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If 2y\(^2\) + 7 = 3y - xy, find \(\frac{dy}{dx}\)
A fair die is tossed 60 times and the results are recorded in the table
| Number of die | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 15 | 10 | 14 | 2 | 8 | 11 |
Find the probability of obtaining a prime number.
A body of mass 15kg is placed on a smooth plane which is inclined at 60° to the horizontal. If the box is at rest,
calculate the normal reaction to the plane. [ Take g = 10m/s\(^2\) ]
Given that P = { x: 0 ≤ x ≤ 36, x is a factor of 36 divisible by 3} and Q = { x: 0 ≤ x ≤ 36, x is an even number and a perfect square}, find P n Q.
Find the inverse of \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\)
For what value of k is 4x\(^2\) - 12x + k, a perfect square?
If f(x) = 4x\(^3\) + px\(^2\) + 7x - 23 is divided by (2x -5), the remainder is 7. find the value of p
If α and β are the roots of 3x\(^2\) - 7x + 6 = 0, find \(\frac{1}{α}\) + \(\frac{1}{β}\)
In how many ways can 8 persons be seated on a bench if only three seats are available?
Using binomial expansion of ( 1 + x)\(^6\) = 1 + 6x + 15x\(^2\) + 20x\(^3\) + 6x\(^5\) + x)\(^6\), find, correct to three decimal places, the value of (1.998))\(^6\)
g(x) = 2x + 3 and f(x) = 3x\(^2\) - 2x + 4
find f {g (-3)}.
Solve (\(\frac{1}{9}\))\(^{x + 2}\) = 243\(^{x - 2}\)
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 ( \(\frac{1}{2 - √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)