Quiz about BC Unit 8 Review

Question 1

Find the average value of $$h\left(x\right)=3x^2-6x+1$$ on [-2,1].

Accepted Answer

7

Answer

33

Answer

11

Answer

21

Question 2

Find the average value of $$g\left(x\right)=5\pi\cos x$$ on the interval $$\left[0,\frac{\pi}{2}\right]$$ .

Accepted Answer

10

Answer

$$5\pi$$

Answer

$$25\pi^2$$

Answer

1

Question 3

Find the average value of the function $$g\left(x\right)=\frac{3}{2x}$$ from x=1 to x=e.

Accepted Answer

$$\frac{3}{2e-2}$$

Answer

$$e-1$$

Answer

$$\frac{3-e}{2-2e}$$

Answer

$$\frac{3}{2}$$

Question 4

Find the average rate of change of g(x) on the interval $$\left[1,e\right]$$ given $$g"\left(x\right)=\frac{1}{x^2}$$ and $$g$$

Accepted Answer

$$\frac{3-e}{2-2e}$$

Answer

$$\frac{3}{2e-2}$$

Answer

$$e-1$$

Answer

$$1-\frac{1}{e^2}$$

Question 5

A particle is moving along the x-axis for $$t\ge0$$ . The position of the particle is given by $$x\left(t\right)=t^3-9t^2-21t+6$$ . At what time, t, does the particle change direction?

Accepted Answer

7

Answer

5

Answer

2

Answer

1

Question 6

The velocity of a particle for t on [0,9] is given in the graph. At which of the following value for t is the particle speeding up?

Accepted Answer

5

Answer

3

Answer

4

Answer

7

Question 7

A particle is moving along the x-axis. The position and velocity of the particle is recorded for various times in the table. At which time, t, is the particle moving towards the origin?

Accepted Answer

1

Answer

2

Answer

4

Answer

6

Answer

8

Question 8

The velocity of a particle is given in the graph for t on [0,11]. What is the total distance traveled by the particle on the interval [4,9]?

Accepted Answer

6

Answer

0

Answer

2

Answer

10

Question 9

The position of a bug moving along a straight path is given by $$s\left(t\right)=t^2-2t+3$$ . At what time, t, is the instantaneous velocity equal to the average velocity of the bug on [0,6]?

Accepted Answer

3

Answer

4

Answer

2

Answer

6

Question 10

Snow is falling at a rate of $$r\left(t\right)=2e^{-0.1t}$$ inches per hour, where t is the time in hours since the beginning of the snowfall. There initially was 5 inches of snow on the ground. Which of the following gives the amount of snow, in inches, that falls from time t=0 to t=5 hours?

Accepted Answer

7.869 inches

Answer

5.869 inches

Answer

2.869 inches

Answer

12.869 inches

Question 11

The rate at which ants arrive at a picnic is modeled by the function A, where A(t) is measured in ants per minute and t is measured in minutes. The graph for A(t) is given. How many ants arrive at the picnic during [0,30]?

Accepted Answer

140

Answer

8

Answer

70

Answer

120

Question 12

The rate at which people arrive at a theater box office is modeled by the function B(t), where B is measured in people per minute and t is measured in minutes. The graph of B is given. Which of the following is closest to the number of people that arrive at the box office during [0,20].

Accepted Answer

188

Answer

175

Answer

162

Answer

190

Question 13

The graphs of the functions f and g are given. What is the arc length of f(x)?

Accepted Answer

$$\int_A^B\sqrt[]{1+\left[f$$

Answer

$$\int_A^B\sqrt[]{1+\left[f\left(x\right)\right]^2}dx$$

Answer

$$\int_A^B\left[1+f\left(x\right)dx\right]$$

Answer

$$\int_A^B\left[1+f$$

Question 14

Let R be the region in the first quadrant enclosed by the graphs of $$y=\sqrt{x-2},\ y=8-x,\ $$ and the x axis. Find the volume of the solid generated when R is revolved around the line $$x=-3$$ .

Accepted Answer

369.451

Answer

92.991

Answer

158.336

Answer

620.779

Question 15

Let R be the region in the first quadrant enclosed by the graphs of $$y=\sqrt{x-2},\ y=8-x,\ $$ and the x axis. Find the perimeter of R.

Accepted Answer

13.475

Answer

12.914

Answer

11.618

Answer

10.359

Question 16

Let R be the region in the first quadrant enclosed by the graphs of $$y=\sqrt{x-2},\ y=8-x,\ $$ and the x axis. Find the volume of the solid generated when R is revolved about y=2.

Accepted Answer

58.643

Answer

79.473

Answer

88.157

Answer

63.975

Question 17

Which of the following expressions gives the length of the graph of $$x=y^3$$ for $$-2\le y\le2.$$

Accepted Answer

$$\int_{-2}^2\left(1+9y^4\right)^{\frac{1}{2}}dy$$

Answer

$$\int_{-2}^2\left(1+y^6\right)dy$$

Answer

$$\int_{-2}^2\left(1+y^6\right)^{\frac{1}{2}}dy$$

Answer

$$\int_{-2}^2\left(1+9y^4\right)dy$$

Question 18

Given $$f\left(x\right)=\frac{x-1}{4x^2+1}$$ , what is the length of the curve on $$-\frac{1}{2}\le x\le1$$ ?

Accepted Answer

2.109

Answer

1.109

Answer

3.973

Answer

4.183

Question 19

A particle moves along a horizontal line with velocity $$v\left(t\right)=t-3\ln\left(t+2\right)+2t\sin\left(\frac{t^2}{12}\right)$$ for $$0\le t\le8$$ . It is known that $$s\left(0\right)=-3$$ . When is the speed of the particle 5 on $$\left[5,7\right]$$ ?

Accepted Answer

5.621 sec

Accepted Answer

6.520 sec

Answer

6.391 sec

Answer

5.487 sec

Question 20

A particle moves along a horizontal line with velocity $$v\left(t\right)=t-3\ln\left(t+2\right)+2t\sin\left(\frac{t^2}{12}\right)$$ for $$0\le t\le8$$ . It is known that $$s\left(0\right)=-3$$ . What is the position of the particle at t=3 ?

Accepted Answer

-6.263

Answer

-4.595

Answer

-0.541

Answer

-2.569

Question 21

A particle moves along a horizontal line with velocity $$v\left(t\right)=t-3\ln\left(t+2\right)+2t\sin\left(\frac{t^2}{12}\right)$$ for $$0\le t\le8$$ . It is known that $$s\left(0\right)=-3$$ . What is the first time the particle changes direction?

Accepted Answer

2.341

Answer

0.685

Answer

4.721

Answer

6.127

Question 22

A particle moves along a horizontal line with velocity $$v\left(t\right)=t-3\ln\left(t+2\right)+2t\sin\left(\frac{t^2}{12}\right)$$ for $$0\le t\le8$$ . It is known that $$s\left(0\right)=-3$$ . Is the speed increasing or decreasing at t=7?

Accepted Answer

Increasing

Answer

Decreasing

Question 23

On an early spring day, a town has temperature, in $$\degree F$$ , t hours after 9AM modeled by $$T\left(t\right)=55+14\sin\left(\frac{\pi t}{12}\right)$$ . Find the average temperature during the period from 9AM to 9PM.

Accepted Answer

63.913

Answer

61.232

Answer

59.595

Answer

68.003

Question 24

Find the average value of the function f, whose graph is given, on the interval [0,8].

Accepted Answer

$$\frac{9}{8}$$

Answer

$$\frac{11}{8}$$

Answer

$$\frac{13}{8}$$

Answer

$$\frac{15}{8}$$

Question 25

Water is pumped into an underground tank at a constant rate of 8 gallons per minute. Water leaks out of the tank at the rate $$L\left(t\right)=\sqrt[]{t+1}$$ gallons per minute for $$0\le t\le120$$ minutes. There are 30 gallons of water in the tank initially. How many gallons of water are in the tank at 3 minutes?

Accepted Answer

49.333

Answer

44.667

Answer

40.5

Answer

39.333

Question 26

Find the area between $$y=x^2-4x+3$$ and $$y=-x^2+2x+3$$ .

Accepted Answer

9

Answer

7

Answer

8

Answer

10

Question 27

Find the area of the REGIONS bounded by $$y=\sqrt[3]{x}$$ and $$y=x$$ .

Accepted Answer

$$\frac{1}{2}$$

Answer

$$\frac{1}{4}$$

Answer

1

Answer

0

Question 28

Let R be the region in the first quadrant enclosed by the graphs of $$y=\sqrt{x-2},\ y=8-x,\ $$ and the x axis. Find the volume of the solid generated when R is revolved around the line $$y=-3$$ .

Accepted Answer

171.740

Answer

125.921

Answer

255.157

Answer

301.823

Question 29

Let R be the region in the first quadrant enclosed by the graphs of $$y=\sqrt{x-2},\ y=8-x,\ $$ and the x axis. Find the volume of the solid generated when R is revolved around the line $$x=10$$ .

Accepted Answer

229.546

Answer

315.123

Answer

243.881

Answer

271.903

Question 30

Region R is bounded by $$y=\sin\left(\pi x\right)$$ and $$y=x^3-4x$$ . What is the perimeter of R?

Accepted Answer

11.244

Answer

9.066

Answer

10.811

Answer

12.059

Question 31

Given $$y=\frac{x^3}{3}+x^2+x+\frac{1}{4x+4}$$ , find the length of the curve on $$0\le x\le2$$ .

Accepted Answer

53/6

Answer

28/3

Answer

56/3

Answer

25/3

Question 32

A particle moves along the x-axis with velocity given by $$v\left(t\right)=3t^2+6t$$ for time $$t\ge0$$ . If the particle is at position x=2 at time t=0, what is the position of the particle at time t=1?

Accepted Answer

6

Answer

4

Answer

9

Answer

11

Answer

12

Question 33

A particle moves along a straight line. The graph of the particle's position x(t) at time t is shown for 0

Accepted Answer

0<t<2

Answer

1<t<5

Answer

2<t<6

Answer

3<t<5

Answer

1<t<2 and 5<t<6

Question 34

Let R be the shaded region bounded by the graph of $$y=\ln x$$ and the line $$y=x-2$$ as shown. Find the volume of the solid generated when R is rotated about the horizontal line $$y=-3$$ .

Accepted Answer

34.199

Answer

14.791

Answer

10.886

Answer

31.875

Question 35

The tide removes sand from Sandy Point Beach at a rate modeled by $$R\left(t\right)=2+5\sin\left(\frac{4\pi t}{25}\right)$$ . A pumping station adds sand to the beach at a rate modeled by $$S\left(t\right)=\frac{15t}{1+3t}$$ . Both R and S have units of cubic yards per hour and t is measured in hours for [0,6]. At time 0, the beach contains 2500 cubic yards of sand. How many cubic yards of sand are present at t=5 hours?

Accepted Answer

2492.384

Answer

2507.616

Answer

2478.183

Answer

2539.002

Question 36

What is the average value of $$y=\frac{\cos x}{x^2+x+2}$$ on the closed interval [-1,3]?

Accepted Answer

0.183

Answer

-0.085

Answer

0.090

Answer

0.244

Answer

0.732

Question 37

The velocity, in ft/sec, of a particle moving along the x-axis is given by the function $$v\left(t\right)=e^t+te^t$$ . What is the average velocity of the particle from time t=0 to t=3?

Accepted Answer

20.086 ft/sec

Answer

26.447 ft/sec

Answer

32.804 ft/sec

Answer

40.671 ft/sec

Answer

79.342 ft/sec

Question 38

A particle moves along the x-axis. At any time t>0, its acceleration is given by $$a\left(t\right)=\ln\left(1+2^t\right)$$ . If the velocity of the particle is 2 at time t=1, then the velocity of the particle at time t=2 is

Accepted Answer

3.346

Answer

0.462

Answer

1.609

Answer

2.555

Answer

2.886

Question 39

A pizza, heated to a temperature of 350 degrees Fahrenheit, is taken out of an oven and placed in a $$75\degree F$$ room at time t=0 minutes. The temperature of the pizza is decreasing at a rate of $$T\left(t\right)=110e^{-0.4t}$$ degrees Fahrenheit per minute. To the nearest degree, what is the temperature of the pizza at time t=5 minutes?

Accepted Answer

$$112\degree F$$

Answer

$$119\degree F$$

Answer

$$147\degree F$$

Answer

$$238\degree F$$

Answer

$$335\degree F$$

Question 40

What is the area enclosed by the curves $$y=x^3-8x^2+18x-5$$ and $$y=x+5$$ ?

Accepted Answer

11.833

Answer

10.667

Answer

14.583

Answer

21.333

Answer

32

Question 41

An object traveling in a straight line has position x(t) at time t. If the initial position is x(0)=2 and the velocity of the object is $$v\left(t\right)=\left(1+t^2\right)^{\frac{1}{3}}$$ , what is the position of the object at time t=3?

Accepted Answer

6.512

Answer

0.431

Answer

2.154

Answer

4.512

Answer

17.408

Question 42

An object traveling in a straight line has position x(t) at time t. If the initial position is x(5)=2 and the velocity of the object is $$v\left(t\right)=\left(1+t^2\right)^{\frac{1}{3}}$$ , what is the position of the object at time t=3?

Accepted Answer

-3.134

Answer

-0.889

Answer

3.059

Answer

-2.159

BC Unit 8 Review

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