0.30
0.50
0.57
1.80
Correct answer is A
P (X or Y) = P(X) + P(Y), when they are independent as given.
0.7 = 0.4 + P(Y)
P(Y) = 0.7 - 0.4 = 0.30
2.50m/s
2.00 m/s
0.25 m/s
0.20 m/s
Correct answer is C
\(V = \frac{2}{3} \pi r^{3}\)
Given: \(\frac{\mathrm d V}{\mathrm d t} = 18\pi m^{3} s^{-1}\)
\(\frac{\mathrm d V}{\mathrm d t} = \frac{\mathrm d V}{\mathrm d r} \times \frac{\mathrm d r}{\mathrm d t}\)
\(\frac{\mathrm d V}{\mathrm d r} = 2\pi r^{2}\)
\(18\pi = 2\pi r^{2} \times \frac{\mathrm d r}{\mathrm d t}\)
\(\frac{\mathrm d r}{\mathrm d t} = \frac{18\pi}{2\pi r^{2}} = \frac{9}{r^{2}}\)
The rate of change of the radius when r = 6m,
\(\frac{\mathrm d r}{\mathrm d t} = \frac{9}{6^{2}} = \frac{1}{4}\)
= \(0.25 ms^{-1}\)
7π cubic units
15π/2 cubic units
8π cubic units
17π/2 cubic units
Correct answer is B
∫30 π(y+1) dy = π[y2 + y30
= π(9/2 + 3) = 15π/2
If y = 2x - sin2x, find dy/dx when x = π/4
π
-π
π/2
-π/2
Correct answer is D
y = 2x cos2x - sin2x
dy/dx = 2 cos2x +(-2x sin2x) - 2 cos2x
= 2 cos2x - 2x sin2x - cos2x
= -2x sin2x
= -2 x (π/4) sin2 x (π/4)
= -(π/2) x 1 = -(π/2)
Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)
π
π/2
-π/2
-π
Correct answer is D
\(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta = \int^{\pi}_{0}\frac{-sin^{2}\theta}{sin^{2}\theta}\\ = \int^{\pi}_{0}d\theta = -\pi\)