1
2
3
9
Correct answer is A
Using the two - point from
\(\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}\)
\(\frac{y - 2}{-2 - 2} = \frac{x - 4}{-8 - 4}\)
\(\frac{y - 2}{-4} = \frac{x - 4}{-12}\)
\(\frac{-12(y -2)}{-4}\) = x - 4
3(y -2) = x -4
3y - 6 = x - 4
3y = x - 4 + 6
3y = x + 2...
By comparing the equations;
3y = px + , p = 1
If M and N are the points (-3, 8) and (5, -7) respectively, find |MN|
8 units
11 units
15 units
17 units
Correct answer is D
|MN| = \(\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)
= \(\sqrt{(-3 -5)^2 + (8 - 7)^2}\)
= \(\sqrt{(-8)^2 + (8 + 7)^2}\)
= \(\sqrt{64 + (15)^2}\)
= \(\sqrt{64 + 225}\)
= \(\sqrt{289}\)
= 17 units
\(45^o\)
\(95^o\)
\(84^o\)
\(85^o\)
Correct answer is C
x + 2x + 2x + (x + \(30^o\)) + (x + \(20^o\)) + (x - \(10^o\)) = (2n - 4) x \(90^o\)
8x + 50 \(^o\) - 10\(^o\) = (2 x 6 -4) x 90\(^o\)
8x + 40\(^o\) = 8 x 90\(^o\) = 720\(^o\)
8x = 720\(^o\) - 40\(^o\) = 680\(^o\)
x = \(\frac{680^o}{8}\)
= 85\(^o\)
113\(cm^3\)
131\(cm^3\)
311\(cm^3\)
414\(cm^3\)
Correct answer is A
Surface area of a sphere = \(4 \pi r^2\) \(4 \pi r^2\) = \(\frac{792}{7}cm^2\) 4 x \(\frac{22}{7}\) x \(r^2\) = \(\frac{792}{7}\) \(r^2\) = \(\frac{792}{7}\) x \(\frac{7}{4 \times 22}\) = 9 r = \(\sqrt{9}\) = 3cm Hence, volume of sphere = \(\frac{4}{3} \pi r^3\) = \(\frac{4}{3} \times \frac{22}{7} \times 3 \times 3 \times 3 \) = \(\frac{4 \times 22 \times 9}{7}\) \(\approx\) = 113.143 = 113\(cm^3\) (to the nearest whole number)
14m
10m
7m
5m
Correct answer is C
Volume of a cylinder = \( \pi r^2\)h
385 = \(\frac{22}{7}\) x \(r^2\) x 10
385 x 7 = 22 x \(r^2\) x 10
\(r^2\) = \(\frac{385 \times 7}{22 \times 10}\)
= 12.25
r = \(\sqrt{12.25}\)
= 3.5m
Hence, diameter of tank = 2r
= 2 x 3.5 = 7m