Find the range of values of x for which \(\frac{(x+2)}{4}-\frac{2x-3}{3}<4\)
x > -6
x > -3
x < 8
x < 4
Correct answer is A
\(\frac{x + 2}{4} - \frac{2x - 3}{3} < 4\)
\(\frac{3(x + 2) - 4(2x - 3)}{12} < 4\)
\(3x + 6 - 8x + 12 < 48\)
\(18 - 5x < 48 \implies -5x < 48 - 18\)
\(-5x < 30 \implies x > -6\)
15 days
12 days
5 days
9 days
Correct answer is D
The time (t) to do the work is inversely proportional to the number of workers (n).
\(\implies t \propto \frac{1}{n}\)
\(t = \frac{k}{n}\)
\(5 = \frac{k}{45} \implies k = 45 \times 5 = 225\)
\(\therefore t = \frac{225}{n}\)
For 25 men, \(t = \frac{225}{25} = 9\)
\(\therefore\) 25 men will do the work in 9 days.
Solve for x in the equation x\(^3\) - 5x\(^2\) - x + 5 = 0
1, - 1, or 5
1, 1, or -5
-1, 1, or -5
1, 1, or 5
Correct answer is A
x\(^3\) - 5x\(^2\) - x + 5 = 0.
\(x^{2}(x - 5) - 1(x - 5) = 0\)
\((x^2 - 1)(x - 5) = 0 \implies (x - 1)(x + 1)(x - 5) = 0\)
\(\therefore x = 1, -1, 5\)
If \(y = x^2 - \frac{1}{x}\). find dy/dx
2x - (1/x2)
2x + x2
2x - x2
2x + (1/x2)
Correct answer is D
\(y = x^{2} - \frac{1}{x} = x^{2} - x^{-1}\)
\(\frac{\mathrm d y}{\mathrm d x} = 2x - (- x^{-2})\)
= \(2x + \frac{1}{x^{2}}\)
2π
5π
π
4π
Correct answer is A
Area of the circle (A) = \(\pi r^{2}\)
\(\frac{\mathrm d A}{\mathrm d r} = 2\pi r\)
\(\frac{\mathrm d A}{\mathrm d t} = \frac{\mathrm d A}{\mathrm d r} . \frac{\mathrm d r}{\mathrm d t}\)
\(\frac{\mathrm d A}{\mathrm d t} = 2\pi \times 5 \times 0.2 = 2\pi\)