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Find the nth term of the linear sequence (A.P) (5y + 1), ( 2y + 1), (1- y),...
If the binomial expansion of (1 + 3x)\(^6\) is used to evaluate (0.97)\(^6\), find the value of x.
In which of the following series can be the formula S = \(\frac{a}{1 - r}\) where a is the first term and r is the common ratio, be used to find the sum of all the terms?
A stone was dropped from the top of a building 40m high. Find, correct to one decimal place, the time it took the stone to reach the ground. [Take g = 9.8ms\(^{-2}\)]
Given that F = 3i - 12j, R = 7i + 5j and N = pi + qj are forces acting on a body, if the body is in equilibrium. find the values of p and q.
Find the angle between i + 5j and 5i - J
Calculate the probability that the product of two numbers selected at random with replacement from the set {-5,-2,4, 8} is positive
Find the median of the numbers 9,7, 5, 2, 12,9,9, 2, 10, 10, and 18.
If X = \(\frac{3}{5}\) and cos y = \(\frac{24}{25}\), where X and Y are acute, find the value of cos (X + Y).
Given that P = {x : 1 \(\geq\) x \(\geq\) 6} and Q = {x : 2 < x < 10}. Where x are integers, find n(p \(\cap\) Q)
Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x)
If V = plog\(_x\), (M + N), express N in terms of X, P, M and V
Given that 2x + 3y - 10 = 0 and 3x = 2y - 11, calculate the value of (x - y).
Differentiate \(\frac{x}{x + 1}\) with respect to x.
If \(\frac{6x + k}{2x^2 + 7x - 15}\) = \(\frac{4}{x + 5} - \frac{2}{2x - 3}\). Find the value of k.
Simplify; \(\frac{\sqrt{5} + 3}{4 - \sqrt{10}}\)
Given that X : R \(\to\) R is defined by x = \(\frac{y + 1}{5 - y}\) , y \(\in\) R, find the domain of x.
If \(\begin{pmatrix} p+q & 1\\ 0 & p-q \end {pmatrix}\) = \(\begin{pmatrix} 2 & 1 \\ 0 & 8 \end{pmatrix}\)
Find the values of p and q
If \(\int^3_0(px^2 + 16)dx\) = 129. Find the value of p.
If cos x = -0.7133, find the values of x between 0\(^o\) and 360\(^o\)