x varies jointly as the square of m and the code of n, when x=9, m=3/4 and n=1/2.

Question

a. Determine the relationship between x, m and n.
b. calculate correct to 3 significant figures, the value of x the m=2/3 and n=1/5.
c. the value of m when x=5 and n=1/8.

Answer 1

a. Since x varies jointly as the square of m and the code (inverse) of n, we can write the equation:

x = k(m^2/n)

where k is the constant of proportionality. To find k, we can substitute the values given:

9 = k((3/4)^2/(1/2))

9 = k(9/8)

k = 8

So the equation relating x, m, and n is:

x = 8(m^2/n)

b. To find x when m=2/3 and n=1/5, we can use the equation we found in part a:

x = 8((2/3)^2/(1/5))

x = 35.56

Rounding to 3 significant figures, x ≈ 35.6

c. To find m when x=5 and n=1/8, we can use the equation we found in part a:

5 = 8(m^2/(1/8))

5 = 64m^2

m^2 = 5/64

m ≈ ± 0.354

Since m must be positive (as given in the initial values), we take the positive square root and round to 3 significant figures:

m ≈ 0.354