If 163x=14(32x−1), find the value of x.
−1
−13
−37
−519
Correct answer is A
163x=14(32x−1)
(24)3x=(2−2)((25)x−1)
212x=2−2+5x−5
12x=−7+5x
7x=−7⟹x=−1
If 5√2−√88=m√2, where m is a constant. Find m.
112
114
214
212
Correct answer is C
5√2=5×√2√2×√2=5√22
√88=2√28=√24
5√2−√88=(52−14)√2
= 94√2
= 214√2
Find the value of \cos(60° + 45°) leaving your answer in surd form
\frac{6 + \sqrt{2}}{4}
\frac{3 + \sqrt{6}}{4}
\frac{\sqrt{2} - \sqrt{6}}{4}
\frac{3 - \sqrt{6}}{4}
Correct answer is C
\cos (x + y) = \cos x \cos y - \sin x \sin y
\cos (60 + 45) = \cos 60 \cos 45 - \sin 60 \sin 45
= \frac{1}{2} \times \frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}
= \frac{\sqrt{2} - \sqrt{6}}{4}
Find the domain of f(x) = \frac{x}{3 - x}, x \in R, the set of real numbers.
{x : x \in R, x \neq 3}
{x : x \in R, x \neq 1}
{x : x \in R, x \neq 0}
{x : x \in R, x\neq -3}
Correct answer is A
f(x) = \frac{x}{3 - x}
f(x) has a defined value except at x = 3 where the function is undefined.
23.52°
24.50°
29.52°
29.82°
Correct answer is B
p . q = |p||q|\cos \theta
156 + 70 = (\sqrt{13^{2} + 14^{2}})(\sqrt{12^{2} + 5^{2}}) \cos \theta
226 = (\sqrt{365})(13) \cos \theta
\frac{226}{13\sqrt{365}} = \cos \theta
\cos \theta = 0.9099
\theta = 24.50°