| Topic | Problem | Solution |
|---|---|---|
| None | Solve $\frac{8}{x+3}+\frac{3}{x+8}=1$ | \(\frac{8}{x+3} + \frac{3}{x+8} = 1\) |
| None | Use derivatives to find the critical points and i… | First, find the first and second derivatives of the function \(f(x) = x^5 - 10x^3 - 12\): |
| None | If $f(x)=4 x-3$, find the following value. \[ \fr… | Find the values of f(9), f(7), and f(3) using the given function f(x) = 4x - 3: |
| None | $y=(x+3)^{2}+2$ | \(y = (x+3)^2 + 2\) |
| None | Find an equation of the tangent line to the graph… | Find the derivative of the function using the chain rule: \(\frac{dy}{dx} = -2xe^{-x^2}\) |
| None | The point $P(-4,9)$ lies on the terminal arm of a… | Given point P(-4, 9), we need to find the exact value of cos(θ) using the formula cos(θ) = x / r, w… |
| None | $\frac{11 x^{2}}{10}-\frac{3 x}{5}=\frac{x}{2}$ | Move all terms to one side of the equation to get a quadratic equation in the form of $ax^2 + bx + … |
| None | Five hundred consumers are surveyed about a new b… | Find the probabilities P(A and B) and P(B) from the given table: |
| None | Find the prime factorization of 156. | Find the prime factorization of 156. |
| None | Write the fraction as a percent. Write the percen… | Convert the fraction to a decimal: \(\frac{1}{8} = 0.125\) |
| None | Find $\nabla f$ at the given point. \[ f(x, y, z)… | Find the partial derivatives of the function: \(f(x, y, z) = x^{3} + y^{3} - 4z^{2} + z \ln x\) |
| None | 4. Write the transformed equation if $f(x)=x^{2}$… | f(x) = x^2 |
| None | 6. The observation deck of the Skylon Tower in Ni… | Let T be the position of the tourist, A be the position of boat A, and B be the position of boat B. |
| None | Find the equation of the parabola $f(x)=a x^{2}+b… | Plug in the given points into the equation to create a system of linear equations: |
| None | $5 \frac{1}{4}-2 \frac{5}{16}$ | Convert the mixed numbers to improper fractions: $5 \frac{1}{4} = \frac{21}{4}$ and $2 \frac{5}{16}… |
| None | $2 \frac{3}{8}$ as an improper fraction | Convert the mixed number to an improper fraction by multiplying the whole number by the denominator… |
| None | $F(x)=3 \cdot \cos 2=\frac{\pi}{3}$ | \(F(x) = 3 \cdot \cos 2x = \frac{\pi}{3}\) |
| None | 2. If $p=\frac{q^{2}}{\pi}, q=3 \cos (r)+\sin (r)… | First, substitute the expression for r into the expression for q: \(q = 3 \cos (\ln (s^\pi)) + \sin… |
| None | $4 \times 4$ | \(4 \times 4\) |
| None | $\begin{array}{c}y=\frac{3}{2} x+3 \\ x=-4\end{ar… | Substitute x = -4 into the equation y = \(\frac{3}{2}\)x + 3 |
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