(a) Find the smallest integer that satisfies the inequality \(x + 8 < 4x -
(a) Find the smallest integer that satisfies the inequality \(x + 8 < 4x - 15\).
(b) A sales girl is paid a monthly salary of N2,500 in addition to a commission of 5 kobo in the naira on all sales made by her during the month. If her sales for a month amounts to N200,000.00, calculate her income for that month.
(c)_LI(1).jpg)
The diagram shows a window consisting of a rectangular and semi- circular parts. The radius of the semi- circular part is 35 cm and the height of the rectangular part is 50 cm. Find the area of the window. [Take \(\pi = \frac{22}{7}\)].
Explanation
(a) \(x + 8 < 4x - 15 \implies 4x - 15 > x + 8\)
\(4x - x > 8 + 15 \implies 3x > 23\)
\(x > \frac{23}{3}\)
\(x > 7\frac{2}{3}\).
(b) Extra income = 5k of N200,000
= \(\frac{5}{100} \times N200,000\)
= \(N10,000\)
Total income = Monthly income + commission
= N(2,500 + 10,000)
= N12,500.
(c) Area of semi- circle = \(\frac{\pi r^{2}}{2}\)
= \(\frac{1}{2} \times \frac{22}{7} \times 35 \times 35\)
= \(1925 cm^{2}\)
Length of rectangular part = 50 cm
Breadth = Diameter of semi- circle = 2(35 cm) = 70 cm
Area of rectangular part = \(length \times \breadth\)
= \(50 \times 70\)
= \(3500 cm^{2}\)
Total area of window = \((3500 + 1925) cm^{2}\)
= \(5425 cm^{2}\)
(a) \(x + 8 < 4x - 15 \implies 4x - 15 > x + 8\)
\(4x - x > 8 + 15 \implies 3x > 23\)
\(x > \frac{23}{3}\)
\(x > 7\frac{2}{3}\).
(b) Extra income = 5k of N200,000
= \(\frac{5}{100} \times N200,000\)
= \(N10,000\)
Total income = Monthly income + commission
= N(2,500 + 10,000)
= N12,500.
(c) Area of semi- circle = \(\frac{\pi r^{2}}{2}\)
= \(\frac{1}{2} \times \frac{22}{7} \times 35 \times 35\)
= \(1925 cm^{2}\)
Length of rectangular part = 50 cm
Breadth = Diameter of semi- circle = 2(35 cm) = 70 cm
Area of rectangular part = \(length \times \breadth\)
= \(50 \times 70\)
= \(3500 cm^{2}\)
Total area of window = \((3500 + 1925) cm^{2}\)
= \(5425 cm^{2}\)