Evaluate (int_{-1}^{0} (x+1)(x-2) mathrm{d}x)
Evaluate (int_{-1}^{0} (x+1)(x-2) mathrm{d}x) A. (frac{7}{6}) B. (frac{5}{6}) C. (frac{-5}{6}) D. (frac{-7}{6}) Correct Answer: Option D Explanation Expanding…
If (y = frac{1+x}{1-x}), find (frac{dy}{dx}).
If (y = frac{1+x}{1-x}), find (frac{dy}{dx}). A. (frac{2}{(1-x)^{2}}) B. (frac{-2}{(1-x)^{2}}) C. (frac{-1}{sqrt{1-x}}) D. (frac{1}{sqrt{1-x}}) Correct Answer: Option A…
Given that (f(x) = 5x^{2} – 4x + 3), find the coordinates of the point…
Given that (f(x) = 5x^{2} – 4x + 3), find the coordinates of the point where the gradient…
A circle with centre (4,5) passes through the y-intercept of the line 5x – 2y…
A circle with centre (4,5) passes through the y-intercept of the line 5x – 2y + 6 =…
Given that (sin x = frac{5}{13}) and (sin y = frac{8}{17}), where x and y…
Given that (sin x = frac{5}{13}) and (sin y = frac{8}{17}), where x and y are acute, find…
If (B = begin{pmatrix} 2 & 5 \ 1 & 3 end{pmatrix}), find (B^{-1}).
If (B = begin{pmatrix} 2 & 5 \ 1 & 3 end{pmatrix}), find (B^{-1}). A. (A = begin{pmatrix}…
(alpha) and (beta) are the roots of the equation (2x^{2} – 3x + 4 =…
(alpha) and (beta) are the roots of the equation (2x^{2} – 3x + 4 = 0). Find (alpha…
A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.
A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line. A. 2x-3y=2 B.…
Express cos150° in surd form.
Express cos150° in surd form. A. (-sqrt{3}) B. (-frac{sqrt{3}}{2}) C. (-frac{1}{2}) D. (frac{sqrt{2}}{2}) Correct Answer: Option B Explanation…
If (begin{pmatrix} 2 & 1 \ 4 & 3 end{pmatrix})(begin{pmatrix} 5 \ 4 end{pmatrix}) =…
If (begin{pmatrix} 2 & 1 \ 4 & 3 end{pmatrix})(begin{pmatrix} 5 \ 4 end{pmatrix}) = k(begin{pmatrix} 17.5 \…