Given that \(R = (4, 180°)\) and \(S = (3, 300°)\), find the dot product
\(-6\sqrt{3}\)
-6
6
\(6\sqrt{3}\)
Correct answer is B
No explanation has been provided for this answer.
0.024
0.336
0.664
0.976
Correct answer is D
\(P(\text{at least one solves the problem}) = 1 - P(\text{none solving the problem})\)
= 1 - (0.4)(0.3)(0.2)
= 1 - 0.024
= 0.976
1 sec and 7 sec
1 sec and 8 sec
2 sec and 5 sec
2 sec and 7 sec
Correct answer is A
\(s = ut + \frac{1}{2}at^{2}\)
\(s = ut - \frac{1}{2}gt^{2}\) (Upward movement against gravity)
\(35 = 40t - \frac{1}{2}10t^{2}\)
\(35 = 40t - 5t^{2}\)
\(5t^{2} - 40t + 35 = 0\)
\(t^{2} - 8t + 7 = 0\)
\((t - 1)(t - 7) = 0 \implies t = \text{1 sec and 7 sec}\)
Given that \(p = 4i + 3j\), find the unit vector in the direction of p.
\(\frac{1}{3}(4i + 3j)\)
\(\frac{1}{3}(3i + 4j)\)
\(\frac{1}{5}(3i + 4j)\)
\(\frac{1}{5}(4i + 3j)\)
Correct answer is D
\(\hat {n} = \frac{\overrightarrow{p}}{|p|}\)
where \(\hat {n}\) is the unit vector in the direction of p.
\(|p| = \sqrt{4^{2} + 3^{2}} = \sqrt{25} = 5\)
\(\hat {n} = \frac{1}{5} (4i + 3j)\)
\(\frac{2}{3}\)
\(\frac{2}{5}\)
\(\frac{1}{3}\)
\(\frac{1}{5}\)
Correct answer is A
For independent events \(P(X \cap Y) = P(X) \times P(Y)\)
\(\frac{2}{15} = \frac{1}{5} \times P(Y)\)
\(P(Y) = \frac{2}{15} ÷ \frac{1}{5} = \frac{2}{3}\)