My Maths and I: WAEC Mathematics Question 2015 ( Essay Question Four 4b )

QUESTION 4b

4b. The height, h m, of a dock above sea level is given by $h = 6+4\cos (15p)^{o}$ $h = 6 + 4 \cos (15 p) °, 0 < p < 6$ . Find :

(i) the value of h when p = 4 ;

(ii) correct to two significant figures, the value of p when h = 9m

SOLUTION

(i) Given the equation;

$h = 6+4\cos (15p)^{o}$

with p = 4

Substituting the valiie of p into the equation, we have;

h=6+4cos(15 x 4)°

h=6+4cos60°

But cos60° = $\tfrac{1}{2}$

$\therefore$ h=6+4 ( $\tfrac{1}{2}$ )

h=6+2

h= 8m ANSWERED

(ii) Given the equation;

h=6+4cos(15p)°

with h=9m

Substituting h=9 into into the equation. we have;

9=6+4cos(15p)°

9 - 6 = 4cos(15p)°

3 = 4cos(15p)°

Dividing both sides by 4

$\tfrac{3}{4}= \tfrac{4}{4}$ cos(15p)°

0.75 = cos(15p)°

or cos(15p)° = 0.75

$p ° = \frac{41.4}{15}$

p°=2.76°

$p ≊ 2.8 °$ (2 significant figures).ANSWERED

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