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Simplify \(\frac{1}{3}\) log8 + \(\frac{1}{3}\) log 64 - 2 log6
Given that M = \(\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}\) and N = \(\begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix}\), calculate (3M - 2N)
For what range of values of x is x\(^2\) - 2x - 3 ≤ 0
Simplify ( \(\frac{1}{2 - √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)
Consider the statements:
x: Birds fly
y: The sky is blue
Which of the following statements can be represented as x \(\to\) y?
If log 5(\(\frac{125x^3}{\sqrt[ 3 ] {y}}\) is expressed in the values of p, q and k respectively.
If the sum of the roots of 2x\(^2\) + 5mx + n = 0 is 5, find the value of m.
Find the unit vector in the direction opposite to the resultant of forces. F\(_1\) = (-2i - 3j) and F\(_2\) = (5i - j)
P(3,4) and Q(-3, -4) are two points in a plane. Find the gradient of the line that is normal to the line PQ.
The distance(s) in metres covered by a particle in motion at any time, t seconds, is given by S =120t - 16t\(^2\). Find in metres, the distance covered by the body before coming to rest.
A bag contains 5 red and 5 blue identical balls. Three balls are selected at random without replacement. Determine the probability of selecting balls alternating in color.
The variables x and y are such that y =2x\(^3\) - 2x\(^2\) - 5x + 5. Calculate the corresponding change in y and x changes from 2.00 to 2.05.
A three-digit odd number less than 500 is to be formed from 1,2,3,4 and 5. If repetition of digits is allowed, in how many ways can this be done?
Calculate the variance of \(\sqrt{2}\), (1 + \(\sqrt{2}\)) and (2 + \(\sqrt{2}\))
A force of 230N acts in its direction 065\(^o\). Find its horizontal component.
In what interval is the function f : x -> 2x - x\(^2\) increasing?
A function f defined by f : x -> x\(^2\) + px + q is such that f(3) = 6 and f(3) = 0. Find the value of q.
Which of the following is not an equation of a circle?
In how many ways can the letters of the word MEMBER be arranged?
A circle with centre (5,-4) passes through the point (5, 0). Find its equation.