4MA0 Higher June 2015 Paper 3 Q22
22 \(A\), \(r\) and \(T\) are three variables.
\(A\) is proportional to \(T^2\)
\(A\) is also proportional to \(r^3\)
\(T = 47\) when \(r = 0.25\)
Find \(r\) when \(T = 365\)
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
\(A = KT^2\) and \(A = kr^3\) or \(T^2 = \dfrac{k}{K}r^3\) or \(T^2 = pr^3\) \(r^3 = \dfrac{K}{k}T^2\) or \(r^3 = qT^2\) | M1 |
\(47^2 = \dfrac{k}{K}0.25^3\) or \(47^2 = m0.25^3\) or \(\dfrac{47^2}{0.25^3}\) (= 141376) or \(\dfrac{0.25^3}{47^2}\) \(\left(= \dfrac{1}{141376} = 7.07(3\ldots) \times 10^{-6}\right)\) | M1 |
\((r^3 =)\;\dfrac{0.25^3}{47^2} \times 365^2\) or \(365^2 \div 141376\) or \(365^2 \times 7.07(3\ldots) \times 10^{-6}\) or 0.942… | M1 |
| 0.980 | A1 |
| (4) |
Notes
M1: condone the same constant used in both equations
NB: Values may be substituted in place of the variables
M1: NB: 2209 may be seen in place of \(47^2\)
\(\dfrac{1}{64}\) or 0.015625 may be seen in place of \(0.25^3\)
A1: awrt 0.980 accept 0.98