| Topic | Problem | Solution |
|---|---|---|
| None | The line with equation $y=-2 x+c$ is tangent to t… | Rearrange the equation of the line: $y = -2x + c$ to get $-2x = y - c$ |
| None | Use the substitution $u=-x$ to evaluate $\int_{-2… | Let $u = -x$. Then, $x = -u$ and $d x = -d u$. Also, when $x = -2$, $u = 2$, and when $x = 2$, $u =… |
| None | If $I=\int e^{x} \cos ^{2} x d x$, find $I$ using… | Given the integral, \(I = \int e^x \cos^2 x dx\) |
| None | $200 \times 2$ | Multiply 200 by 2: \(200 \times 2\) |
| None | $17 \tan x>\sqrt{3}$ | Divide both sides of the inequality by 17: \(\tan x > \frac{\sqrt{3}}{17}\) |
| None | Convert the following decimal value to percent. \… | Convert the following decimal value to percent: \(0.0062\) |
| None | Convert the following percent value to decimal. \… | Convert the following percent value to decimal: \[75 \%\] |
| None | 14. $-3 x+y=4$ | Rearrange the equation to solve for y in terms of x: \( -3x + y = 4 \) |
| None | 6. Deux édifices, A et $B$, sont séparées par une… | Form two right triangles using the angles of depression and the distance between the buildings. |
| None | Exercise 12 1. In the diagram, the graphs of $y=x… | a) To solve the equation $x^2 - 2x - 3 = -2$, we can rewrite it as $x^2 - 2x - 1 = 0$ |
| None | Find the value of each trigonometric ratio. 5) $\… | \(\sin^2 Z + \cos^2 Z = 1\) |
| None | The function $f$ is given by $f(x)=\frac{1}{3} e^… | \(f(x) = \frac{1}{3} e^{-3x} + 1\) |
| None | Work out the value of $k$ if \[ k \times 3^{-2}=4… | Rewrite the equation as: \(k = \frac{4}{3^{-2}}\) |
| None | A right triangle has an angle that measures 34 an… | Given a right triangle with an angle of \(34^\circ\) and an adjacent side of \(17\), we want to fin… |
| None | 2. A parabola has zeros at 4 and 6 and passes thr… | Given that the parabola has zeros at 4 and 6, we can write its equation in factored form as: \(y = … |
| None | If $f(x)=\sin ^{-1}(x)$, then what is the value o… | Given the function $f(x) = \sin^{-1}(x)$, we need to find the derivative $f'(x)$ and then evaluate … |
| None | 1. Find the equation ( in factored form) of the q… | Given x-intercepts: x1 = -2, x2 = 4 and y-intercept: y = -5 |
| None | CRITICAL THINKING In the figure, $A B=12, B C=8$,… | Let the radius of the circle be \(r\). Since A is a point of tangency, AP is perpendicular to the t… |
| None | A prototype rocket takes off from a launchpad on … | \(v(t) = 0.5 e^t \sin\left(\frac{\pi t}{a}\right)\) |
| None | Guy invests $S c$ at the beginning of each quarte… | A_1 = A_0(1.01) + c(1.01) = 0(1.01) + c(1.01) = c(1.01) |
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