(a) Simplify : (625^{frac{3}{8}} times 5^{frac{1}{2}} div 25)
(b) Solve the following equations correct to one decimal place.
(i) (tan (theta + 25)° = 5.145)
(ii) (5cos theta – 1 = 0), where (0° leq theta leq 90°).
Explanation
(a) (625^{frac{3}{8}} times 5^{frac{1}{2}} div 25)
= ((5^{4})^{frac{3}{8}} times 5^{frac{1}{2}} div 5^{2})
= (5^{frac{3}{2}} times 5^{frac{1}{2}} div 5^{2})
= (5^{frac{3}{2} + frac{1}{2} – 2})
= (5^{0} = 1)
(b)(i) (tan (theta + 25)° = 5.145)
(theta + 25 = tan^{-1} (5.145))
(implies theta + 25 = 79°)
(theta = 79° – 25° = 54°)
(ii) (5 cos theta – 1 = 0)
(implies 5 cos theta = 1)
(cos theta = frac{1}{5} = 0.2)
(theta = cos^{-1} (0.2) = 78.463°)
(approxeq 78.5°) (to one d.p)