If the binomial expansion of (1 + 3x)\(^6\) is used to evaluate (0.97)\(^6\), find the value of x.
0.03
0.01
-0.01
-0.03
Correct answer is C
(1 + 3x )\(^6\) = (0.97)\(^6\)
1 + 3x = 0.97
3x = 0.97.1
\(\frac{3x}{3} = \frac{0.03}{3}\)
x = -0.01
4 + 8 + 16 + 32 + ...
\(\frac{1}{2}\) + 2 \(\frac{1}{2}\) + 12\(\frac{1}{2}\) + 62 \(\frac{1}{2}\) + ..
\(\frac{4}{81}\) + \(\frac{2}{27}\) + \(\frac{1}{9}\) + \(\frac{1}{6}\) + ...
128 + 64 + 32 + 16 + ...
Correct answer is D
No explanation has been provided for this answer.
2.9.seconds
2.8 seconds
2.6 seconds
1.4 seconds
Correct answer is A
s = \(\frac{1}{2}gt^2\)
40 = \(\frac{1}{2} \times 9.8 \times t^2\)
\(\frac{80}{9.8} = t^2\)
t = \(\sqrt{8.16326}\)
t ≈ 2.9 secs
p=-10, q=7
p=-10, q=-7
p=10, q=- 7
p-10, q=7
Correct answer is C
If the body is in equilibrium then
F + R = N
3i - 12j + 7i + 5j = pi + qj
10i - 7j = pi + qj
p = 10, q = -7
Find the angle between i + 5j and 5i - J
0\(^o\)
45\(^o\)
60\(^o\)
90\(^o\)
Correct answer is D
a = i + 5j and b = 5i - j
cos\(\theta\) = \(\frac{a.b}{|a|.|b|}\)
= \(\frac{(1 \times 5) + (5x - 1)}{(\sqrt{1^2 + 5^2}) (5^2 + (-1))^2}\)
= \(\frac{5 - 5}{\sqrt{26}\times \sqrt{26}}\) = 0
x = cos\(^{-1}\)(0), x = 90\(^o\)