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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 4.9, Problem 67E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
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
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 79E
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

An object is projected upward with initial velocity v0, meters per second from a point s0 meters above the ground. Show that

[ v ( t ) ] 2 = v 0 2 − 19.6 [ s ( t ) − s 0 ]

To determine

To show: The equation [v(t)]2=v02−19.6[s(t)−s0] .

Explanation

Given data:

Initial velocity is v0 , and initial displacement is s0 .

Formula Used:

Write the expression for acceleration function a(t) .

a(t)=v′(t) (1)

Here,

v′(t) is first derivative of velocity function v(t) .

Write the expression for velocity function v(t) .

v(t)=s′(t) (2)

Here,

s′(t) is first derivative of displacement function s(t) .

Antiderivative of t is 12t2 and 1 is t .

Calculation:

Initial velocity is v0 , that is v(0)=v0 and the initial displacement is s0 , that is s(0)=s0 .

The motion of stone is close to ground, so the motion is considered as gravitational constant (g) , which is 9.8 ms2 .

Write the expression for acceleration function (a(t)) .

a(t)=−9.8

Substitute −9.8 for a(t) in equation (1),

v′(t)=−9.8

Antiderivate the expression with respect to t,

v(t)=−9.8t+C (3)

Here,

C is arbitrary constant.

Substitute 0 for t in equations (3),

v(0)=−9.8(0)+C=C

Substitute v0 for v(0) ,

C=v0

Substitute v0 for C in equation (3),

v(t)=−9.8t+v0 (4)

Substitute −9.8t+v0 for v(t) in equation (2),

s′(t)=−9.8t+v0

Antiderivate the expression with respect to t,

s(t)=−9.8(12t2)+v0t+D

s(t)=−4

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Find each of the following probabilities for a normal distribution. a. p(z1.25) b. p(z0.60) c. p(z0.70) d. p(z1...

Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate expressions in Exercises 3756, rounding your answer to four significant digits where necessary. 4

Finite Mathematics

31. Solve for t.

Mathematical Applications for the Management, Life, and Social Sciences

Use sets toshow that 06=0.

Mathematical Excursions (MindTap Course List)

For Problems 51-78, simplify each of the numerical expressions. Objective 3 2022027

Intermediate Algebra

Every corporation has a governing board of directors. The number of individuals on a board varies from one corp...

Probability and Statistics for Engineering and the Sciences

Evaluate the integral. 71. e2x1+exdx

Single Variable Calculus: Early Transcendentals

To construct a regular octagon, what measure would be necessary for each interior angle? Construct an angle of ...

Elementary Geometry For College Students, 7e

Divide: +85+5

Elementary Technical Mathematics

Estimate the following by rounding each number all the way; then add to find the exact answer. Estimate Rounded...

Contemporary Mathematics for Business & Consumers

Exercises Determine wether the given figure has rotational symmetry or reflective symmetry.

Elements Of Modern Algebra

Find all degree solutions for each of the following: cos8=12

Trigonometry (MindTap Course List)

CONCEPT CHECK Existence of a Limit Determine whether limx3f(x) exists. Explain. limx3f(x)=1andlimx3+f(x)=1

Calculus of a Single Variable

Proof Show that the function f(x)=arcsinx222arcsin(x2),x1 is constant for 0x4.

Calculus: Early Transcendental Functions (MindTap Course List)

Exam Scores The following table gives the scores of 30 students in a mathematics examination: Scores 9099 8089 ...

Finite Mathematics for the Managerial, Life, and Social Sciences

In exercises 21 to 30. Use the drawings. Where provided, to solve each problem. Angle measures should be found ...

Elementary Geometry for College Students

Differentiation of Piecewise Functions Describe how you would differentiate a piecewise function. Use your appr...

Calculus (MindTap Course List)

The graph of y = f(3x) is obtained from the graph of y = f(x) by: stretching vertically by a factor of 3. compr...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

By the method of variation of parameters, a particular solution to, where , and:

Study Guide for Stewart's Multivariable Calculus, 8th

Finding an Indefinite Integral In Exercises 1534, find the indefinite integral. ( Note: Solve by the simplest m...

Calculus

Solving an Exact Differential Equation In Exercises3-6, verify that the differential equation is exact. Then fi...

Multivariable Calculus

The following data give the percentage of women working in five companies in the retail and trade industry. The...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Explain how the process of randomly assigning participants to treatment conditions should prevent a participant...

Research Methods for the Behavioral Sciences (MindTap Course List)

In each of Exercises 23 through 26, three views of the angular portion of a tool with front clearance are shown...

Mathematics For Machine Technology

Find the number of possible positive, negative, and nonreal zeros for each polynomial function. P(x)=3x4+2x34x+...

College Algebra (MindTap Course List)

In a Latin square, each treatment condition occurs first one time, second one time, third one time, and so on. ...

Research Methods for the Behavioral Sciences (MindTap Course List)

A person is interested in constructing a portfolio. Two stocks are being considered. Letx = percent return for ...

Statistics for Business & Economics, Revised (MindTap Course List)

The article Estimation of the Economic Threshold of Infestation for Cotton Aphid (Mesopotamia Journal of Agricu...

Introduction To Statistics And Data Analysis

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