| Topic | Problem | Solution |
|---|---|---|
| None | 31. The three points $A, B$ and $C$ make a triang… | Given the coordinates of the three points A, B and C as A(-7,-8), B(-6,-13), and C(-31,-8). |
| None | Find the area of the shaded region. The area of t… | The area of the outer square is \(4^2 = 16\) square inches. |
| None | $8 \frac{2}{3}$ | SOLUTION: \(8 \frac{2}{3}\) |
| None | Consider the function $f(x)=5(x-4)^{2 / 3}$. For … | Consider the function \(f(x)=5(x-4)^{2 / 3}\). For this function there are two important intervals:… |
| None | Use linear approximation, i.e. the tangent line, … | Let's start by finding the derivative of the function \(f(x)=\sqrt[3]{x}\) at \(x=1\). This will gi… |
| None | Use linear approximation, i.e. the tangent line, … | Let's use linear approximation to solve the problem. We start by defining the function \(f(x)=\frac… |
| None | The concentration, C, of phenylbutazone, in micro… | The concentration, C, of phenylbutazone, in micrograms per milliliter $(\mu \mathrm{g} / \mathrm{mL… |
| None | Find the area of the region enclosed by $f(x)$ an… | The function is defined differently for \(x<3\) and \(x\geq3\), so we need to split the integral in… |
| None | Find the area under the graph of $f$ over the int… | The function is defined differently for \(x \leq 2\) and \(x > 2\), so we will need to split the in… |
| None | Consider the function $f(x)=3 x^{2}-6 x+9,0 \leq … | Consider the function \(f(x)=3 x^{2}-6 x+9\), for \(0 \leq x \leq 8\) |
| None | Let $f(x)=(6 \sin x+3 \cos x) \tan ^{-1} x$ | Let's consider the function \(f(x)=(6 \sin x+3 \cos x) \tan ^{-1} x\). |
| None | For the function $y=f(x)=5 x^{3}+4$ : a. Find $\f… | Find the derivative of the function \(f(x) = 5x^3 + 4\). The derivative of a constant is zero and t… |
| None | If $\sqrt{x}+\sqrt{y}=11$ and $y(4)=81$, find $y^… | We are given the equation \(\sqrt{x} + \sqrt{y} = 11\) and the value of y at x=4, which is 81. |
| None | 1. The monthly revenue, $\mathrm{R}(\mathrm{x})$,… | Let's denote the monthly revenue as \(R(x)\) and the monthly advertising expenses as \(x\). The rel… |
| None | Convert to a logarithmic equation. \[ e^{4}=t \] | Convert the given exponential equation to a logarithmic equation: \(e^4 = t\) |
| None | Solve the given system of equations. \[ \begin{ar… | Given the system of equations: \[\begin{array}{lr} 5 x+4 y-5 z= & -39 \\ 2 x-5 y+2 z= & 7 \\ 4 x-3 … |
| None | 5. Identify the identity matrix for the given mat… | Given the matrix \[\begin{bmatrix} -4 \\ 10 \\ 7 \end{bmatrix}\] |
| None | 14. What type of transformation occurs when the v… | The given matrix is a 2x2 matrix with -1 on the diagonal and 0 elsewhere. This is a special type of… |
| None | 10. On a separate sheet of paper, transform the v… | The problem is asking for the y-value of the terminal point of a vector after it has been transform… |
| None | 9. Perform the indicated operation: \[ \left[\beg… | Given two matrices A and B, where A = \(\left[\begin{array}{cc} 4 & 8 \\ -10 & -3 \end{array}\right… |
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