| Topic | Problem | Solution |
|---|---|---|
| None | Differentiate. \[ y=\frac{\ln x}{x^{13}} \] \[ \f… | Given the function \(y = \frac{\ln x}{x^{13}}\). |
| None | Dilierentiate. \[ f(x)=x^{6} \ln 5 x \] \[ f^{\pr… | The given function is a product of two functions, \(x^6\) and \(\ln 5x\). To find the derivative of… |
| None | Differentiate the following function. \[ f(x)=x^{… | Given the function \(f(x)=x^{6} e^{4 x}\) |
| None | Differentiate. \[ f(x)=\ln \left(\frac{x^{3}-5}{x… | Given the function \(f(x)=\ln \left(\frac{x^{3}-5}{x}\right)\), we are asked to find its derivative. |
| None | 4. Right triangular pyramid \[ \begin{array}{l} V… | Given the volume formula for a right triangular pyramid: V = (1/3) * (1/2) * leg1 * leg2 * h |
| None | Differentiate. \[ F(x)=\frac{e^{5 x}}{x^{15}} \] … | Given the function \(F(x)=\frac{e^{5 x}}{x^{15}}\) |
| None | 5. Determine whether to reject or fail to reject … | Given the t-value is 2.35, degrees of freedom is 50, and significance level is 0.01 for a one-taile… |
| None | Consider a function $f$. The line $L_{1}$ with eq… | Find the slope of the tangent line $L_1$ at $x=2$ from its equation: $y=3x+1$. The slope is the coe… |
| None | A car rental agency charges $\$ 175$ per week plu… | Express the weekly cost to rent the car, $f$, as a function of the number of miles driven during th… |
| None | 6. Hugh estimates the volume of a cylindrical jar… | Given a cylindrical jar with diameter 4 in and height 5 in, first find the radius: \(r = \frac{d}{2… |
| None | 13) $(3 x+8)\left(4 x^{2}-4 x+7\right)$ | Expand the expression: \((3x + 8)(4x^2 - 4x + 7) = 3x(4x^2 - 4x + 7) + 8(4x^2 - 4x + 7)\) |
| None | 12) $(6 m-3)(4 m-5)$ | Expand the expression: \((6m-3)(4m-5) = 6m(4m) - 6m(5) - 3(4m) + 3(5)\) |
| None | 11) $(5 k-7)(3 k-3)$ | Expand the expression: \((3k - 3)(5k - 7)\) |
| None | Write down the type of each angle below. a) $198^… | Determine the type of each angle based on its degree measure: Acute angle (0-90 degrees), Right ang… |
| None | The distance from the Earth to the Sun is about \… | Set up a proportion:\(\frac{d_{Moon}}{100} = \frac{3.8 \times 10^5}{1.5 \times 10^8}\) |
| None | (a) Write $7 \times 7 \times 7 \times 7 \times 7$… | Write the expression as a power of 7: \(7 \times 7 \times 7 \times 7 \times 7 = 7^5\) |
| None | Perform the following calculation: \[ \left(7.85 … | The problem is asking for the density of a substance, given its mass and volume. The mass is given … |
| None | 8. Find the value of $\sin 72^{\circ}$ correct to… | Convert angle from degrees to radians: \(72^\circ = 72 \cdot \frac{\pi}{180} \approx 1.2566 \) radi… |
| None | 15. Which of the following is equal to $\left(\op… | Calculate the values of the trigonometric functions: \(\operatorname{cosec} 30^\circ = 2\), \(\cos … |
| None | 24. Using the law of cosine, which of the followi… | Use the law of cosine to find the measure of side c: \(c^{2} = a^{2} + b^{2} - 2ab(\cos C)\) |
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