Chapter 10 Test Flashcards Preview

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Flashcards in Chapter 10 Test Deck (25):
1

Suppose that a bicyclist is biking with a velocity function of v (t) = 2t − 1 ft / min. Starting at t = 0, how long does it take the bicyclist to go 30 ft?

6 min

2

There is a hill which has parallel train tracks on it. The tracks run for 6 miles up the hillside. One train is at the top of the hill, moving down at 19 mi / h. Another train is on the other set of tracks, moving up the hill at 10 mi / h. The first train accelerates at 10 mi / h2 as it goes down the hill, but the second train does not accelerate or decelerate. How far up the hill are they when they pass?

2 mi

3

A professional ski jumper wants to jump 100 feet. He knows that once he goes off the end of the jump platform, he decelerates at 2 ft / s2. How fast does he need to be going off the end of the platform to make the 100-foot jump?

20 ft / s

4

A Happy Fun Ball is dropped and bounces on a concrete surface. The speed it has when it rebounds is half of the speed it had at the moment it hit the ground. If you drop Happy Fun Ball from atop a 40-foot tall building, how high does it get on the first bounce?

10 ft

5

What is the area of the region between the curves y = x^ 3 + x^ 2 − 1 and y = 2x^ 2 + 2x − 1?

37/12

6

What is the area of the regular hexagon whose sides are formed by the following lines?
y=√3/2y=x√3+√3y=√3−x√3,y=−x√3−√3y=x√3−√3y=−√3/2

3√3/2

7

What is the area between the curves y = x − 1 and y = e^ x between x = 0 and x = 1?

e−1/2

8

What is the area between y=1/x and x=−y from y=2 to y=5 ?

21/2+ln5/2

9

What is the area between x=y^3+2y, y=−2x+7, and the x-axis?

2

10

What is the area between the curves y=x^2−4 and x=−y+2 ?

20 5/6

11

What is the area between the curves x=cosy+4 and x=cosy−2 from y=−π2 to y=3π2 ?

12π

12

What is the average value of √2x+1 on [0, 4]?

13/6

13

What is the average value of xe^x^2 on [0, 1]?

(e - 1)/2

14

What is the volume of the solid whose cross-sections are squares perpendicular to the x-axis and with one side on the region bounded by the curves y=sin x and the x-axis on the interval [0, π/2]?

π/4

15

What is the volume of the solid whose cross-sections are squares perpendicular to the x-axis where the solid is based on the region bounded by curves y=x^3, the x-axis, and x=1?

1/7

16

What is the volume of the solid of revolution obtained by rotating the region bounded by x = 1, x = 2, y = 0, and y = x ^2 around the y-axis?

15π/2

17

Find the volume of the solid of revolution obtained by rotating the region bounded by
y = x + 1 and y = x^ 2 + 1
about the x-axis.

7π/15

18

Find the volume of the solid of revolution obtained by rotating the region bounded by
y=1x,y=1 and y=2
about the x-axis.

19

The cylindrical tank shown is half full of a certain fluid that weighs 12 pounds per cubic foot. Find the work done in pumping the fluid out of the tank from the top outlet.

4608π ft-lb

20

A force of 20 lb is needed to stretch a spring 10 cm from its natural position. How much work is needed to stretch it from x = 5 to x = 15 cm? (The natural length corresponds to x = 0.)

2 m-lb

21

Find the center of the lamina defined by the region bounded by x = 1, x = 2, y = 1/x and the x-axis.

(1/ln2,1/4ln2)

22

Find the center of mass of the lamina bounded by f (x) = 4 − x ^2 and the x-axis.

(0, 8/5)

23

Find the center of mass of the lamina bounded by: x=1, y=√x and the x-axis.

(3/5, 3/8)

24

Compute the length of the arc
f(x)=x2+x−18ln(2x+1),x∈[0,3].

12+1/8ln7

25

Compute the length of the arc
f(x)=1+e^x+1/4e^−x,x∈[0,1]

e−1/4e-3/4

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