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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.9, Problem 62E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Chapter
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Problem 1E
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Problem 3E
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Problem 5E
Problem 6E
Problem 7E
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Problem 10E
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Problem 19E
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Problem 21E
Problem 22E
Problem 23E
Problem 24E
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Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
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Problem 38E
Problem 39E
Problem 40E
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Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
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Problem 66E
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Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Two balls are thrown upward from the edge of the cliff in Example 7. The first is thrown with a speed of 48 ft/s and the other is thrown a second later with a speed of 24 ft/s. Do the balls ever pass each other?

To determine

To find:

The required time for the two balls to pass each other.

Explanation

1) Concept:

i. If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is Fx+c, where c is an arbitrary constant.

ii.

αt=ddxvt

iii.

vt=ddxst

2) Calculations:

Here, two balls are thrown upward from the edge of the cliff above the ground.

The motion is vertical and we choose the positive direction to be upward.

At time t  the distance above the ground is s(t) and the velocity v(t) is decreasing. Therefore, the acceleration must be negative.

αt=dvdt=-32

⇒αt=-32

Taking the general antiderivative of αt by using the rules of antiderivative is

vt=-32t+v0, using v0(initial velocity) as a constant term

Now, take general antiderivative of vt, using the rules of antiderivative is

st=-32×t22+v0t+s0, using s0 (initial position) as a constant term

⇒ st=-16t2+v0t+s0

Now, the first ball is thrown with a speed of 48 feet/s

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The top, front, and right side views of a compound-angular surface are shown in the figure. a. Sketch and label...

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Consider the following population: {2, 3, 3, 4, 4}. The value of is 3.2, but suppose that this is not known to...

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Consider the following time series data. a. Construct a time series plot. What type of pattern exists in the da...

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Explain how holding a participant variable such as gender constant prevents the variable from becoming a confou...

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Describe and explain the independent relationship between main effects and interactions.

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