Differentiate \(\frac{x}{x + 1}\) with respect to x
\(\frac{1}{x + 1}\)
\(\frac{1}{(x + 1)^{2}}\)
\(\frac{1 - x}{x + 1}\)
\(\frac{1 - x}{(x + 1)^{2}}\)
Correct answer is B
\(y = \frac{x}{x + 1}\)
Using quotient rule because the function is of the form \(\frac{u(x)}{v(x)}\)
\(\frac{\mathrm d y}{\mathrm d x} = \frac{v\frac{\mathrm d u}{\mathrm d x} - u\frac{\mathrm d v}{\mathrm d x}}{v^{2}}\)
\(\frac{\mathrm d y}{\mathrm d x} = \frac{(x + 1) . 1 - x . 1}{(x + 1)^{2}}\)
= \(\frac{1}{(x + 1)^{2}}\)
3.0 seconds
4.5 seconds
5.0 seconds
9.0 seconds
Correct answer is A
\(s = ut + \frac{1}{2}gt^{2}\)
\(u = 0; s = 45m; g = 10ms^{-2}\)
\(45 = 0 + \frac{1}{2}(10)t^{2} = 5t^{2}\)
\(t^{2} = \frac{45}{5} = 9\)
\(t = 3.0s\)
\(0 < r \leq 1\)
\(-1 \leq r < 1\)
\(-1 < r \leq 0\)
\(-1 \leq r \leq 1\)
Correct answer is D
No explanation has been provided for this answer.
8.25
8.50
9.00
9.17
Correct answer is A
Mean \(\bar{x}\) = \(\frac{3 + 7 + 6 + 2 + 8 + 5 + 9 + 1 + 4 + 10}{10} \)
= \(\frac{55}{10} = 5.50\)
| \(x\) | 3 | 7 | 6 | 2 | 8 | 5 | 9 | 1 | 4 | 10 | Total |
| \(x - \bar{x}\) | -2.5 | 1.5 | 0.5 | -3.5 | 2.5 | -0.5 | 3.5 | -4.5 | -1.5 | 4.5 | |
| \((x - \bar{x})^{2}\) | 6.25 | 2.25 | 0.25 | 12.25 | 6.25 | 0.25 | 12.25 | 20.25 | 2.25 | 20.25 | 82.5 |
Variance = \(\frac{\sum (x - \bar{x})^{2}}{n}\)
= \(\frac{82.5}{10}\)
= 8.25
4.50
5.50
6.50
6.75
Correct answer is B
Mean \(\bar{x}\) = \(\frac{3 + 7 + 6 + 2 + 8 + 5 + 9 + 1 + 4 + 10}{10} \)
= \(\frac{55}{10} = 5.50\)