Pearson eText for Thomas' Calculus -- Instant Access (Pearson+)
14th Edition
ISBN: 9780137442997
Author: Joel Hass, Christopher Heil
Publisher: PEARSON+
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Chapter 1.3, Problem 63E
To determine
Calculate the length a of the side opposite A of the triangle.
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A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.
A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as:
dx/dt = k(a-x)(b-x)
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Chapter 1 Solutions
Pearson eText for Thomas' Calculus -- Instant Access (Pearson+)
Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - Which of the graphs are graphs of functions of x,...Ch. 1.1 - Which of the graphs are graphs of functions of x,...Ch. 1.1 - Prob. 9ECh. 1.1 - Express the side length of a square as a function...
Ch. 1.1 - Express the edge length of a cube as a function of...Ch. 1.1 - A point P in the first quadrant lies on the graph...Ch. 1.1 - Consider the point (x, y) lying on the graph of...Ch. 1.1 - Consider the point (x, y) lying on the graph of ....Ch. 1.1 - Find the natural domain and graph the functions in...Ch. 1.1 - Find the natural domain and graph the functions in...Ch. 1.1 - Find the natural domain and graph the functions in...Ch. 1.1 - Find the natural domain and graph the functions in...Ch. 1.1 - Functions and Graphs
Find the natural domain and...Ch. 1.1 - Functions and Graphs
Find the natural domain and...Ch. 1.1 - Find the domain of .
Ch. 1.1 - Find the range of .
Ch. 1.1 - Graph the following equations and explain why they...Ch. 1.1 - Graph the following equations and explain why they...Ch. 1.1 - Graph the functions in Exercise.
Ch. 1.1 - Piecewise-Defined Functions
Graph the functions in...Ch. 1.1 - Graph the functions in Exercise.
Ch. 1.1 - Piecewise-Defined Functions
Graph the functions in...Ch. 1.1 - Find a formula for each function graphed in...Ch. 1.1 - Prob. 30ECh. 1.1 - Find a formula for each function graphed in...Ch. 1.1 - Find a formula for each function graphed in...Ch. 1.1 - For what values of x is
Ch. 1.1 - What real numbers x satisfy the equation
Ch. 1.1 - Does for all real x? Give reasons for your...Ch. 1.1 - Graph the function
Why is f(x) called the integer...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Prob. 38ECh. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - Prob. 51ECh. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - Prob. 53ECh. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - Prob. 55ECh. 1.1 - Prob. 56ECh. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - Prob. 59ECh. 1.1 - Prob. 60ECh. 1.1 - Prob. 61ECh. 1.1 - Prob. 62ECh. 1.1 - Prob. 63ECh. 1.1 - Kinetic energy The kinetic energy K of a mass is...Ch. 1.1 - Prob. 65ECh. 1.1 - Prob. 66ECh. 1.1 - A box with an open top is to be constructed from a...Ch. 1.1 - Prob. 68ECh. 1.1 - Prob. 69ECh. 1.1 - Prob. 70ECh. 1.1 - Prob. 71ECh. 1.1 - Prob. 72ECh. 1.1 - For a curve to be symmetric about the x-axis, the...Ch. 1.1 - Prob. 74ECh. 1.1 - A pen in the shape of an isosceles right triangle...Ch. 1.1 - Industrial costs A power plant sits next to a...Ch. 1.2 - In Exercises 1 and 2, find the domains of f, g, f...Ch. 1.2 - In Exercises 1 and 2, find the domains of f, g, f...Ch. 1.2 - In Exercises 3 and 4, find the domains of f, g,...Ch. 1.2 - Prob. 4ECh. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - In Exercises 7–10, write a formula for .
7.
Ch. 1.2 - Prob. 8ECh. 1.2 - In Exercises 7–10, write a formula for .
9.
Ch. 1.2 - In Exercises 7–10, write a formula for .
10.
Ch. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Copy and complete the following table.
Ch. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - Prob. 34ECh. 1.2 - Prob. 35ECh. 1.2 - Prob. 36ECh. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Prob. 39ECh. 1.2 - Prob. 40ECh. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Prob. 55ECh. 1.2 - Prob. 56ECh. 1.2 - Prob. 57ECh. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - Prob. 72ECh. 1.2 - Prob. 73ECh. 1.2 - Prob. 74ECh. 1.2 - Prob. 75ECh. 1.2 - Prob. 76ECh. 1.2 - Graph the function .
Ch. 1.2 - Prob. 78ECh. 1.2 - Prob. 79ECh. 1.2 - Prob. 80ECh. 1.2 - Prob. 81ECh. 1.2 - Prob. 82ECh. 1.3 - On a circle of radius 10 m, how long is an arc...Ch. 1.3 - Prob. 2ECh. 1.3 - Prob. 3ECh. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Copy and complete the following table of function...Ch. 1.3 - In Exercises 7–12, one of sin x, cos x, and tan x...Ch. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - In Exercises 7–12, one of sin x, cos x, and tan x...Ch. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Graph the functions in Exercises 13–22. What is...Ch. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Graph y = sin x and together. What are the domain...Ch. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - In Exercises 39–42, express the given quantity in...Ch. 1.3 - Evaluate as .
Ch. 1.3 - Evaluate as .
Ch. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.3 - Prob. 47ECh. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - Using the Half-Angle Formulas
Find the function...Ch. 1.3 - Prob. 51ECh. 1.3 - Solving Trigonometric Equations
For Exercise...Ch. 1.3 - Prob. 53ECh. 1.3 - Prob. 54ECh. 1.3 - The tangent sum formula The standard formula for...Ch. 1.3 - (Continuation of Exercise 55.) Derive a formula...Ch. 1.3 - Prob. 57ECh. 1.3 - Prob. 58ECh. 1.3 - Prob. 59ECh. 1.3 - A triangle has sides a = 2 and b = 3 and angle C =...Ch. 1.3 - Prob. 61ECh. 1.3 - Prob. 62ECh. 1.3 - Prob. 63ECh. 1.3 - Prob. 64ECh. 1.3 - Prob. 65ECh. 1.3 - Prob. 66ECh. 1.3 - Prob. 67ECh. 1.3 - Prob. 68ECh. 1.3 - General Sine Curves
For
identify A, B, C, and D...Ch. 1.3 - Prob. 70ECh. 1.4 - Prob. 1ECh. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1.4 - Prob. 35ECh. 1.4 - Prob. 36ECh. 1.5 - In Exercises 1–6, sketch the given curves together...Ch. 1.5 - Prob. 2ECh. 1.5 - Prob. 3ECh. 1.5 - Prob. 4ECh. 1.5 - Prob. 5ECh. 1.5 - Prob. 6ECh. 1.5 - Prob. 7ECh. 1.5 - In each of Exercises 7–10, sketch the shifted...Ch. 1.5 - Prob. 9ECh. 1.5 - Prob. 10ECh. 1.5 - Prob. 11ECh. 1.5 - Prob. 12ECh. 1.5 - Prob. 13ECh. 1.5 - Prob. 14ECh. 1.5 - Prob. 15ECh. 1.5 - Prob. 16ECh. 1.5 - Prob. 17ECh. 1.5 - Prob. 18ECh. 1.5 - Prob. 19ECh. 1.5 - Prob. 20ECh. 1.5 - Find the domain and range for each of the...Ch. 1.5 - Find the domain and range for each of the...Ch. 1.5 - Prob. 23ECh. 1.5 - Prob. 24ECh. 1.5 - Prob. 25ECh. 1.5 - Prob. 26ECh. 1.5 - Prob. 27ECh. 1.5 - Prob. 28ECh. 1.5 - Prob. 29ECh. 1.5 - Prob. 30ECh. 1.5 - In Exercises 29-36, use an exponential model and a...Ch. 1.5 - Prob. 32ECh. 1.5 - Prob. 33ECh. 1.5 - In Exercises 29-36, use an exponential model and a...Ch. 1.5 - Prob. 35ECh. 1.5 - Prob. 36ECh. 1.6 - Which of the functions graphed in Exercise are...Ch. 1.6 - Prob. 2ECh. 1.6 - Prob. 3ECh. 1.6 - Prob. 4ECh. 1.6 - Prob. 5ECh. 1.6 - Prob. 6ECh. 1.6 - Prob. 7ECh. 1.6 - Prob. 8ECh. 1.6 - Prob. 9ECh. 1.6 - Prob. 10ECh. 1.6 - Prob. 11ECh. 1.6 - Prob. 12ECh. 1.6 - Prob. 13ECh. 1.6 - Prob. 14ECh. 1.6 - Prob. 15ECh. 1.6 - Prob. 16ECh. 1.6 - Prob. 17ECh. 1.6 - Prob. 18ECh. 1.6 - Prob. 19ECh. 1.6 - Prob. 20ECh. 1.6 - Prob. 21ECh. 1.6 - Prob. 22ECh. 1.6 - Prob. 23ECh. 1.6 - Prob. 24ECh. 1.6 - Prob. 25ECh. 1.6 - Prob. 26ECh. 1.6 - Each of Exercises 25–36 gives a formula for a...Ch. 1.6 - Prob. 28ECh. 1.6 - Prob. 29ECh. 1.6 - Prob. 30ECh. 1.6 - Prob. 31ECh. 1.6 - Each of Exercises 25–36 gives a formula for a...Ch. 1.6 - Prob. 33ECh. 1.6 - Prob. 34ECh. 1.6 - Prob. 35ECh. 1.6 - Prob. 36ECh. 1.6 - Prob. 37ECh. 1.6 - Prob. 38ECh. 1.6 - Prob. 39ECh. 1.6 - Prob. 40ECh. 1.6 - Prob. 41ECh. 1.6 - Prob. 42ECh. 1.6 - Prob. 43ECh. 1.6 - Prob. 44ECh. 1.6 - Prob. 45ECh. 1.6 - Prob. 46ECh. 1.6 - Prob. 47ECh. 1.6 - Prob. 48ECh. 1.6 - Prob. 49ECh. 1.6 - Prob. 50ECh. 1.6 - Prob. 51ECh. 1.6 - Prob. 52ECh. 1.6 - Prob. 53ECh. 1.6 - Prob. 54ECh. 1.6 - Prob. 55ECh. 1.6 - Prob. 56ECh. 1.6 - Prob. 57ECh. 1.6 - In Exercises 57–64, solve for t.
58.
e−0.01t =...Ch. 1.6 - Prob. 59ECh. 1.6 - Prob. 60ECh. 1.6 - Prob. 61ECh. 1.6 - Prob. 62ECh. 1.6 - Prob. 63ECh. 1.6 - Prob. 64ECh. 1.6 - Prob. 65ECh. 1.6 - Prob. 66ECh. 1.6 - Prob. 67ECh. 1.6 - Prob. 68ECh. 1.6 - Prob. 69ECh. 1.6 - Prob. 70ECh. 1.6 - In Exercises 71-74, find the exact value of each...Ch. 1.6 - Prob. 72ECh. 1.6 - Prob. 73ECh. 1.6 - Prob. 74ECh. 1.6 - If f(x) is one-to-one, can anything be said about...Ch. 1.6 - If f(x) is one-to-one, can anything be said about...Ch. 1.6 - Suppose that the range of g lies in the domain of...Ch. 1.6 - If a composition f ◦ g is one-to-one, must g be...Ch. 1.6 - Prob. 79ECh. 1.6 - The identity arcsin x + arccos x = π/2 Figure 1.69...Ch. 1.6 - Prob. 81ECh. 1.6 - Prob. 82ECh. 1.6 - Prob. 83ECh. 1.6 - Prob. 84ECh. 1.6 - Prob. 85ECh. 1.6 - Prob. 86ECh. 1.6 - Prob. 87ECh. 1.6 - Prob. 88ECh. 1 - Prob. 1GYRCh. 1 - Prob. 2GYRCh. 1 - Prob. 3GYRCh. 1 - Prob. 4GYRCh. 1 - Prob. 5GYRCh. 1 - Prob. 6GYRCh. 1 - Prob. 7GYRCh. 1 - Prob. 8GYRCh. 1 - How do you change the equation y = f(x) to shift...Ch. 1 - Prob. 10GYRCh. 1 - Prob. 11GYRCh. 1 - Prob. 12GYRCh. 1 - Prob. 13GYRCh. 1 - Prob. 14GYRCh. 1 - Prob. 15GYRCh. 1 - Name three issues that arise when functions are...Ch. 1 - Prob. 17GYRCh. 1 - Prob. 18GYRCh. 1 - Prob. 19GYRCh. 1 - Prob. 20GYRCh. 1 - Prob. 21GYRCh. 1 - Prob. 22GYRCh. 1 - Prob. 23GYRCh. 1 - Prob. 24GYRCh. 1 - Prob. 1PECh. 1 - Prob. 2PECh. 1 - Prob. 3PECh. 1 - Prob. 4PECh. 1 - Prob. 5PECh. 1 - Prob. 6PECh. 1 - Prob. 7PECh. 1 - Prob. 8PECh. 1 - Prob. 9PECh. 1 - Prob. 10PECh. 1 - Prob. 11PECh. 1 - Prob. 12PECh. 1 - Prob. 13PECh. 1 - Prob. 14PECh. 1 - Prob. 15PECh. 1 - Prob. 16PECh. 1 - Prob. 17PECh. 1 - Prob. 18PECh. 1 - Prob. 19PECh. 1 - Prob. 20PECh. 1 - Prob. 21PECh. 1 - Prob. 22PECh. 1 - Prob. 23PECh. 1 - Prob. 24PECh. 1 - Prob. 25PECh. 1 - Prob. 26PECh. 1 - Prob. 27PECh. 1 - Prob. 28PECh. 1 - Prob. 29PECh. 1 - Prob. 30PECh. 1 - Prob. 31PECh. 1 - Prob. 32PECh. 1 - Prob. 33PECh. 1 - Prob. 34PECh. 1 - Prob. 35PECh. 1 - Prob. 36PECh. 1 - Prob. 37PECh. 1 - Prob. 38PECh. 1 - Prob. 39PECh. 1 - Prob. 40PECh. 1 - Prob. 41PECh. 1 - Prob. 42PECh. 1 - Prob. 43PECh. 1 - Prob. 44PECh. 1 - Prob. 45PECh. 1 - Prob. 46PECh. 1 - Prob. 47PECh. 1 - Prob. 48PECh. 1 - Prob. 49PECh. 1 - Prob. 50PECh. 1 - Prob. 51PECh. 1 - Prob. 52PECh. 1 - Prob. 53PECh. 1 - Prob. 54PECh. 1 - Prob. 55PECh. 1 - Prob. 56PECh. 1 - Prob. 57PECh. 1 - Prob. 58PECh. 1 - Prob. 59PECh. 1 - Prob. 60PECh. 1 - Prob. 61PECh. 1 - Prob. 62PECh. 1 - Prob. 63PECh. 1 - Prob. 64PECh. 1 - Prob. 65PECh. 1 - Prob. 66PECh. 1 - Prob. 67PECh. 1 - Prob. 68PECh. 1 - Prob. 69PECh. 1 - Prob. 70PECh. 1 - Prob. 71PECh. 1 - Prob. 72PECh. 1 - Prob. 73PECh. 1 - Prob. 74PECh. 1 - Prob. 75PECh. 1 - Prob. 76PECh. 1 - Prob. 77PECh. 1 - Prob. 78PECh. 1 - Prob. 79PECh. 1 - Prob. 80PECh. 1 - Prob. 81PECh. 1 - Prob. 82PECh. 1 - Prob. 83PECh. 1 - Prob. 84PECh. 1 - Prob. 85PECh. 1 - Prob. 86PECh. 1 - Prob. 87PECh. 1 - Prob. 88PECh. 1 - Prob. 1AAECh. 1 - Prob. 2AAECh. 1 - Prob. 3AAECh. 1 - Prob. 4AAECh. 1 - Prob. 5AAECh. 1 - Prob. 6AAECh. 1 - Prob. 7AAECh. 1 - Prob. 8AAECh. 1 - Prob. 9AAECh. 1 - Prob. 10AAECh. 1 - Show that if f is both even and odd, then f(x) = 0...Ch. 1 - Prob. 12AAECh. 1 - Prob. 13AAECh. 1 - Prob. 14AAECh. 1 - Prob. 15AAECh. 1 - Find the slope of the line from the origin to the...Ch. 1 - Consider the quarter-circle of radius 1 and right...Ch. 1 - Prob. 18AAECh. 1 - Prob. 19AAECh. 1 - Prob. 20AAECh. 1 - Prob. 21AAECh. 1 - Prob. 22AAECh. 1 - Prob. 23AAECh. 1 - Prob. 24AAECh. 1 - Prob. 25AAECh. 1 - Prob. 26AAECh. 1 - Prob. 27AAECh. 1 - Prob. 28AAE
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