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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
The table shows the height of a projectile that is shot into the air.(a) Uses (t) = -16t2 + v0t + h0 to model the data. (b) After how long did the projectile strike the ground? t (seconds) s (feet) 0 1 2 32 176 288 3 368 4 416
The price of one airline ticket is $250. For each additional ticket sold to a group, the price of every ticket is reduced by $2. For example, 2 tickets cost 2 · 248= $496 and 3 tickets cost 3 · 246 = $738.(a) Write a quadratic function that gives the total cost of buying x tickets. (b) What
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United States, and by 2020 this number will increase to 25 million. Let t be years after 2015 and L, Q, and
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United States, and by 2020 this number will increase to 25 million. Let t be years after 2015 and L, Q, and
The following table shows Facebook's monthly active users in millions who use a mobile only platform.(a) Discuss the general trend in users during this time period. (b) Would a linear function model this data well? Explain. (c) What other type of function might work? (d) If a parabola is used to
Use least-squares regression to find a quadratic function f that models the data given in the table. Estimate f(3.5) to the nearest hundredth. x 0 f(x) -1 2 16 4 57 6 124
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United States, and by 2020 this number will increase to 25 million. Let t be years after 2015 and L, Q, and
A window comprises a square with sides of length x and a semicircle with diameter x, as shown in the figure. If the total area of the window is 463 square inches, estimate the value of x to the nearest hundredth of an inch.
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United States, and by 2020 this number will increase to 25 million. Let t be years after 2015 and L, Q, and
Use least-squares regression to find a quadratic function f that models the data given in the table. Estimate f(3.5) to the nearest hundredth. 10 20 30 f(x) 4.2 24.3 84.1 4 40 184
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United States, and by 2020 this number will increase to 25 million. Let t be years after 2015 and L, Q, and
A frame for a picture is 2 inches wide. The picture inside the frame is 4 inches longer than it is wide. See the figure. If the area of the picture is 320 square inches, find the outside dimensions of the picture frame. $2 in. 2 in.
A smart home contains a stand-alone device that is connected to the Internet and can either be monitored or controlled from a remote location. In 2015 there were 5 million smart homes in the United States, and by 2020 this number will increase to 25 million. Let t be years after 2015 and L, Q, and
The heart rate of an athlete while weight training is recorded for 4 minutes. The table lists the heart rate after x minutes.(a) Explain why the data are not linear. (b) Find a quadratic function f that models the data. (c) What is the domain of your function? Time (min) 0 1 2 4 Heart rate (bpm)
The table shows the heart rate of an athlete upon stopping a moderate activity.(a) Model the data with H(t) = a(t = h)2 + k. What is the domain of H? (b) Approximate the athlete's heart rate for t = 1.5 minutes. Time (min) 012 3 Heart rate (bpm) 122 108 98 92 4 90
Explain how to find the coordinates of the vertex on the graph of a parabola. Then give an example.
Explain the effect that the constant a has on the graph of y = ax2. Be sure to consider a < 0 and a > 0.
The following table shows approx- imate global sales of personal computers in millions of units for selected years.(a) Discuss the general trend in sales during this time period. (b) Would a linear function model this data well? What other type of function might work? Explain. (c) If a parabola
The table lists the number of iPhones sold in millions in the first 5 years on the market. Find a quadratic function f that models the data. Year 1 2 3 4 5 1 20 50 100 180 Units sold
A company charges $20 to make one monogrammed shirt but reduces this cost by $0.10 per shirt for each additional shirt ordered up to 100 shirts. If the cost of an order is $989, how many shirts were ordered?
A rectangular pen for a pet is under construction using 100 feet of fence. (a) Find the dimensions that give an area of 576 square feet. (b) Find the dimensions that give maximum area.
Explain why the vertex is important when you are trying to find either the maximum y-value or the minimum y-value on the graph of a quadratic function.
Repeat Exercise 133 for a suspension bridge that has 100-foot towers, a length of 200 feet, and a cable that comes within 15 feet of the road at the center of the bridge.Data from Exercise 133If the weight of the deck and the cars is significantly greater than weight of the cables supporting a
How do the values of a, h, and k affect the graph of f(x) = a (x - h)2 + k?
Braking distance for cars on level pavement can be approximated by D(x) = x2/30k The input x is the car's velocity in miles per hour and the output D(x) is the braking distance in feet. The positive constant k is a measure of the traction of the tires. Small values of k indicate a slippery road or
Find f(x) = a(x - h)2 + k so that f models the data exactly. x-2 2 A -1 0 2 1 -4-14 2
Find f(x) = a(x - h)2 + k so that f models the data exactly. x-1 y 5 0 1 2
A cylindrical aluminum can is being constructed to have a height h of 4 inches. If the can is to have a volume of 28 cubic inches, approximate its radius r.
If the weight of the deck and the cars is significantly greater than weight of the cables supporting a suspension bridge, such as the Golden Gate Bridge, then the shape of these cables can be modeled by parabolas. (If a cable without any additional weight is suspended between two towers, then this
A box is being constructed by cutting 4-inch squares from the corners of a rectangular sheet of metal that is 10 inches longer than it is wide. If the box is to have a volume of 476 cubic inches, find the dimensions of the metal sheet.
A box is being constructed by cutting 2-inch squares from the corners of a square sheet of metal. If the box is to have a volume of 1058 cubic inches, find the dimensions of the metal sheet.
The width of a rectangular computer screen is 2 inches more than its height. If the area of the screen is 143 square inches, determine its dimensions symbolically, graphically, and numerically. Do your answers agree?
If air resistance is ignored, the height h of a projectile above the ground after x seconds is given by h(x) = -1/2gx + v0x + h0 where g is the acceleration due to gravity. This formula is also valid for other celestial bodies. Suppose a ball is thrown straight up at v0= 88 feet per second from a
If air resistance is ignored, the height h of a projectile above the ground after x seconds is given by h(x) = -1/2gx + v0x + h0 where g is the acceleration due to gravity. This formula is also valid for other celestial bodies. Suppose a ball is thrown straight up at v0= 88 feet per second from a
From 1984 to 1994 the cumulative number of AIDS cases can be modeled by the equation C(x) = 3034x2 + 14,018x + 6400, where x represents years after 1984. Estimate the year when 200,000 AIDS cases had been diagnosed.
The number of unique monthly visitors in millions to Facebook can be approximated by V(x) = 16x2 + 7x + 32, where x is the number of years after 2008. Estimate the year when Facebook averaged 55 million unique monthly visitors symbolically and graphically.
If air resistance is ignored, the height h of a projectile above the ground after x seconds is given by h(x) = -1/2gx + v0x + h0 where g is the acceleration due to gravity. This formula is also valid for other celestial bodies. Suppose a ball is thrown straight up at v0= 88 feet per second from a
A baseball is thrown downward with an initial velocity of 30 feet per second from a stadium seat that is 80 feet above the ground. Estimate to the nearest tenth of a second how long it takes for the baseball to strike the ground.
A baseball is dropped from a stadium seat that is 75 feet above the ground. Its heights in feet after seconds is given by s(t) = 75 - 16t2. Estimate to the nearest tenth of a second how long it takes for the baseball to strike the ground.
A larger square has sides that are 4 inches longer than a smaller square. The sum of the areas of the two squares is 80 square inches. Find the dimensions of each square.
Two rectangles both have lengths that are double their widths. The larger rectangle has a width that is 2 inches greater than the width of the smaller rectangle. If the sum of the areas of the two rectangles is 104 square inches, find the dimensions of each rectangle.
A rectangle is three times as long as it is wide. Find the dimensions of this rectangle if its area is numerically triple its perimeter.
If air resistance is ignored, the height h of a projectile above the ground after x seconds is given by h(x) = -1/2gx + v0x + h0 where g is the acceleration due to gravity. This formula is also valid for other celestial bodies. Suppose a ball is thrown straight up at v0= 88 feet per second from a
The graph of f(x) = ax2 + bx + c is shown. Complete each of the following. Use interval notation when appropriate. (a) Give the zeros off. Is the discriminant for the equation ax2 + bx + c = 0 positive, negative or zero? (b) Give any x- and y-intercepts on the graph of f. (c) Identify where is
The graph of f(x) = ax2 + bx + c is shown. Complete each of the following. Use interval notation when appropriate. (a) Give the zeros off. Is the discriminant for the equation ax2 + bx + c = 0 positive, negative or zero? (b) Give any x- and y-intercepts on the graph of f. (c) Identify where is
A baseball is hit straight up with an initial velocity of v0 = 96 feet per second (about 65 miles per hour) and leaves the bat with an initial height of h0= 2.5 feet. (a) Write a formula s(t) that models the height after 1 seconds. (b) How high is the baseball after 4 seconds? (c)
A stone is thrown downward with a velocity of 66 feet per second (45 miles per hour) from a bridge that is 120 feet above a river, as illustrated in the figure. (a) Write a formula s(t) that models the height of the stone after / seconds. (b) Does the stone hit the water within the first 2
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? -2 2 y = f(x)
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? -3-2-1 -3 بنا 2 y = f(x)
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. I = (ε = xç)x
A baseball is hit so that its height in feet after / seconds is s(t) = -16t2 + 44t + 4. (a) How high is the baseball after 1 second? (b) Find the maximum height of the baseball. Support your answer graphically.(c) Graphically estimate the domain and range of sin this application.
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? -8 6 -2 2 y = f(x) 2468
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 3x² = 1- x
Find the dimensions of a square whose area numerically equals its perimeter.
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? y=f(x) 2
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? -3-2-1 2 y = f(x) 123
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. if + 3x = x - 4
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. zx + 9 = x7
A rancher plans to fence a rectangular area for cattle using the straight portion of a river as one side of the rectangle. If the farmer has P feet of fence, find the dimensions of the rectangle that give the maximum area for the cattle.
A farmer wants to fence a rectangular area by using the wall of a barn as one side of the rectangle and then enclosing the other three sides with 160 feet of fence. Find the dimensions of the rectangle that give the maximum area inside.
The figure shows the graph of f(x) = ax2 + bx + c. (a) State whether a > 0 or a (b) Solve the equation ax2 + bx + c = 0. (c) Is the discriminant positive, negative, or zero? 2 y=f(x) 2
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 2x² + 3x = 12 - 2x
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. ヤー=(-x)x
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. x(x + 2) = -13
A large hotel is considering giving the following group discount on room rates: the regular price of $120 decreases by $2 for each room rented. For example, one room costs $118, two rooms cost $116 * 2 = $232, three rooms cost $114 * 3 = $342, and so on. (a) Write a formula for a function R
A publisher is trying to minimize its average cost per book printed (total cost divided by the number of books printed). This average cost in dollars is given by f(x) = 0.000000015x2 -0.0007x + 26, where x represents the total number of books printed. (a) Describe the graph of f. (b) Find
Suppose the revenue R in thousands of dollars that a company receives from producing x thousand DVD players is given by the formula R(x) = x(40 - 2x). (a) Evaluate R(2) and interpret the result. (b) How many DVD players should the company produce to maximize its revenue? (c) What is
A business that produces color copies is trying to minimize its average cost per copy (total cost divided by the number of copies). This average cost in cents is given by f(x) = 0.00000093x2 -0.0145x + 60, where x represents the total number of copies. (a) Describe the graph of f. (b)
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 16x² + 9 = 24x
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 2x² + x = 2
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. 3x² + 3 = 5x
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. x² + 1 = x X
The height h in feet of a golf ball after 1 seconds is given by h(t) = 96t - 16t2. (a) Find the height of the ball after 4 seconds. Is the golf ball moving upward or downward after 4 seconds? (b) Find the maximum height of the golf ball. (c) Determine the domain and range of h in
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. zx = x+
A homeowner has 200 feet of fence to enclose an area for a pet. (a) If the area is given by 4(x) = x(100-x), what dimension maximize the area inside the fence? (b) What is the maximum area? (c) Determine the domain and range of A in this application.
A homeowner has 80 feet of fence to enclose a rectangular garden. What dimen- sions for the garden result in the maximum area enclose by the fence?
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 6x² = 4x
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 1- = x2 - ₂x
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 3x² = 12
A farmer has 1000 feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enclosed by the fence?
Complete the following. (a) Write the equation as ax2 + bx + c = 0 with a > 0. (b) Calculate the discriminant b2 - 4ac and determine the number of real solutions. (c) Solve the equation. 8x²= 2 = 14
Match the situation with the graph of the quadratic function (a-d) that models it best.The temperature after x hours in a house where the furnace quits and a repair person fixes it يا b. y d. ۲
(a) Calculate the average rates of change in I(x) = 0.6x2 + 5.2x + 29 from 2015 to 2018 and from 2018 to 2020. (b) Interpret the average rate of change from 2015 to 2018. (c) Use your average rate of change from 2018 to 2020 to predict the global investment in 2022. Explain your
Match the situation with the graph of the quadratic function (a-d) that models it best.The cumulative number of reported AIDS cases in year x, where 1982 ≤ x ≤ 1994 يا b. y d. ۲
Match the situation with the graph of the quadratic function (a-d) that models it best.The height y of a stone thrown from ground level after x seconds يا b. y d. ۲
Match the situation with the graph of the quadratic function (a-d) that models it best.The number of people attending a popular movie x weeks after its opening يا b. y d. ۲
Global investments in $ billions in IoT can be modeled by I(x) = 0.6x2 + 5.2x + 29, where x represents years after 2015. Use I (x) to determine global investments in 2015, 2018, and 2020.
Solve for the specified variable. T²kTk² = 0 for T
Solve for the specified variable. s=-16r² + 100t for t
Find the difference quotient of f. f(x) = 1 + 2x - ²
Solve for the specified variable. S = 4m² + x² for r
Find the difference quotient of f. f(x) = 3 + 4x - x²
Find the difference quotient of f. f(x) = 5-4x²
Find the formula for a quadratic function that satisfies the given conditions.Vertex (2, 1), passing through (0, 13)
Solve for the specified variable. W = F²R for I
Find the average rate of change of f from 1 to 3. I + X£ = -XĐ = (x)f
Solve for the specified variable. a + b² = c² for b
Find the formula for a quadratic function that satisfies the given conditions.Vertex (-1,-5), passing through (0, -7)
Find the difference quotient of f. f(x) = 3x² - 2x
Find the formula for a quadratic function that satisfies the given conditions.Vertex (-3, 4), passing through (-2, 1)
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