base and rises to a single point 5' up. Compute the volume of the tent. 6 ft 7 ft

Identify the graph and area of the region bounded by the curves . Use only one integral. The figures below are not necessarily to scale.

Compute the volume of the solid formed by revolving the region bounded by and about the x-axis.

Find the area between the following curves on the given interval.

A given sample of a particular polymer will have molecules with a range of molecular weights, MW. If the molecular weight pdf is , what fraction of the molecules will have a molecular weight less than 500?

Show that the volume of a solid formed by revolving the region bounded by x = y2 and x = r about x = r is .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Show that the volume of a solid formed by revolving the region bounded by x = y² and x = r about x = r is .