In Exercises 920, solve the problem.A radiator contains 8 quarts of fluid, 40% ofwhich

In Exercises 14, a problem situation is given. a. Decide what is being asked for, and label the unknown quantities. b. Translate the verbal statements in the problem and the relationships between the known and unknown quantities into mathematical language, using a table like those in Examples 13. The table is provided in Exercises 12. You need not find an equation to be solved. The sum of two numbers is 15 and the difference of their squares is 5. What are the numbers? Mathematical English Language Language the two numbers Their sum is 15. The difference of their squares is 5.

In Exercises 14, a problem situation is given. a. Decide what is being asked for, and label the unknown quantities. b. Translate the verbal statements in the problem and the relationships between the known and unknown quantities into mathematical language, using a table like those in Examples 13. The table is provided in Exercises 12. You need not find an equation to be solved.The sum of the squares of two consecutive integers is 4513. What are the integers? Mathematical English Language Language the two integers The integers are consecutive. The sum of their squares is 4513.

In Exercises 14, a problem situation is given. a. Decide what is being asked for, and label the unknown quantities. b. Translate the verbal statements in the problem and the relationships between the known and unknown quantities into mathematical language, using a table like those in Examples 13. The table is provided in Exercises 12. You need not find an equation to be solved.A rectangle has a perimeter of 45 centimeters and an area of 112.5 square centimeters. What are its dimensions? 4. A triangle has an area of 96 square inches, and its height is two-thirds of its base. What are the base and height of the triangle?

In Exercises 14, a problem situation is given. a. Decide what is being asked for, and label the unknown quantities. b. Translate the verbal statements in the problem and the relationships between the known and unknown quantities into mathematical language, using a table like those in Examples 13. The table is provided in Exercises 12. You need not find an equation to be solved.

In Exercises 58, set up the problem by labeling the unknowns, translating the given information into mathematical language, and finding an equation that will produce the solution to the problem. You need not solve this equation.A worker gets an 8% pay raise and now makes $1600 per month. What was the workers old salary?

In Exercises 58, set up the problem by labeling the unknowns, translating the given information into mathematical language, and finding an equation that will produce the solution to the problem. You need not solve this equation.A merchant has 5 pounds of mixed nuts that cost $30. He wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. How many pounds of peanuts are needed?

In Exercises 58, set up the problem by labeling the unknowns, translating the given information into mathematical language, and finding an equation that will produce the solution to the problem. You need not solve this equation. The diameter of a circle is 16 cm. By what amount must the radius be decreased in order to decrease the area by square centimeters?

In Exercises 58, set up the problem by labeling the unknowns, translating the given information into mathematical language, and finding an equation that will produce the solution to the problem. You need not solve this equation.A corner lot has dimensions 25 by 40 yards. The city plans to take a strip of uniform width along the two sides bordering the streets in order to widen these roads. How wide should the strip be if the remainder of the lot is to have an area of 844 square yards?

In Exercises 920, solve the problem.You have already invested $550 in a stock with an annual return of 11%. How much of an additional $1100 should be invested at 12% and how much at 6% so that the total return on the entire $1650 is 9%?

In Exercises 920, solve the problem.If you borrow $500 from a credit union at 12% annual interest and $250 from a bank at 18% annual interest, what is the effective annual interest rate (that is, what single rate of interest on $750 would result in the same total amount of interest)?

In Exercises 920, solve the problem.A radiator contains 8 quarts of fluid, 40% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 60% antifreeze?

In Exercises 920, solve the problem.A radiator contains 10 quarts of fluid, 30% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 40% antifreeze?

In Exercises 920, solve the problem. Two cars leave a gas station at the same time, one traveling north and the other south. The northbound car travels at 50 mph. After 3 hours the cars are 345 miles apart. How fast is the southbound car traveling?

In Exercises 920, solve the problem. An airplane flew with the wind for 2.5 hours and returned the same distance against the wind in 3.5 hours. If the cruising speed of the plane was a constant 360 mph in air, how fast was the wind blowing? Hint: If the wind speed is r miles per hour, then the plane travels at mph with the wind and at mph against the wind.

In Exercises 920, solve the problem. The average of two real numbers is 41.375 and their product is 1668. What are the numbers? 1360 r2 1360 r2 48p 106 Chapter 2 Equations and Inequalities

In Exercises 920, solve the problem.A rectangle is four times as long as it is wide. If it has an area of 36 square inches, what are its dimensions?

In Exercises 920, solve the problem.A 13-foot-long ladder leans on a wall. The bottom of the ladder is 5 feet from the wall. If the bottom is pulled out 3 feet farther from the wall, how far does the top of the ladder move down the wall? Hint: The ladder, ground, and wall form a right triangle. Draw pictures of this triangle before and after the ladder is moved. Use the Pythagorean Theorem to set up an equation.

In Exercises 920, solve the problem.A factory that makes can openers has fixed costs for building, fixtures, machinery, etc. of $26,000. The variable cost for material and labor for making one can opener is $2.75. a. What is the total cost of making 1000 can openers? 20,000? 40,000? b. What is the average cost per can opener in each case?

In Exercises 920, solve the problem.Red Riding Hood drives the 432 miles to Grandmothers house in 1 hour less than it takes the Wolf to drive the same route. Her average speed is 6 mph faster than the Wolfs average speed. How fast does each drive?

In Exercises 920, solve the problem.To get to work Sam jogs 3 kilometers to the train, then rides the remaining 5 kilometers. If the train goes 40 km per hour faster than Sams constant rate of jogging and the entire trip takes 30 minutes, how fast does Sam jog?

In Exercises 2124, an object is thrown upward, dropped, or thrown downward and travels in a vertical line subject only to gravity with wind resistance ignored. The height h, in feet, of the object above the ground after t seconds is given by where is the initial height of the object at starting time and is the initial velocity (speed) of the object at time The value of is taken as posi- tive if the object starts moving upward at time and negative if the object starts moving downward at An object that is dropped (rather than thrown downward) has initial velocity How long does it take an object to reach the ground in each case? a. It is dropped from the top of a 640-foot-high building. v0 0.b. It is thrown downward from the top of the same building, with an initial velocity of 52 feet per second.

In Exercises 2124, an object is thrown upward, dropped, or thrown downward and travels in a vertical line subject only to gravity with wind resistance ignored. The height h, in feet, of the object above the ground after t seconds is given by where is the initial height of the object at starting time and is the initial velocity (speed) of the object at time The value of is taken as posi- tive if the object starts moving upward at time and negative if the object starts moving downward at An object that is dropped (rather than thrown downward) has initial velocity You are standing on a cliff 200 feet high. How long will it take a rock to reach the ground at the bottom of the cliff in each case? a. You drop it. b. You throw it downward at an initial velocity of 40 feet per second. c. How far does the rock fall in 2 seconds if you throw it downward with an initial velocity of 40 feet per second.

In Exercises 2124, an object is thrown upward, dropped, or thrown downward and travels in a vertical line subject only to gravity with wind resistance ignored. The height h, in feet, of the object above the ground after t seconds is given by where is the initial height of the object at starting time and is the initial velocity (speed) of the object at time The value of is taken as posi- tive if the object starts moving upward at time and negative if the object starts moving downward at An object that is dropped (rather than thrown downward) has initial velocity A rocket is fired straight up from ground level with an initial velocity of 800 feet per second. a. How long does it take the rocket to rise 3200 feet? b. When will the rocket hit the ground?

In Exercises 2124, an object is thrown upward, dropped, or thrown downward and travels in a vertical line subject only to gravity with wind resistance ignored. The height h, in feet, of the object above the ground after t seconds is given by where is the initial height of the object at starting time and is the initial velocity (speed) of the object at time The value of is taken as posi- tive if the object starts moving upward at time and negative if the object starts moving downward at An object that is dropped (rather than thrown downward) has initial velocity A rocket loaded with fireworks is to be shot vertically upward from ground level with an initial velocity of 200 feet per second. When the rocket reaches a height of 400 feet on its upward trip, the fireworks will be detonated. How many seconds after lift-off will this take place?

The dimensions of a rectangular box are consecutive integers. If the box has volume of 13,800 cubic centimeters, what are its dimensions?

Find a real number that exceeds its cube by 2.

The lateral surface area S of the right circular cone at the left in the figure below is given by What radius should be used to produce a cone of height 5 inches and lateral surface area 100 square inches?

The lateral surface area of the right square pyramid at the right in the figure above is given by If the pyramid has height 10 feet and lateral surface area 100 square feet, what is the length of a side b of its base? S b2b2 4h2

Suppose that the open-top box being made from a sheet of cardboard in Example 7 is required to have at least one of its dimensions greater than 18 inches. What size square should be cut from each corner?

A homemade loaf of bread turns out to be a perfect cube. Five slices of bread, each 0.6 inch thick, are cut from one end of the loaf. The remainder of the loaf now has a volume of Section 2.4 Other Types of Equations 107 235 cubic inches. What were the dimensions of the original loaf?

. A rectangular bin with an open top and volume of 38.72 cubic feet is to be built. The length of its base must be twice the width and the bin must be at least 3 feet high. Material for the base of the bin costs $12 per square foot and material for the sides costs $8 per square foot. If it costs $538.56 to build the bin, what are its dimensions?