Combined Variation

Combined Variation

Multiple Choice

It is given that m varies directly as the square of n and inversely as p. Given m=10.8 when n=18 and p=6. Express m in terms of n and p.

•  $m=5n^2p$  

•  $m=\frac{5n^2}{p}$  

•  $m=\frac{n^2}{5p}$  

•  $m=\frac{27n^2}{5p}$  

Multiple Choice

y varies directly as x and inversely as z. It is given that y = 51 when x = 1.7 and z = 5. Express y in terms of x and z.

• $y=\frac{150x}{z}$

• $y=\frac{6x}{z}$

• $y=\frac{x}{6z}$

• $y=\frac{x}{150z}$

Multiple Select

 $It\ is\ given\ that\ y\propto\frac{\sqrt{x}}{z}and\ y=32\ when\ x=2.56\ and\ z=0.4.$  Find the value of y when x = 81 and z = 6.

•  $y=\frac{\sqrt{x}}{8z}$  

•  $y=\frac{8\sqrt{x}}{z}$  

•  y = 12

•  $y=\frac{3}{16}$  

Multiple Select

It is given that 

 $p\propto\frac{1}{qr^3}$  and p =1 0, q = 35 and r = 0.2
(i) What is the equation of p in terms of q and r.
(ii) Find the value of q when p = 6.25 and r = 4.

•  $p=\frac{35.7}{qr^3}$  

•  $p=\frac{2.8}{qr^3}$  

• q = 0.007

• q = 0.009

Multiple Select

The time taken T minutes, to boil water varies directly as the weight, w kg, of the water and inversely as the power, P watts, of a kettle. Shamsiah uses 4 minutes to boil 2 kg water using a kettlw with the power of 1 500 watts. (T = 4, w = 2, P = 1 500)

(I) Express T in terms of w and P. (Find k and then express...)

(ii) If the power of the kettle used is 1 200 watts, what is the time needed, in minutes, to boil 1.8 kg water? (Find T, when P = 1 200, w = 1.8)

• $T\ =\ \frac{3\ 000w}{P}$

• $T\ =\ \frac{750w}{P}$

• T = 1.13 minutes

• T = 4.5 minutes