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Solve: \(3^{2x-2} - 28(3^{x-2}) + 3 = 0\)
In how many ways can six persons be paired?
If Un = kn\(^2\) + pn, U\(_1\) = -1, U\(_5\) = 15, find the values of k and p.
A particle moving with a velocity of 5m/s accelerates at 2m/s\(^2\). Find the distance it covers in 4 seconds.
Given that P = {x: x is a multiple of 5}, Q = {x: x is a multiple of 3} and R = {x: x is an odd number} are subsets of μ = {x: 20 ≤ x ≤ 35}, (P⋃Q)∩R.
Find the coefficient of x\(^2\)in the binomial expansion of \((x + \frac{2}{x^2})^5\)
Evaluate \(4p_2 + 4C_2 - 4p_3\)
A linear transformation T is defined by T: (x,y) → (3x - y, x + 4y). Find the image of (2, -1) under T.
Given \(\begin{vmatrix} 2 & -3 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} -6 \\ k \end{vmatrix} \begin{vmatrix} 3 \\ -26 \end{vmatrix} = 15\). Solve for k.
Evaluate\({1_0^∫} x^2(x^3+2)^3\)
If \(x^2+y^2+-2x-6y+5 =0\), evaluate dy/dx when x=3 and y=2.
Given that \(\frac{8x+m}{x^2-3x-4} ≡ \frac{5}{x+1} + \frac{3}{x-4}\)
Differentiate \(\frac{5x^ 3+x^2}{x}\), x ≠ 0 with respect to x.
If 36, p,\(\frac{9}{4}\) and q are consecutive terms of an exponential sequence (G.P), find the sum of p and q.
Evaluate \(∫^0_{-1}\) (x + 1)(x - 2) dx
Which of the following is the semi-interquartile range of a distribution?
A straight line makes intercepts of -3 and 2 on the x and y axes respectively. Find the equation of the line.
Express \(\frac{4π}{2}\) radians in degrees.
The functions f:x → 2x\(^2\) + 3x -7 and g:x →5x\(^2\) + 7x - 6 are defined on the set of real numbers, R. Find the values of x for which 3f(x) = g(x).
Consider the following statement:
x: All wrestlers are strong
y: Some wresters are not weightlifters.
Which of the following is a valid conclusion?