Solve: 8\(^{x - 2}\) = 4\(^{3x}\)
-2
-1
1
2
Correct answer is B
8\(^{x - 2}\) = 4\(^{3x}\)
2\(^{3(x - 2)}\) = 2\(^{2(3x)}\)
2 \(^{3x - 4}\) = 2\(^{6x}\)
2 \(^{x - 4}\) = 6\(^x\)
\(\frac{-4x}{-4}\) = \(\frac{4}{-4}\)
x = -1
14.11
13.81
12.06
11.05
Correct answer is C
No explanation has been provided for this answer.
16 N
\(16 \sqrt{3}\) N
18 N
\(18 \sqrt{3}\) N
Correct answer is B
No explanation has been provided for this answer.
1s
3s
7s
9s
Correct answer is D
No explanation has been provided for this answer.
Calculate, correct to one decimal place, the angle between 5i + 12j and -2i + 3j.
54.8°
56.3°
66.4°
76.3°
Correct answer is B
\(a . b = |a||b|\cos \theta\)
\((5i + 12j).(2i + 3j) = -10 + 36 = 26\)
\(26 = |5i + 12j||-2i + 3j|\cos \theta\)
\(|5i + 12j| = \sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = 13\)
\(|2i + 3j| = \sqrt{2^{2} + 3^{2}} = \sqrt{4 + 9} = \sqrt{13}\)
\(26 = 13(\sqrt{13})\cos \theta\)
\(\cos \theta = \frac{26}{13\sqrt{13}} = 0.5547\)
\(\theta = 56.3°\)