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please need help with 2 problems. problem 1. Suppose y is directly proportional

ID: 2856561 • Letter: P

Question


please need help with 2 problems.
problem 1. Suppose y is directly proportional to x^2 and inversely proportional to z. When y=3 and x =6, z is 4. (a) what is the constant of proportuonality? (b) Solve for z in the terms of x and y. What is the relationship between z and x? (c) what is z when x and y are both 12?

problem 2.
The time it takes to build a race track is proportional to the length of the road and inversely proportional to the number of Toads building the road. Building Toads Turn Puke, 106p meters long, took 20 Toads 10 days to build. How long will it take 30 Toads to build Koopa Troops Beach -a course that is 690 meters long?

Explanation / Answer

Problem 1

y = kx^2/z

a) y=3 and x=6, when z=4

3 = k(36)/4

k = 1/3, hence the proportionality constant is equal to 1/3

b) y = 1/3 *x^2/z

z = x^2/3y

C) z = x^2/3y = (12)^2/3(12) = 4

Problem 2

Number of Days = Length of road/number of toads

Hence the number of days it will take for build 690m Koopa Troops

=> 20 * (Length of Koopa Troops)/(Length of Turn Puke) * (number of toads at koopa troops)/(number of toads at Turn Puke)

=> 20 * 690/106 * 30/20

=> 30 * 690/106

=> 195.28

Hence number of days will be equal to 196 days