Please solve the circle part.

SECTION 1.7 Building Mathematical Models Using Variation 115 Applications and Extensions In Problems 17-22, write an equation that relates the quantities. 17. Geometry The volume V of a sphere varies directly with 27. Physics: Stretching a Spring The elongation E of a spring the cube of its radius r. The constant of proportionality balance varies directly with the applied weight W (see the ATT figure). If E = 3 when W = 20, find E when W = 15. $3' 18. Geometry The square of the length of the hypotenuse c of a right triangle varies jointly with the sum of the squares of the lengths of its legs a and b. The constant of proportionality km- is 1. 19. Geometry The area A of a triangle varies jointly with the W lengths of the base b and the height h. The constant of 28. Physics: Vibrating String The rate of vibration of a string proportionality is 2 under constant tension varies inversely with the length of the string. If a string is 48 inches long and vibrates 20. Geometry The perimeter p of a rectangle varies jointly with 256 times per second, what is the length of a string that vibrates the sum of the lengths of its sides / and w. The constant of proportionality is 2. 576 times per second? 21, Physics: Newton's Law The force F (in newtons) of attraction 29) Revenue Equation At the corner Shell station, the between two bodies varies jointly with their masses m and M revenue R varies directly with the number g of gallons of in kilograms) and inversely with the square of the distance gasoline sold. If the revenue is $47.40 when the number d (in meters) between them. The constant of proportionality of gallons sold is 12, find a linear equation that relates revenue R to the number g of gallons of gasoline. Then find is G = 6.67 X 10". the revenue R when the number of gallons of gasoline sold is 10.5. 22. Physics: Simple Pendulum The period of a pendulum is the time required for one oscillation; the pendulum is usually 30. Cost Equation The cost C of roasted almonds varies referred to as simple when the angle made to the vertical is directly with the number A of pounds of almonds purchased. less than 5. The period T of a simple pendulum (in seconds) If the cost is $23.75 when the number of pounds of roasted varies directly with the square root of its length L (in feet). almonds purchased is 5, find a linear equation that relates the cost C to the number A of pounds of almonds purchased. The constant of proportionality is - Then find the cost C when the number of pounds of almonds V32 purchased is 3.5. 23) Mortgage Payments The monthly payment p on a mortgage Demand Suppose that the demand D for candy at the varies directly with the amount borrowed B. If the monthly movie theater is inversely related to the price p. payment on a 30-year mortgage is $6.49 for every $1000 (a) When the price of candy is $2.75 per bag, the theater borrowed, find a linear equation that relates the monthly sells 156 bags of candy. Express the demand for candy in payment p to the amount borrowed B for a mortgage with terms of its price. the same terms. Then find the monthly payment p when the b) Determine the number of bags of candy that will be sold amount borrowed B is $145,000. if the price is raised to $3 a bag. 24. Mortgage Payments The monthly payment p on a mortgage 32. Driving to School The time : that it takes to get to school varies directly with the amount borrowed B. If the monthly varies inversely with your average speed s. payment on a 15-year mortgage is $8.99 for every $1000 (a) Suppose that it takes you 40 minutes to get to school borrowed, find a linear equation that relates the monthly when your average speed is 30 miles per hour. Express payment p to the amount borrowed B for a mortgage with the driving time to school in terms of average speed. he same terms. Then find the monthly payment p when the (b) Suppose that your average speed to school is 40 miles amount borrowed B is $175,000. per hour. How long will it take you to get to school? 25. Physics: Falling Objects The distance s that an object falls 33. Pressure The volume of a gas V held at a constant temperature is directly proportional to the square of the time / of the in a closed container varies inversely with its pressure P. If fall. If an object falls 16 feet in 1 second, how far will it the volume of a gas is 600 cubic centimeters (cm') when all in 3 seconds? How long will it take an object to fall the pressure is 150 millimeters of mercury (mm Hg), find the 64 feet? volume when the pressure is 200 mm Hg. 26. Physics: Falling Objects The velocity v of a falling object 34 Resistance The current i in a circuit is inversely proportional is directly proportional to the time t of the fall. If, after to its resistance Z measured in ohms. Suppose that when the 2 seconds, the velocity of the object is 64 feet per second, current in a circuit is 30 amperes, the resistance is 8 ohms. Find the what will its velocity be after 3 seconds? current in the same circuit when the resistance is 10 ohms