350
455
462
571
Correct answer is C
No explanation has been provided for this answer.
If \(h(x) = x^{3} - \frac{1}{x^{3}}\), evaluate \(h(a) - h(\frac{1}{a})\)
-1
0
\(2a^{3} - \frac{2}{a^{3}}\)
\(\frac{2}{a^{3}} - 2a^{3}\)
Correct answer is C
\(h(x) = x^{3} - \frac{1}{x^{3}}\)
\(h(a) = a^{3} - \frac{1}{a^{3}}\)
\(h(\frac{1}{a}) = (\frac{1}{a})^{3} - \frac{1}{(\frac{1}{a})^{3}} = \frac{1}{a^{3}} - a^{3}\)
\(h(a) - h(\frac{1}{a}) = (a^{3} - \frac{1}{a^{3}}) - (\frac{1}{a^{3}} - a^{3}) = 2a^{3} - \frac{2}{a^{3}}\)
\(x^{3} - 4x - 9\)
\(x^{3} - 4x + 9\)
\(x^{3} + 4x - 9\)
\(x^{3} + 4x + 9\)
Correct answer is A
\(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 4\)
\(y = \int (3x^{2} - 4) \mathrm {d} x = x^{3} - 4x + c\)
y = 6 when x = 3
\(6 = 3^{3} - 4(3) + c \implies 6 = 27 - 12 + c\)
\(c = 6 - 15 = -9\)
\(y = x^{3} - 4x - 9\)
45. 25 m
45.50 m
56.00 m
56.25 m
Correct answer is D
\(h = 45t - 9t^{2}\)
\(\frac{\mathrm d h}{\mathrm d t} = 45 - 18t = 0\)
\(45 = 18t \implies t = 2.5 s\)
\(h(2.5) = 45(2.5) - 9(2.5)^{2} = 112.5 - 56.25\)
= \(56.25 m.\)
\((4\sqrt{2} N, 000°)\)
\((4\sqrt{2} N, 045°)\)
\((4\sqrt{2} N, 090°)\)
\((4\sqrt{2} N, 180°)\)
Correct answer is B
\(F_{1} = (7i + 8j)N ; F_{2} = (3i + 4j)N\)
\(|F_{1} - F_{2}| = |(7i + 8j) - (3i + 4j)| = |4i + 4j|\)
\(|4i + 4j| = \sqrt{4^{2} + 4^{2}} = \sqrt{32} = 4\sqrt{2}\)
\(\tan \theta = \frac{y}{x} = \frac{4}{4} = 1\)
\(\theta = \tan^{-1} 1 = 045°\)
= \((4\sqrt{2} N, 045°)\)