1. [-/1 Points] DETAILS SPRECALC7 1.12.004. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If z is directly proportional to the product of x and y and if z is 15 when x is 5 and y is 6, then x, y, and z are related by the equation z = Need Help? Read It 2. [-/1 Points] DETAILS SPRECALC7 1.12.009. Write an equation that expresses the statement. (Use k as the constant of proportionality.) x is inversely proportional to y. Need Help? Read It Watch It MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 3. [-/1 Points] DETAILS SPRECALC7 1.12.011. Write an equation that expresses the statement. (Use k as the constant of proportionality.) z is proportional to s and inversely proportional to t. Need Help? Read It Watch It 4. [-/1 Points] DETAILS SPRECALC7 1.12.018.MI. Write an equation that expresses the statement. (Use k as the constant of proportionality.) A is jointly proportional to the square roots of s and t. Need Help? Read It Master It MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 5. [-/2 Points] DETAILS SPRECALC7 1.12.021.MI. Express the statement as an equation. (Use k as the constant of proportionality.) A varies inversely as r. Use the given information to find the constant of proportionality. If r3, then A = 7. k = Need Help? Read It Master It MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 6. [-/3 Points] DETAILS SPRECALC7 1.12.036.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The cost C of printing a magazine is jointly proportional to the number of pages p in the magazine and the number of magazines printed m. (a) Write an equation that expresses this joint variation. (Use k for the constant of proportionality.) (b) Find the constant of proportionality if the printing cost is $51,300 for 4500 copies of a 114-page magazine. k = (c) How much would the printing cost be for 7000 copies of a 62-page magazine? $ Need Help? Read It Watch It Master It 7. [-/4 Points] DETAILS SPRECALC7 1.12.047.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The resistance R of a wire varies directly as its length L and inversely as the square of its diameter d. (a) Write an equation that expresses this joint variation. (Use k for the constant of proportionality.) (b) Find the constant of proportionality if a wire 1.6 m long and 0.005 m in diameter has a resistance of 190 ohms. (Round your answer to six decimal places.) k = (c) Find the resistance of a wire made of the same material that is 3 m long and has a diameter of 0.009 m. (Round your answer to the nearest whole number.) R = ohms (d) If the diameter is doubled and the length is tripled, by what factor is the resistance changed? Need Help? Read It Watch It Master It 8. [-/1 Points] DETAILS SPRECALC7 1.12.052. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The heat experienced by a hiker at a campfire is proportional to the amount of wood on the fire and inversely proportional to the cube of his distance from the fire. If the hiker is 12 ft from the fire and someone doubles the amount of wood burning, how far from the fire would he have to be so that he feels the same heat as before? (Round your answer to one decimal place.) ft Need Help? Read It -x- 9. [-/2 Points] DETAILS SPRECALC7 1.12.053. MY NOTES ASK YOUR TEACHER The frequency f of vibration of a violin string is inversely proportional to its length L. The constant of proportionality k is positive and depends on the tension and density of the string. (a) Write an equation that represents this variation. (b) What effect does doubling the length of the string have on the frequency of its vibration? O The frequency of its vibration is halved. The frequency of its vibration is doubled. The frequency of its vibration remains the same. Need Help? Read It Watch It