Find the angle between forces of magnitude 7N and 4N if t...
Find the angle between forces of magnitude 7N and 4N if their resultant has a magnitude of 9N.
39.45°
73.40°
75.34°
106.60°
Correct answer is B
\(F_{1} = 7i + 0j\)
\(F_{2} = (4\cos\theta)i + (4\sin\theta)j\)
\(9 = \sqrt{(7 + 4\cos\theta)^{2} + (4\sin\theta)^{2}}\)
\(9^{2} = (7 + 4\cos\theta)^{2} + (4\sin\theta)^{2} \implies 81 = 49 + 56\cos\theta + 16\cos^{2}\theta + 16\sin^{2}\theta\)
\(81 = 49 + 56\cos\theta + 16(\cos^{2}\theta + \sin^{2}\theta)\)
Recall, \(\cos^{2}\theta + \sin^{2}\theta = 1\)
\(81 = 49 + 56\cos\theta + 16 \implies 81 - 49 -16 = 56\cos\theta\)
\(16 = 56\cos\theta \implies \cos\theta = \frac{16}{56} = 0.2857\)
\(\theta = \cos^{-1} 0.2857 = 73.40°\)
Which of the following is the same as \(\sin (270 + x)°\)?...
A binary operation ♦ is defined on the set R, of real numbers by \(a ♦ b = \fr...
A fair die is tossed twice. Find the probability of obtaining a 3 and a 5. ...
Solve the inequality \(x^{2} - 2x \geq 3\)...
Given that \(P = \begin{pmatrix} 3 & 4 \\ 2 & x \end{pmatrix}; Q = \begin{pmatrix} 1 & 3...