Given that loga2 = 0.693 and loga3 = 1.097, find loga 13.5
1.404
1.790
2.598
2.790
Correct answer is C
loga 13.5 = loga \(\frac{27}{2}\)
= 3loga 3 - log2a
= 3 x 1.097 - 0.693
= 2.598
Find the value of (0.006)3 + (0.004)3 in standard form
2.8 x 10-9
2.8 x 10-7
2.8 x 10-8
2.8 x 10-6
Correct answer is B
(0.006)3 + (0.004)3 = 2.16 x 10-7
(2.16 + 0.64) x 10-7
= 2.8 x 10-7
Evaluate 64.764\(^2\) - 35.236\(^2\) correct to 3 significant figures
2960
2950
2860
2850
Correct answer is B
(64.764 - 35.236)(64.764 + 35.236)
= 29.528 x 100
= 2950 to 3 sig. fig.
If \(1P03{_4} = 115_{10}\) find P
0
1
2
3
Correct answer is D
\(1 x 4^3 + P x 4^2 + 0 x 4 + 3 = 115_{10}\)
16p + 67 = 115 p = \(\frac{48}{16}\)
= 3
12\(\frac{1}{2}\)
32\(\frac{1}{2}\)
57\(\frac{1}{2}\)
147\(\frac{1}{2}\)
Correct answer is C
y = 6 sin (2x - 25)o
\(\frac{dy}{dx}\) = -12 cos(2x - 25o)
\(\frac{dy}{dx}\) = 0
-12 cos x (2x - 25o) = 0
= cos(2x - 25o) = 0
= 2x - 25o = cos-1(0)
= 2x - 25o
= 90o
x = \(\frac{115}{2}\)