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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
Conical Water Tank A water tank in the shape of an inverted cone has a height of 11 feet and a radius of 3.5 feet, as illustrated in the figure. If the volume of the cone is V = 1/3πr2h, find the volume of the water in the tank when the water is 7 feet deep. 3.5 ft 11 ft
In order to receive an A in a college course it is necessary to obtain an average of 90% correct on three 1-hour exams of 100 points each and on one final exam of 200 points. If a student scores 82. 88, and 91 on the 1-hour exams, what is the minimum score that the person can receive on the final
A boat travels upstream for 30 minutes to reach a swimming beach. The same trip traveling downstream takes 20 minutes. If the current is 4 miles per hour and the speed of the boat is constant, find the boat speed without any current.
Suppose that a lawn can be raked by one gardener in 3 hours and by a second gardener in 5 hours. (a) Mentally estimate how long it will take the two gardeners to rake the lawn working together. (b) Solve part (a) symbolically.
A conical water tank holds 100 cubic feet of water and has a diameter of 6 feet. Estimate its height to the nearest tenth of a foot.Data from Exercise 135Conical Water Tank A water tank in the shape of an inverted cone has a height of 11 feet and a radius of 3.5 feet, as illustrated in the figure.
Suppose that a large pump can empty a swimming pool in 50 hours and a small pump can empty the pool in 80 hours. How long will it take to empty the pool if both pumps are used?
An airplane travels against the wind for 4 hours to reach its destination. The same trip traveling with the wind takes 3 hours. If the wind speed is 30 miles per hour and the speed of the airplane is constant, find the speed of the airplane without any wind.
A car went 372 miles in 6 hours, traveling part of the time at 55 miles per hour and part of the time at 70 miles per hour. How long did the car travel at each speed?
Two types of candy sell for $2.50 per pound and $4.00 per pound. A store clerk is trying to make a 5-pound mixture worth $17.60. How much of each type of candy should be included in the mixture?
At 2:00 P.M. a runner heads north on a highway, jogging at 10 miles per hour. At 2:30 P.M. a driver heads north on the same highway to pick up the runner. If the car travels at 55 miles per hour, how long will it take the driver to catch the runner?
A person 66 inches tall is standing 15 feet from a streetlight. If the person casts a shadow 84 inches long, how tall is the streetlight?
A total of $5000 was invested in two accounts. One pays 5% annual interest, and the second pays 7% annual interest. If the first-year interest is $325, how much was invested in each account?
Determine how much water should be added to 2 liters of 4% saline solution to reduce the concentration to 3%.
Determine how much pure acid should be mixed with 2 liters of 25% acid to increase the concentration to 60%.
Determine how much pure water should be mixed with 5 liters of a 40% solution of sulfuric acid to make a 15% solution of sulfuric acid.
In 1.25 hours an athlete travels 12 miles by first running at 12 miles per hour and then at 8 miles per hour. How many minutes did the athlete run at each speed?
In 3 hours and 15 minutes a driver travels 210 miles by first traveling at 60 miles per hour and then 80 miles per hour. How many hours did the driver travel at each speed?
The following data can be modeled by a linear function. Estimate the value of x when y = 2.99. 1 y -1.66 2 2.06 3 5.78 9.50
Find the length of the longest side of the rectangle if its perimeter is 25 feet. Σχ £x-l
The following data can be modeled by a linear function. Estimate the value of x when y = 2.99. x y 2 4 0.51 1.23 6 1.95 8 2.67
A 174-foot-long fence is being placed around the perimeter of a rectangular swimming pool that has a 3-foot-wide sidewalk around it. The actual swimming pool without the sidewalk is twice as long as it is wide. Find the dimensions of the pool without the sidewalk.
A radiator holds 5 gallons of fluid. If it is full with a 15% solution, how much fluid should be drained and replaced with a 65% antifreeze mixture to result in a 40% antifreeze mixture?
Older two-cycle engines, used in snowmobiles, chain saws, and outboard motors, require a mixture of gasoline and oil. For certain engines the amount of oil in pints that should be added to x gallons of gasoline is computed by f(x) = 0.16x. (a) Why is it reasonable to expect f to be
A company manufactures DVDs. The master disc costs $2000 to produce and copies cost $0.45 each. If a company spent $2990 producing DVDs, how many copies did the company manu- facture?
Describe a basic graphical method used to solve a linear equation. Give an example.
Describe verbally how to solve ax + b = 0. What assumptions have you made about the value of a?
Match the settings for a viewing rectangle with the correct figure (a-d). [-4, 8, 1] by [-600, 600, 100]
Match the settings for a viewing rectangle with the correct figure (a-d). [-2, 2, 0.5] by [-4.5, 4.5, 0.5]
S is given by the table. x y 1 1 2 1 3 1
Evaluate each expression with a calculator. Round answers to the nearest hundredth. (a) √1.2 + 7³ (c) √5² +2.1 3.2 +5.7 7.9-4.5 (d) 1.2(6.3)² + (b) 3.2
Sort the list of numbers from smallest to largest and display the result in a table. (a) Determine the maximum and minimum values. (b) Calculate the mean and median. 8.9,-1.2, -3.8, 0.8, 1.7, 1.7
Evaluate each expression. Write your answer in scientific notation and in standard form. 6 x 10-² 3 x 10-5 (9) (-01 × S) (₂O1 X+) (²)
Evaluate by hand. 3.3² + 3-5 6+2
Write each number in standard form. 1.52 x 104
Evaluate by hand. 4-3²-5
Classify each number listed as one or more of the following: natural number, whole number, integer, rational number, or real number. −2, 5, 0, 1.23, V7, V16
Geometry Suppose that the radius of a circle on a computer monitor is increasing at a constant rate of 1 inch per second. (a) Does the circumference of the circle increase at a constant rate? If it does, find this rate. (b) Does the area of the circle increase at a constant rate? Explain.
Write each number in standard form. -7.2 x 10-³
Classify each number listed as one or more of the following: natural number, whole number, integer, rational number, or real number. 55, 1.5, 104, 23, V3, -1000 17
Sort the list of numbers from smallest to largest and display the result in a table. (a) Determine the maximum and minimum values. (b) Calculate the mean and median. -5, 8, 19, 24, -23
Complete the following. (a) Express the data as a relation S. (b) Find the domain and range of S. x y -15-10 -3 05 -1 1 3 20 5
If a quantity changes from A to B calculate the percent change. A = 150, B = 120
Complete the following. (a) Express the data as a relation S. (b) Find the domain and range of S. x y -0.6 -0.2 0.1 0.5 1.2 10 20 25 30 80
If a quantity changes from A to B calculate the percent change. A = 250, B = 400
Write each number in scientific notation.1,891,000
Make a scatterplot of the relation. Determine if the relation is a function. {(10, 13),(-12,40), (-30, -23), (25,-22), (10,20)}
Write each number in scientific notation.0.0001001
Make a scatterplot of the relation. Determine if the relation is a function. {(1.5.2.5), (0, 2.1), (-2.3.3.1), (0.5, -0.8),(-1.1,0)}
Find the midpoint of the line segment with the given endpoints. (24,-16), (-20, 13)
Find the distance between the points. (-4,5), (2, -3)
Find the distance between the points. (1.2,-4), (0.2, 6)
Find the midpoint of the line segment with the given endpoints. 3) (1.-
A diameter of a circle has endpoints (-2, 4) and (6, 6). Find the standard equation of the circle.
Use the graph to determine the domain and range of each function. Evaluate f(-2). Use set-builder notation. (a) 7 N - 7 y = f(x) (b) L -2-1 N y = f(x) 12 X
Graph y = f(x) by first plotting points to determine the shape of the graph. f(x) = 4 - 2x²
Graph y = f(x) by first plotting points to determine the shape of the graph. f(x) = -x + 1
Graph y = f(x) by first plotting points to determine the shape of the graph. f(x)=2x-3
Graph y = f(x) by first plotting points to determine the shape of the graph. f(x) = x² - 1
Find the center and radius of the circle whose general equation is x2 - 2x + y2 + 2y = 2.
If f(3) = -9.7, identify a point on the graph of f.
Find the standard equation of a circle with center (-5, 3) and radius 9.
If (7, 8) lies on the graph of f, then f(__) = ___.
If (-3,2) lies on the graph of f, then f(__) = ___.
Graph y = f(x) by first plotting points to determine the shape of the graph. f(x) = √3-x
Complete the following for the function f. (a) Evaluate f(x) at the indicated values of x. (b) Find the domain of f. Use interval notation. f(x) = 4-5x for x = -5,6
Graph y = f(x) by first plotting points to determine the shape of the graph. f(x) = |x + 3|
Complete the following for the function f. (a) Evaluate f(x) at the indicated values of x. (b) Find the domain of f. Use interval notation. f(x) = -4 x- for x = -3, a + 1
Complete the following for the function f. (a) Evaluate f(x) at the indicated values of x. (b) Find the domain of f. Use interval notation. f(x) = 5 for x = -3, 1.5
Complete the following for the function f. (a) Evaluate f(x) at the indicated values of x. (b) Find the domain of f. Use interval notation. f(x) = x² - 3 for x = -10, a + 2
Complete the following for the function f. (a) Evaluate f(x) at the indicated values of x. (b) Find the domain of f. Use interval notation. f(x) = x³ 3x for x = -10, a +1
Use the verbal representation to express the function f symbolically, graphically, and numer- ically. Let y = f(x) with 0 ≤ x ≤ 100. For the numerical representation, use a table with x = 0, 25, 50, 75, 100.To find the area y of a square, multiply the length x of a side by itself.
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write a formula for f. (c) Find any zeros of f. -40-20 40 20
Complete the following for the function f. (a) Evaluate f(x) at the indicated values of x. (b) Find the domain of f. Use interval notation. f(x) = √x + 3 for x = 1,4-3
Use the verbal representation to express the function f symbolically, graphically, and numer- ically. Let y = f(x) with 0 ≤ x ≤ 100. For the numerical representation, use a table with x = 0, 25, 50, 75, 100.To convert x pounds to y ounces, multiply x by 16.
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write a formula for f. (c) Find any zeros of f. -4-2 42 2 y=f(x) 2 6
Determine if the graph represents a function. -3+ m
Determine if the graph represents a function. 2- 3
Determine if S represents a function. S = {(1, 3), (0, 2), (-1,7), (3, -3)}
Determine if y is a function of x in x = y + 5.
Write 5 ≤ x < 10 in interval notation.
State the slope of the graph of f. 틀 - X = (x)/
Determine if S represents a function. S = {(-3,4), (-1,2), (3,-5), (4, 2)}
Determine where the graph of f(x) = |x - 3| is increasing and where it is decreasing.
State the slope of the graph of f. f(x) = 7
If possible, find the slope of the line pass- ing through each pair of points. (-1,7), (3, 4)
If possible, find the slope of the line pass- ing through each pair of points. (1,-4), (2, 10)
If possible, find the slope of the line pass- ing through each pair of points. (8,4), (-2,4)
If possible, find the slope of the line pass- ing through each pair of points. (-). (- -)
Decide whether the function f is constant, linear, or nonlinear. f(x) = 8 - 3x
Decide whether the function f is constant, linear, or nonlinear. f(x) = 2x²-3x - 8
Determine if a line passes through every point in the table. If it does, give its slope. X y -2 50 0 2 42 34 4 26
Decide whether the function f is constant, linear, or nonlinear. f(x) = |x + 21
Decide whether the function f is constant, linear, or nonlinear. f(x) = 6
Find the difference quotient for f(x). = f(x) = 5x + 1
Find the difference quotient for f(x). f(x) = 3x² - 2
For each function f. find f(x + h) and f(x) + f(h). f(x) = 2x²
For each function f. find f(x + h) and f(x) + f(h). f(x) = 1 - 3x + x²
Graph the function f. State the slope m and y-intercept of the graph. f(x) = 4 - 2x
Graph the function f. State the slope m and y-intercept of the graph. f(x) = 3x - 6 =
Sketch a graph for a 2-hour period showing the dis- tance between two cars meeting on a straight high- way, each traveling 60 miles per hour. Assume that the cars are initially 120 miles apart.
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