MATHEMATICS VARIATION

P varies directly as the cube root of Q. Find the relation between P and Q.

• $P\propto Q^3$

• $P\propto\frac{1}{Q^3}$

• $P\propto Q^{\frac{1}{3}}$

• $P\propto\frac{1}{Q^{\frac{1}{3}}}$

It is given that S varies directly as T and inversely as the square root of U. Find the relation between S, T and U.

• $S\propto\frac{U^2}{T}$

• $S\propto\frac{T}{U^2}$

• $S\propto\frac{T}{\sqrt{U}}$

• $S\propto\frac{\sqrt{U}}{T}$

y varies directly as x and inversely as the square of z. Given that the constant is k,find the relation between x, y and z.

• $y=\frac{kx^2}{z}$

• $y=\frac{kx}{z^2}$

• $y=\frac{kx}{\sqrt{z}}$

• $y=\frac{k\sqrt{z}}{x}$

It is given that X varies directly as the square root of Y and inversely as the square of Z. Find the relation betzveen X, Y and Z.

• $X\propto\frac{\sqrt{Y}}{Z^2}$

• $X\propto\frac{\sqrt{Z}}{Y^2}$

• $X\propto\frac{Y^2}{\sqrt{Z}}$

• $X\propto\frac{Z^2}{\sqrt{Y}}$

It is given that PQ² = k, where k is a constant. Which of the following statements is true?

• P varies directly as the square of Q.

• P varies directly as the square root of Q.

• P varies inversely as the square of Q.

• P varies inversely as the square root of Q.

The table shows some values of the variables p, q and r such that p varies directly as the square of q and inversely as r.

Calculate the value of d.

• 19

• 74

• 84

• 108

The table below shows some values of the variables L and M such that M varies inversely as the square root of L.

Find the relation between M and L.

• $M=\frac{3}{L^{\frac{1}{2}}}$

• $M=3L^{\frac{1}{2}}$

• $M=\frac{3}{L^2}$

• $M=3L^2$

The table shows two sets of values of the variables D and N.

It is given that D varies directly as N. Find the value of x.

• 72

• 60

• 36

• 3

The table below some values of the variables p, q and r which satisfy  $r\propto pq$  . Calculate the value of d.

•  $\frac{1}{3}$  

•  $\frac{1}{2}$  

•  $\frac{1}{4}$  

•  $6$  

The table shows some values of the variables P and Q.

It is given that P varies inversely as Q. Find the value of R.

• 15

• 18

• 27

• 31