Activity 4.2.5 Variation Application Problems Direct, Indirect, and Joint – The volume of a cone varies jointly as the height and the square of the radius of the base. The constant of variation is . The equation is the volume of a cone if V = π r2 h. Find the radius is 5 cm and height is 6 cm. The temperature, T (in degrees Kelvin), of an enclosed gas varies jointly with the product of the volume, V (in cubic centimeters), and the pressure, P (in kilograms per square centimeter). The temperature of a gas is 266oK when the volume is 7000 cubic centimeters and the pressure is 0.76 kilogram per square centimeter. What is the temperature when the volume is 8000 cubic centimeters and the pressure is 0.87 kilogram per square centimeter? Supposed varies jointly with and the square of When = and x y z. x –81 = 3, then = 3. Find when = 15 and = 5. y z y x z When a boat is going at a high speed, most of the goes into generating the boat’s motor wake (the track of waves left in the water). The power used to generate the wake is p directly proportional to the seventh power of the speed s. boat’s If a speed is 10 knots (nautical miles per hour) and uses 0.2 horsepower, write boat’s the equation for this situation. If a speed is 30 knots, how much power will it need to generate a wake? boat’s The maximum weight (in pounds) that a board could hold varies directly as its width M w (in inches) and the square of its thickness (in inches) and inversely from the distance t d (in feet) of its supports. Find the maximum weight that a board can support if it the supports are 18 feet apart, the board is 11 in wide and 2 in. thick and the constant of variation is . 70
Activity 4.2.5 Variation Application Problems – Direct, Indirect, and Joint The volume of a cone varies jointly as the height and the square of the radius of the base. The constant of variation is . The equation is V = π r2 h. Find the volume of a cone if the radius is 5 cm and height is 6 cm. The temperature, T (in degrees Kelvin), of an enclosed gas varies jointly with the product of the volume, V (in cubic centimeters), and the pressure, P (in kilograms per square centimeter). The temperature of a gas is 266oK when the volume is 7000 cubic centimeters and the pressure is 0.76 kilogram per square centimeter. What is the temperature when the volume is 8000 cubic centimeters and the pressure is 0.87 kilogram per square centimeter? Supposed x varies jointly with y and the square of z. When x = –81 and y = 3, then z = 3. Find y when x = 15 and z = 5. When a boat is going at a high speed, most of the boat’s motor goes into generating the wake (the track of waves left in the water). The power p used to generate the wake is directly proportional to the seventh power of the boat’s speed s. If a boat’s speed is 10 knots (nautical miles per hour) and uses 0.2 horsepower, write the equation for this situation. If a boat’s speed is 30 knots, how much power will it need to generate a wake? The maximum weight M (in pounds) that a board could hold varies directly as its width w (in inches) and the square of its thickness t (in inches) and inversely from the distance d (in feet) of its supports. Find the maximum weight that a board can support if it the supports are 18 feet apart, the board is 11 in wide and 2 in. thick and the constant of variation is 70 .
Activity_4_2_5.docx