Open Box Case Study
1. Suppose that an open box is to be made from a square sheet of cardboard by cutting out 6-inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 486 cubic inches, find the original dimensions of the sheet of cardboard.
2. A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in 5 seconds is given by s(t) = -16t2 + 169t. At what time or times will the ball be 162 ft. from the ground? Round your answer to the nearest tenth, if necessary.
3. In Country X, the average hourly wage in dollars from 1945 to 1995 can be modeled by f(x) = {0.074(x-1945) + 0.33 if 1945 ≤ x < 1970 {0.182(x-1970) + 0.28 if 1970 ≤ z ≤ 1995
4. A faucet …show more content…
is used to add water to a large bottle that already contained some water. After it has been filling for 5 seconds, the gauge on the bottle indicates that it contains 22 ounces of water. After it has been filling for 11 seconds, the gauge indicates the bottle contains 46 ounces of water. Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that models the amount of water in the bottle in terms of x.
5.
A rectangular garden has dimensions of 17 feet by 14 feet. A gravel path of consistent width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square …show more content…
feet?
6. The volume V of a gas at constant temperature varies inversely as the pressure P on it. The volume of a gas is 240 cm3 under a pressure of 18 kg/cm2. What will be its volume under a pressure of 30 kg/ cm2? {Assume that the temperature remains constant}.
7. The average of a certain type of automobile was $15,860 in 1993 and depreciated to $7800 in 1996. Let y be the average value of the automobile in the year x, where x = 0 represents 1993. What was the value of the automobile in the year 1998?
8.
A sales person has two job offers. Company A offers a weekly salary of $320 plus commission of 16% of sales. Company B offers a weekly salary of $ 640 plus commission of 8% of sales. What is the amount of sales above which Company A‘s offer is the better of the two?
9. A square has an area of 49 square inches. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.
10. The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 60 miles per hour in 25 minutes, how fast must it travel to cover the same distance in 30 minutes?
11. Jim wants to plan a meal with 75 grams of carbohydrates and 1230 calories. If green beans have 7 grams of carbohydrates and 30 calories per half cup serving and if French fried shrimp have 9 grams of carbohydrates and 190 calories per three-ounce serving, how many servings of green beans and shrimp should he use?
12. Your grades in the four tests in College Algebra are 91, 66, 82 and 71. If the final carries double weight, how many points do you need on the final to average 80?
13. The sides of a rectangle garden are in the ration 3:2. The area of the rectangle is 216 square meters. Find the length of the
rectangle.
14. Solve the equation: 2 3 2x x + 3
15. Find the composite for the given function: Find f=g, given f(x) + and g(x) + 7 8x
16. Solve the equation 8x-3 = 324x
17. Find the real or imaginary solutions by using the quadratic formula: x2 = 15 +5x
18. Suppose a cost=benefit model is given by y = 8.8x 100 – x, where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 955 to the nearest dollar.
19. To remodel a bathroom, a contractor charges $25 per hour plus material cost, which amount to $3600. Therefore, the total cost to remodel the bathroom is give by f(x) = 25x + 3600 where x is the number of hours the contractor works. Find f-1(x). What does f-1(x) compute?
20. Solve the inequality |7x – 2| ≥ 7
21. Find the vertex of the parabola 7= -2x2 + 3x -4.
22. Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. f(x) = x4 – 8x2 + 12
23. Use a graphing calculator to find the coordinates of the relative extremum of the graph of function in the indicated domain interval. Give answers to the nearest hundredth. f(x) = -x3 - 8x2 + 21x +108; interval in the domain: |1, 2|
24. Randy invested his inheritance in an account that paid 6.1% interest, compounded continuously. After 6 years, he found that he now had $54,380.46. What was the original amount of his inheritance?
25. The function graphed is in a window that causes hidden behavior. Experiment with various windows to locate the extrema of the function.
y = 1 x 3 – 5 x 2 + 4x + 4 2 2
26. The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). Find the equation of the least-squares regression line that models the data.
Temp | 62 76 50 51 71 46 51 44 79 Growth| 36 39 50 13 33 33 17 6 16
27. Use the intersection of-the-graphs methods to approximate the solution to the nearest hundredth. 2(0.30x _ √5) = 3√12x – 5
28. The concentration of a drug in the bloodstream, measured in milligrams per liter, can be modeled by the function, C(t) = 12t + 4 , where t is the number of 3t2 + 2 minutes after injection of the drug. Approximate your answer rounded to two decimal places.
29. The polynomial G(x) = - 0.006x4 + 0.140x3 + 1/79X measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase between 11 and 12 seconds?
30. S(x) = - x3 + 6x2 + 288X + 4000, 4≤ x ≤ 20 is an approximation to the number of salmon swimming upstream to spawn, where x represents the water temperature in degrees Celsius. Find the temperature that produces the maximum number of salmon.
31. Using a graphing utility to find the solution of the equation. Round to the nearest thousandth. x2 + 2x – 10 = ex-3 -3
32. Banks use the following formula to calculate Annual Percentage yield
APY= { 1 + r }n – 1 for a Certified Deposit account, where r is the nominal { n } rate and n is the number of compounded periods per year.
33. Using a graphing calculator, find the nominal rate if the interest is compounded quarterly and the APY = 0.03.
34. By using a graphic calculator, find the increasing interval(s) for the function.
Y = 2x3 – 3x2 – 36x + 30
2. A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in 5 seconds is given by s(t) = -16t2 + 169t. At what time or times will the ball be 162 ft. from the ground? Round your answer to the nearest tenth, if necessary.
3. In Country X, the average hourly wage in dollars from 1945 to 1995 can be modeled by f(x) = {0.074(x-1945) + 0.33 if 1945 ≤ x < 1970 {0.182(x-1970) + 0.28 if 1970 ≤ z ≤ 1995
4. A faucet …show more content…
is used to add water to a large bottle that already contained some water. After it has been filling for 5 seconds, the gauge on the bottle indicates that it contains 22 ounces of water. After it has been filling for 11 seconds, the gauge indicates the bottle contains 46 ounces of water. Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that models the amount of water in the bottle in terms of x.
5.
A rectangular garden has dimensions of 17 feet by 14 feet. A gravel path of consistent width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square …show more content…
feet?
6. The volume V of a gas at constant temperature varies inversely as the pressure P on it. The volume of a gas is 240 cm3 under a pressure of 18 kg/cm2. What will be its volume under a pressure of 30 kg/ cm2? {Assume that the temperature remains constant}.
7. The average of a certain type of automobile was $15,860 in 1993 and depreciated to $7800 in 1996. Let y be the average value of the automobile in the year x, where x = 0 represents 1993. What was the value of the automobile in the year 1998?
8.
A sales person has two job offers. Company A offers a weekly salary of $320 plus commission of 16% of sales. Company B offers a weekly salary of $ 640 plus commission of 8% of sales. What is the amount of sales above which Company A‘s offer is the better of the two?
9. A square has an area of 49 square inches. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.
10. The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 60 miles per hour in 25 minutes, how fast must it travel to cover the same distance in 30 minutes?
11. Jim wants to plan a meal with 75 grams of carbohydrates and 1230 calories. If green beans have 7 grams of carbohydrates and 30 calories per half cup serving and if French fried shrimp have 9 grams of carbohydrates and 190 calories per three-ounce serving, how many servings of green beans and shrimp should he use?
12. Your grades in the four tests in College Algebra are 91, 66, 82 and 71. If the final carries double weight, how many points do you need on the final to average 80?
13. The sides of a rectangle garden are in the ration 3:2. The area of the rectangle is 216 square meters. Find the length of the
rectangle.
14. Solve the equation: 2 3 2x x + 3
15. Find the composite for the given function: Find f=g, given f(x) + and g(x) + 7 8x
16. Solve the equation 8x-3 = 324x
17. Find the real or imaginary solutions by using the quadratic formula: x2 = 15 +5x
18. Suppose a cost=benefit model is given by y = 8.8x 100 – x, where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 955 to the nearest dollar.
19. To remodel a bathroom, a contractor charges $25 per hour plus material cost, which amount to $3600. Therefore, the total cost to remodel the bathroom is give by f(x) = 25x + 3600 where x is the number of hours the contractor works. Find f-1(x). What does f-1(x) compute?
20. Solve the inequality |7x – 2| ≥ 7
21. Find the vertex of the parabola 7= -2x2 + 3x -4.
22. Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. f(x) = x4 – 8x2 + 12
23. Use a graphing calculator to find the coordinates of the relative extremum of the graph of function in the indicated domain interval. Give answers to the nearest hundredth. f(x) = -x3 - 8x2 + 21x +108; interval in the domain: |1, 2|
24. Randy invested his inheritance in an account that paid 6.1% interest, compounded continuously. After 6 years, he found that he now had $54,380.46. What was the original amount of his inheritance?
25. The function graphed is in a window that causes hidden behavior. Experiment with various windows to locate the extrema of the function.
y = 1 x 3 – 5 x 2 + 4x + 4 2 2
26. The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). Find the equation of the least-squares regression line that models the data.
Temp | 62 76 50 51 71 46 51 44 79 Growth| 36 39 50 13 33 33 17 6 16
27. Use the intersection of-the-graphs methods to approximate the solution to the nearest hundredth. 2(0.30x _ √5) = 3√12x – 5
28. The concentration of a drug in the bloodstream, measured in milligrams per liter, can be modeled by the function, C(t) = 12t + 4 , where t is the number of 3t2 + 2 minutes after injection of the drug. Approximate your answer rounded to two decimal places.
29. The polynomial G(x) = - 0.006x4 + 0.140x3 + 1/79X measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase between 11 and 12 seconds?
30. S(x) = - x3 + 6x2 + 288X + 4000, 4≤ x ≤ 20 is an approximation to the number of salmon swimming upstream to spawn, where x represents the water temperature in degrees Celsius. Find the temperature that produces the maximum number of salmon.
31. Using a graphing utility to find the solution of the equation. Round to the nearest thousandth. x2 + 2x – 10 = ex-3 -3
32. Banks use the following formula to calculate Annual Percentage yield
APY= { 1 + r }n – 1 for a Certified Deposit account, where r is the nominal { n } rate and n is the number of compounded periods per year.
33. Using a graphing calculator, find the nominal rate if the interest is compounded quarterly and the APY = 0.03.
34. By using a graphic calculator, find the increasing interval(s) for the function.
Y = 2x3 – 3x2 – 36x + 30