Calculus of a Single Variable
11th Edition
ISBN: 9781337275361
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Question
Chapter 4.1, Problem 62E
To determine
To calculate: The time taken by the rock to hit the canyon floor, if Grand Canyon is 1800 meters deep.
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Chapter 4 Solutions
Calculus of a Single Variable
Ch. 4.1 - CONCEPT CHECK Antiderivative What does it mean for...Ch. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - General and Particular Solutions Describe the...Ch. 4.1 - Integration and Differentiation In Exercises 5 and...Ch. 4.1 - Prob. 6ECh. 4.1 - Solving a Differential Equation In Exercises 7-10,...Ch. 4.1 - Solving a Differential Equation In Exercises 7-10,...Ch. 4.1 - Solving a Differential Equation In Exercises 7-10,...Ch. 4.1 - Solving a Differential Equation In Exercises 7-10,...
Ch. 4.1 - Rewriting Before Integrating In Exercises 11-14,...Ch. 4.1 - Rewriting Before Integrating In Exercises 11-14,...Ch. 4.1 - Rewriting Before Integrating In Exercises 11-14,...Ch. 4.1 - Rewriting Before Integrating In Exercises 11-14,...Ch. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 20ECh. 4.1 - Prob. 18ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 28ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 26ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 30ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 34ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 36ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 4.1 - Prob. 40ECh. 4.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Slope Field In Exercises 45 and 46, a differential...Ch. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Comparing Functions Consider f(x)=tan2x and...Ch. 4.1 - HOW DO YOU SEE IT? Use the graph of f shown in the...Ch. 4.1 - Prob. 53ECh. 4.1 - Sketching Graphs The graphs of f and f each pass...Ch. 4.1 - Tree Growth An evergreen nursery usually sells a...Ch. 4.1 - Population Growth The rate of growth dP/dt of a...Ch. 4.1 - Vertical Motion In Exercises 57-59, assume the...Ch. 4.1 - Vertical Motion In Exercises 57-59, assume the...Ch. 4.1 - Vertical Motion In Exercises 57-59, assume the...Ch. 4.1 - Vertical Motion In Exercises 60-62, assume the...Ch. 4.1 - Vertical Motion In Exercises 60-62, assume the...Ch. 4.1 - Prob. 62ECh. 4.1 - Lunar Gravity On the moon, the acceleration of a...Ch. 4.1 - Escape Velocity The minimum velocity required for...Ch. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Rectilinear Motion In Exercises 65-68, consider a...Ch. 4.1 - Rectilinear Motion In Exercises 65-68, consider a...Ch. 4.1 - Acceleration The maker of an automobile advertises...Ch. 4.1 - Deceleration A car traveling at 45 miles per hour...Ch. 4.1 - Prob. 71ECh. 4.1 - Acceleration Assume that a fully loaded plane...Ch. 4.1 - Prob. 73ECh. 4.1 - Prob. 74ECh. 4.1 - Prob. 79ECh. 4.1 - Prob. 80ECh. 4.1 - Prob. 75ECh. 4.1 - True or False? In Exercises 73-78, determine...Ch. 4.1 - Prob. 77ECh. 4.1 - Prob. 81ECh. 4.1 - Prob. 78ECh. 4.2 - Prob. 1ECh. 4.2 - CONCEPT CHECK Sums What is the value of n? (a)...Ch. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Finding a Sum In Exercises 5-10, find the sum by...Ch. 4.2 - Prob. 6ECh. 4.2 - Finding a Sum In Exercises 5-10, find the sum by...Ch. 4.2 - Prob. 8ECh. 4.2 - Finding a Sum In Exercises 5-10, find the sum by...Ch. 4.2 - Finding a Sum In Exercises 5-10, find the sum by...Ch. 4.2 - Using Sigma Notation In Exercises 11-16, use sigma...Ch. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Using Sigma Notation In Exercises 11-16, use sigma...Ch. 4.2 - Prob. 16ECh. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Prob. 22ECh. 4.2 - Evaluating a Sum In Exercises 1724, use the...Ch. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Evaluating a Sum In Exercises 2528, use the...Ch. 4.2 - Evaluating a Sum In Exercises 25-28, use the...Ch. 4.2 - Prob. 28ECh. 4.2 - Approximating the Area of a Plane Region In...Ch. 4.2 - Prob. 30ECh. 4.2 - Approximating the Area of a Plane Region In...Ch. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Using Upper and Lower Sums In Exercises 35 and 36,...Ch. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Prob. 40ECh. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Prob. 65ECh. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - EXPLORING CONCEPTS Midpoint Rule Does the Midpoint...Ch. 4.2 - Graphical Reasoning Consider the region bounded by...Ch. 4.2 - Prob. 72ECh. 4.2 - Prob. 73ECh. 4.2 - Prob. 74ECh. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - Seating Capacity A teacher places n scats to form...Ch. 4.2 - Prob. 78ECh. 4.2 - Prob. 79ECh. 4.3 - CONCEPT CHECK Riemann Sum What does a Riemann Mini...Ch. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Evaluating a Definite Integral as a Limit In...Ch. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Evaluating a Definite Integral as a Limit In...Ch. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Writing a Definite Integral In Exercises 13-22,...Ch. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Writing a Definite Integral In Exercises 13-22,...Ch. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Evaluating a Definite Integral Using a Geometric...Ch. 4.3 - Evaluating a Definite Integral Using a Geometric...Ch. 4.3 - Evaluating a Definite Integral Using a Geometric...Ch. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Using Properties of Definite Integrals In...Ch. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Using Properties of Definite Integrals Given...Ch. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Estimating a Definite Integral Use the table of...Ch. 4.3 - Estimating a Definite Integral Use the table of...Ch. 4.3 - Think About It The graph of f consists of line...Ch. 4.3 - Think About It The graph of f consists of line...Ch. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Think About It A function f is defined below. Use...Ch. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Finding a Riemann Sum Find the Riemann sum for...Ch. 4.3 - Prob. 71ECh. 4.3 - Prob. 72ECh. 4.3 - Prob. 73ECh. 4.3 - Prob. 74ECh. 4.3 - Finding Values Find the constants a and b that...Ch. 4.3 - Prob. 76ECh. 4.3 - Prob. 77ECh. 4.3 - Prob. 78ECh. 4.3 - Prob. 79ECh. 4.4 - CONCEPT CHECK Fundamental Theorem of Calculus...Ch. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Graphical Reasoning In Exercises 58, use a...Ch. 4.4 - Graphical Reasoning In Exercises 58, use a...Ch. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 45ECh. 4.4 - Finding the Area of a Region In Exercises 41-46,...Ch. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Using the Mean Value Theorem for Integrals In...Ch. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Prob. 56ECh. 4.4 - Finding the Average Value of a Function In...Ch. 4.4 - Prob. 58ECh. 4.4 - Force The force F (in newtons) of a hydraulic...Ch. 4.4 - Respiratory Cycle The volume V in liters, of air...Ch. 4.4 - Prob. 61ECh. 4.4 - HOW DO YOU SEE IT? The graph of f is shown in the...Ch. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Prob. 66ECh. 4.4 - Analyzing a Function Let g(x)=0xf(t)dt where f is...Ch. 4.4 - Analyzing a Function Let g(x)=0xf(t)dt where f is...Ch. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Finding and Checking an Integral In Exercises...Ch. 4.4 - Prob. 74ECh. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.4 - Prob. 79ECh. 4.4 - Prob. 80ECh. 4.4 - Finding a Derivative In Exercises 81-86, find F( x...Ch. 4.4 - Finding a Derivative In Exercises 81-86, find F( x...Ch. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Graphical Analysis Sketch an approximate graph of...Ch. 4.4 - Prob. 88ECh. 4.4 - Water Flow Water flows from a storage tank at a...Ch. 4.4 - Oil Leak At 1:00 p.m., oil begins leaking from a...Ch. 4.4 - Velocity The graph shows the velocity, in feet per...Ch. 4.4 - Prob. 92ECh. 4.4 - Particle Motion In Exercises 93-98, the velocity...Ch. 4.4 - Prob. 94ECh. 4.4 - Prob. 95ECh. 4.4 - Prob. 96ECh. 4.4 - Prob. 97ECh. 4.4 - Prob. 98ECh. 4.4 - Prob. 99ECh. 4.4 - Prob. 100ECh. 4.4 - Prob. 101ECh. 4.4 - Prob. 102ECh. 4.4 - Prob. 103ECh. 4.4 - Prob. 104ECh. 4.4 - Prob. 105ECh. 4.4 - Prob. 106ECh. 4.4 - Prob. 107ECh. 4.4 - Prob. 108ECh. 4.4 - Prob. 109ECh. 4.4 - Prob. 110ECh. 4.4 - Prob. 111ECh. 4.4 - Finding a Function Find the function f(x) and all...Ch. 4.4 - Prob. 113ECh. 4.4 - Prob. 114ECh. 4.4 - PUTNAM EXAM CHALLENGE For each continuous function...Ch. 4.5 - CONCEPT CHECK Constant Multiple Rule Explain how...Ch. 4.5 - Prob. 2ECh. 4.5 - CONCEPT CHECK The General Power Rule for...Ch. 4.5 - Prob. 4ECh. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Prob. 8ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 10ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 18ECh. 4.5 - Prob. 20ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 30ECh. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Prob. 32ECh. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 49ECh. 4.5 - Finding an Equation Exercises 49-52, find an...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Prob. 54ECh. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Prob. 56ECh. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 61ECh. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Evaluating a Definite Integral In Exercises 61-68,...Ch. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - Prob. 70ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Using Symmetry Use the symmetry of the graphs of...Ch. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Depreciation The rate of depreciation dV/dt of a...Ch. 4.5 - HOW DO YOU SEE IT? The graph shows the flow rate...Ch. 4.5 - Prob. 85ECh. 4.5 - Electricity The oscillating current in an...Ch. 4.5 - Prob. 87ECh. 4.5 - Prob. 88ECh. 4.5 - Prob. 89ECh. 4.5 - Prob. 90ECh. 4.5 - Prob. 91ECh. 4.5 - Prob. 92ECh. 4.5 - True or False? In Exercises 9398, determine...Ch. 4.5 - Prob. 94ECh. 4.5 - Prob. 95ECh. 4.5 - Prob. 96ECh. 4.5 - Prob. 97ECh. 4.5 - True or False? In Exercises 9398, determine...Ch. 4.5 - Prob. 99ECh. 4.5 - Prob. 100ECh. 4.5 - Prob. 101ECh. 4.5 - Prob. 102ECh. 4.5 - Prob. 103ECh. 4.5 - Prob. 104ECh. 4 - Finding an Indefinite Integral In Exercises 1-8,...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 8RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Finding a Particular Solution In Exercises 9-12,...Ch. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Vertical Motion With what initial velocity must an...Ch. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Evaluating a Sum In Exercises 1924, use the...Ch. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 43RECh. 4 - Prob. 46RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 49RECh. 4 - Prob. 52RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 53RECh. 4 - Using the Mean Value Theorem for Integrals In...Ch. 4 - Finding the Average Value of a Function In...Ch. 4 - Prob. 56RECh. 4 - Finding the Area of a Region In Exercises 47 and...Ch. 4 - Prob. 48RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 60RECh. 4 - Prob. 59RECh. 4 - Prob. 63RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Evaluating a Definite Integral In Exercises 67-72,...Ch. 4 - Prob. 72RECh. 4 - Finding the Area of a Region In Exercises 73 and...Ch. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 1PSCh. 4 - Parabolic Arch Archimedes showed that the area of...Ch. 4 - Prob. 14PSCh. 4 - Prob. 5PSCh. 4 - Prob. 6PSCh. 4 - Prob. 7PSCh. 4 - Prob. 8PSCh. 4 - Prob. 9PSCh. 4 - Prob. 10PSCh. 4 - Prob. 11PSCh. 4 - Prob. 12PSCh. 4 - Prob. 13PSCh. 4 - Velocity and Acceleration A car travels in a...Ch. 4 - Prob. 16PSCh. 4 - Prob. 17PSCh. 4 - Prob. 3PSCh. 4 - Prob. 4PSCh. 4 - Prob. 18PSCh. 4 - Upper and Lower Sums Consider the region bounded...Ch. 4 - Prob. 20PSCh. 4 - Finding a Function The graph of f' is shown. Find...
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- Hooke’s Law In Exercises 65-68, use Hooke’s Law, which states that the distance a spring stretches (or compresses) from its natural, or equilibrium, length varies directly as the applied force on the spring. The coiled spring of a toy supports the weight of a child. The weight of a 25-pound child compresses the spring a distance of 1.9 inches. The toy does not work properly when a weight compresses the spring more than 3 inches. What is the maximum weight for which the toy works properly?arrow_forwardHooke’s Law In Exercises 65-68, use Hooke’s Law, which states that the distance a spring stretches (or compresses) from its natural, or equilibrium, length varies directly as the applied force on the spring. An overhead garage door has two springs, one on each side of the door. A force of 15 pounds is required to stretch each spring 1 foot. Because of a pulley system, the springs stretch only one-half the distance the door travels. The door moves a total of 8 feet, and the springs are at their natural lengths when the door is open. Find the combined lifting force applied to the door by the springs when the door is closed.arrow_forwardProjectile Motion In Exercises 75 and 76, consider the path of an object projected horizontally with a velocity of v feet per second at a height of s feet, where the model for the path is x2=v216ys. In this model (in which air resistance is disregarded), y is the height (in feet) of the projectile and x is the horizontal distance (in feet) the projectile travels. A ball is thrown from the top of a 100-foot tower with a velocity of 28 feet per second. (a) Write an equation for the parabolic path. (b) How far does the ball travel horizontally before it strikes the ground?arrow_forward
- Hooke’s Law In Exercises 65-68, use Hooke’s Law, which states that the distance a spring stretches (or compresses) from its natural, or equilibrium, length varies directly as the applied force on the spring. A force of 220 newtons stretches a spring 0.12 meter. What force stretches the spring 0.16 meter?arrow_forwardHooke’s Law In Exercises 65-68, use Hooke’s Law, which states that the distance a spring stretches (or compresses) from its natural, or equilibrium, length varies directly as the applied force on the spring. A force of 265 newtons stretches a spring 0.15 meter. (a) What force stretches the spring 0.1 meter? (b) How far does a force of 90 newtons stretch the spring?arrow_forwardA stone is thrown straight down from the edge of a roof, 1125 feet above the ground, at a speed of 9 feet per second. A. Remembering that the acceleration due to gravity is -32 feet per second squared, how high is the stone 6 seconds later? B. At what time does the stone hit the ground? C. What is the velocity of the stone when it hits the ground? - I answered a question where the stone is thrown up but I don't know what to do with this question. I know there is a -1125 somewhere but where do I put it?arrow_forward
- Wind resistance is jointly proportional to velocity and surface area of the object. If an object is traveling 51 mph and has a surface area of 31 square feet it will experience a wind resistance of 355.725 Newtons. How fast must an object be moving to experience a wind resistance of 405.45 Newtons if it has a surface area of 34 square feet?arrow_forwardAn object is shot upwards from ground level with an initial velocity of 3 meters per second; it is subject only to the force of gravity (no air resistance). Find its maximum altitude and the time at which it hits the ground. (g=32fps^2 = 9.8mps^2)arrow_forwardDraining a tank Water is drained from a 3000-gal tank at a rate that starts at 100 gal/hr and decreases continuously by 5%/hr. If the drain is left open indefinitely, how much water drains from the tank? Can a full tank be emptied at this rate?arrow_forward
- A stone is thrown straight up from the edge of a roof, 700 feet above the ground, at a speed of 18 feet per second.A. Remembering that the acceleration due to gravity is -32 feet per second squared, how high is the stone 3 seconds later? B. At what time does the stone hit the ground? C. What is the velocity of the stone when it hits the ground?arrow_forwardThe period T of a pendulum of length L is T = (2 √L)/√g, where g is the acceleration due to gravity. A pendulum is moved from the Canal Zone, where g = 32.09 feet per second per second, to Greenland, where g = 32.23 feet per second per second. Because of the change in temperature, the length of the pendulum changes from 2.5 feet to 2.48 feet. Approximate the change in the period of the pendulumarrow_forwardWater leaks from a vertical cylindrical tank through a small hole in its base at a volumetric rate proportional to the square root of the volume of water remaining. The tank initially contains 225 liters and 15 liters leak out during the first day. When will the tank be half empty? t= How much water will remain in the tank after 2 days? volume =arrow_forward
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