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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
The survival rates for song spar- rows are shown in the table. The values listed are the numbers of song sparrows that attain a given age from 100 eggs. For example, 6 sparrows reach an age of 2 years from 100 eggs laid in the wild.(a) Make a line graph of the data. Interpret the data. (b) Does
Use a calculator to evaluate the expression. Round your result to the nearest thousandth. 1.53 √2+ = -5 #
Find the average rate of change of f(x)=x2 -x + 1 from x1 = 1 to x2 = 3.
A rectangular swim- ming pool that is 25 feet by 50 feet has a 6-foot-wide sidewalk around it. (a) How much fencing would be needed to enclose the sidewalk? (b) Find the area of the sidewalk.
A driver's distance D in miles from a rest stop after / hours is given by D(t) = 280 - 70t. (a) How far is the driver from the rest stop after 2 hours? (b) Find the slope of the graph of D. Interpret this slope as a rate of change.
The average distance between the planet Mars and the sun is approximately 228 million kilome- ters. Estimate the time required for sunlight, traveling at 300,000 kilometers per second, to reach Mars.
Suppose that 0.25 cubic inch of paint is applied to a circular piece of plastic with a diameter of 20 inches. Estimate the thickness of the paint.
At noon car A is traveling north at 30 miles per hour and is located 20 miles north of car B. Car B is traveling west at 50 miles per hour. Approximate the distance between the cars at 12:45 P.M. to the nearest mile.
The graph shows the cost of taking x credits at a university. (a) Why is it reasonable for the graph to pass through the origin? (b) Find the slope of the graph. (c) Interpret the slope as a rate of change. Tuition (dollars) 900 800 700 600 500 400 300 200 100 012345 45678 Credits
Let f(x) = 0.5x2 + 50 represent the outside temperature in degrees Fahrenheit at x P.M., where 1 ≤ x ≤ 5. (a) Graph f. Is f linear or nonlinear? (b) Calculate the average rate of change of f from 1 P.M. to 4 P.M. (c) Interpret this average rate of change.
The graph of a function f is shown. Complete each of the following. Use interval notation when appropriate. (a) Give the zeros of f. (b) Give any x- and y-intercepts on the graph of f. (c) Identify where f is negative or positive.(d) Identify where f is increasing or decreasing. (e) Is the
The graph of a function f is shown. Complete each of the following. Use interval notation when appropriate. (a) Give the zeros of f. (b) Give any x- and y-intercepts on the graph of f. (c) Identify where f is negative or positive.(d) Identify where f is increasing or decreasing. (e) Is the
Use the diameter to find the standard equation of the circle shown. 6 -5 21 123456 X
Use the given f(x) to complete the following. (a) Calculate the average rate of change of f from x = 1 to x = 2. (b) Illustrate your result from part (a) graphically. f(x) = x²
Use the given f(x) to complete the following. (a) Calculate the average rate of change of f from x = 1 to x = 2. (b) Illustrate your result from part (a) graphically. f(x)=4-x²
If your salary is $50,000 per year, decreases by 50%, and then increases by 50%, what is your new salary?
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. x² + 6x + y² = 2y = -1 -
During inhalation, the typical body generates 0.14 watt of electrical power, which could be used to power tiny electrical circuits. Write this number in scientific notation.
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. x² + y² + 12y + 32 = 0
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. x² + 6x + y² = 2y + 3 = 0
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. x² + 6x + y² + 8y + 9 = 0
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. x² - 4x + y² + 4y = −3
The graph of a function f is shown. Complete each of the following. Use interval notation when appropriate. (a) Give the zeros of f. (b) Give any x- and y-intercepts on the graph of f. (c) Identify where f is negative or positive.(d) Identify where f is increasing or decreasing. (e) Is the
S is given by the table. X y 1 10.5 3 1 2 -0.5
Sketch a graph that illustrates the motion of the person described. Let the x-axis represent time and the y-axis represent distance from home. Be sure to label each axis.A person drives a car away from home for 2 hours at 50 miles per hour and then stops for 1 hour.
Sketch a graph that illustrates the motion of the person described. Let the x-axis represent time and the y-axis represent distance from home. Be sure to label each axis.A person drives to a nearby park at 25 miles per hour for 1 hour, rests at the park for 2 hours, and then drives home at 50 miles
The graph of a function f is shown. Complete each of the following. Use interval notation when appropriate. (a) Give the zeros of f. (b) Give any x- and y-intercepts on the graph of f. (c) Identify where f is negative or positive.(d) Identify where f is increasing or decreasing. (e) Is the
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. x² + 8x + y² − 6y + 16 = 0
Do not use a graphing calculator.On the same coordinate axes, sketch the graphs of a constant function f and a nonlinear function g that intersect exactly twice.
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. x² - 4x + y² + 12y = -4
Do not use a graphing calculator.Sketch a graph of a function that has only positive average rates of change for x ≥ 1 and only negative average rates of change for x ≥ 1.
Do not use a graphing calculator.Sketch a graph that increases on (-4, 0), decreases on (0,4), and has a positive average rate of change from x = -4 to x = 4.
Do not use a graphing calculator.Sketch a graph that decreases on (-3, 1), increases on (1,2), and has a negative average rate of change from x = -3 to x = 2.
For each function find f(x + h) and f(x) + f(h). f(x) = x² - 4
Evaluate f(3 + 4) and f(3) + f(4) for f(x) = 2x2.
Evaluate f(1 + 2) and f(1) + f(2) for f(x) = x3.
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. x² 12x + y² + 10y = -25
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. 4x² + 4x + 4y² - 16y - 19 = 0
For each function find f(x + h) and f(x) + f(h). f(x) = 5x² + x
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. 9x² + 12x +9y² - 18y-23 = 0
For each function find f(x + h) and f(x) + f(h). f(x) = 3x - x²
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 3
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 4x + 3
For each function find f(x + h) and f(x) + f(h). f(x) = x³
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. - 0 = +1 +49 + x2 + ₂x
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = -3x + 4
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 2x + 1
If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle. x² + 4x + y²-8y + 32 = 0
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) -5
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = -6x²-x+4
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 5x - 6
Write a symbolic represen- tation (formula) for a function g that calculates the given quantity. Then evaluate g(10) and interpret the result.The number of inches in x feet
Match the settings for a viewing rect- angle with the correct figure (a-d). [-9,9,1] by [-6, 6, 1]
Match the settings for a viewing rect- angle with the correct figure (a-d). [-6, 6, 1] by [-9, 9, 1]
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. v + z*** = (x)/
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 1 = x²
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 3x² + 1
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. 2 T = x + ₂x = (x)ƒ
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 1 = x³
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 3x²
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. 7- x = (x)f
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. (x) = 늪 2.x
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = -x² + 2x
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = x³
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 2/1/201
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 2x² = x + 1
Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. f(x) = 1 = x³
Let the distance in feet that a car travels in 7 seconds be given by d(t) = 81 for 0 ≤ 1 ≤ 6. (a) Find d(t + h). (b) Find the difference quotient for d and simplify. (c) Evaluate the difference quotient when t = 4 and h = 0.05. Interpret your result.
Let the number of gallons G of water in a pool after t hours be given by the linear function G (t) = 4000 1001 for 0 ≤ t ≤ 40. (a) Find G (1 + h). (b) Find the difference quotient. Interpret your result.
What does the average rate of change represent for a linear function? What does it represent for a nonlinear function? Explain your answers.
Suppose you are given a graphi- cal representation of a function f. Explain how you would determine whether f is constant, linear, or nonlinear. How would you determine the type if you were given a numerical or symbolic representation? Give examples.
Suppose that a function f has a positive average rate of change from 1 to 4. Is it correct to assume that function f only increases on the interval (1,4)? Make a sketch to support your answer.
If f(x) = mx + b. what does the difference quotient for function f equal? Explain your reasoning.
Match the given equation to its graph (a-f) shown in the next column. y = mx + b, m < 0 and b>0
Solve the equation and check your answer. -3x = -(x + 2)
Solve the equation and check your answer. -2=3 −1= 3 = 5x -
Match the given equation to its graph (a-f) shown in the next column. y=b, b
Match the given equation to its graph (a-f) shown in the next column. x=k, k>0
Solve the inequality symbolically. Express the solution set in set-builder or interval notation. -(1-x) = 3x
Solve the inequality symbolically. Express the solution set in set-builder or interval notation. 2-1
Solve the inequality symbolically. Express the solution set in set-builder or interval notation. +225 3
Solve the equation and check your answer. -9-1+ 8x
Find the slope-intercept form for the line satisfying the conditions. Passing through (-1,-4) and (1,2)
Solve the equation and check your answer. 4(2-8)=z
Solve the inequality symbolically. Express the solution set in set-builder or interval notation. x+5 -10 V > 2x + 3
Solve the equation and check your answer. -3 (2z - 1) = 2z
Solve the inequality symbolically. Express the solution set in set-builder or interval notation. 3-X -3 4x – 1 < :
Solve the inequality symbolically. Express the solution set in set-builder or interval notation. -3 (2-4) ≥ 2(1-22)
Find the slope-intercept form for the line satisfying the conditions. Passing through (-1, 6) and (2, -3)
Solve the equation and check your answer. -5(3-4t) = 65
Find the slope-intercept form for the line satisfying the conditions. Passing through (4, 5) and (1.-3)
Solve the equation and check your answer. 6(531) = 66
Solve the inequality symbolically. Express the solution set in set-builder or interval notation. -(2=-6) + = = 5
Find the slope-intercept form for the line satisfying the conditions. Passing through (8,-2) and (-2,3)
Solve the equation and check your answer. 2k3= k + 3
Solve the equation and check your answer. k+8= 5k - 4
Solve the inequality symbolically. Express the solution set in set-builder or interval notation. 1-x V 2x - 2 3
Find the slope-intercept form for the line satisfying the conditions. y-intercept (0, 5), slope -7.8
Solve the inequality symbolically. Express the solution set in set-builder or interval notation. 3x 4 X х+2 2
Find the slope-intercept form for the line satisfying the conditions. y-intercept (0, -155), slope 5.6
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