(a) Evaluate without using calculator, (\(\frac{1}{4} \times 9\frac{1}{7} + \frac{2}{5} (\frac{2}{2} + \frac{3}{4})) \div (\frac{2}{5} - \frac{1}{4})\) (b) ...
Question 1 Report
(a) Evaluate without using calculator, (\(\frac{1}{4} \times 9\frac{1}{7} + \frac{2}{5} (\frac{2}{2} + \frac{3}{4})) \div (\frac{2}{5} - \frac{1}{4})\)
(b) A hunter walked 250 m from point P to Q on a bearing 042\(^o\). Calculate, correct to the nearest meter the vertical distance he has moved.
Answer Details
(a) Work part by part (reading \(\frac{2}{2} = 1\) as written).
\[\tfrac{1}{4} \times 9\tfrac{1}{7} = \tfrac{1}{4} \times \tfrac{64}{7} = \tfrac{16}{7}\] \[\tfrac{2}{5}\left(1 + \tfrac{3}{4}\right) = \tfrac{2}{5} \times \tfrac{7}{4} = \tfrac{7}{10}\] \[\tfrac{16}{7} + \tfrac{7}{10} = \tfrac{160 + 49}{70} = \tfrac{209}{70}\] \[\tfrac{2}{5} - \tfrac{1}{4} = \tfrac{3}{20}\] \[\tfrac{209}{70} \div \tfrac{3}{20} = \tfrac{209}{70} \times \tfrac{20}{3} = \tfrac{418}{21} = 19\tfrac{19}{21}\](b) The vertical (north-south) distance is the northward component of the walk.
\[\text{Vertical distance} = 250\cos 42^{\circ} = 250 \times 0.7431 = 185.8 \approx 186 \text{ m}\]Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning