| Topic | Problem | Solution |
|---|---|---|
| None | Find the area of the surface obtained by rotating… | The formula for the surface area of a curve $y=f(x)$, $a \leq x \leq b$, rotated about the y-axis i… |
| None | $\frac{x+\frac{1}{2}}{2+\frac{1}{x}}=$ | Given the complex fraction \(\frac{x+\frac{1}{2}}{2+\frac{1}{x}}\) |
| None | Evaluate the integral. \[ \int_{0}^{\pi / 6} 3 \s… | The integral of \(\sec^2(x)\) is \(\tan(x)\). Therefore, the integral of \(3\sec^2(x)\) is \(3\tan(… |
| None | A random sample of $\mathrm{n}$ measurements was … | Given that the sample size \(n = 200\), the sample mean \(\bar{x} = 101\), and the population varia… |
| None | Find $\frac{d y}{d r}$ for $y=\int_{0}^{r} \sqrt{… | Given the function \(y=\int_{0}^{r} \sqrt{11+12 t^{2}} d t\), we are asked to find \(\frac{d y}{d r… |
| None | Find the average value of the function $f(t)=(t-5… | The average value of a function \(f(t)\) on the interval \([a, b]\) is given by the formula: \[\fra… |
| None | Evaluate the integral. \[ \int_{-5}^{-4}\left(\fr… | Rewrite the integral by dividing each term in the numerator by \(y^{5}\). This results in two separ… |
| None | Find the real zeros of $\mathrm{f}$. Use the real… | The real zeros of a polynomial are the x-values for which the polynomial equals zero. These are als… |
| None | Express the equation in logarithmic form: (a) $4^… | Express the equation in logarithmic form: $4^{3}=64$ is equivalent to $\log A=B$. |
| None | Evaluate the integral. \[ \int 9 y^{4} \sqrt{1-9 … | Let's start by identifying a part of the integrand that could be a good choice for a u-substitution… |
| None | Evaluate the integral. \[ \int_{1}^{8}\left(\frac… | Separate the integral into two parts: \(\int_{1}^{8}\frac{6}{x} dx\) and \(\int_{1}^{8}-e^{-x} dx\). |
| None | 1. What is the derivative of $\cos ^{2} 3 x$ with… | We are given the function \(f = \cos^2(3x)\) and we are asked to find its derivative with respect t… |
| None | 2. (10 pts) For ten years, you deposit $\$ 700$ e… | Given that you deposit $700 every month for 10 years in an account paying 5.4% annual interest comp… |
| None | Match each improper fraction with its equivalent … | An improper fraction is a fraction whose numerator is greater than or equal to its denominator. We … |
| None | The piston diameter of a certain hand pump is 0.6… | The problem is asking to test the hypothesis that the standard deviation of the piston diameters ha… |
| None | Solve the following equation for $x$ : \[ 2^{-x}=… | We are given the equation \(2^{-x}=15\). |
| None | Condense the following expression by using the pr… | We are given the expression \(4 \log x+6 \log y-10 \log z^{2}\). |
| None | A statistics professor plans classes so carefully… | The problem is asking for the probability that a class period runs between 51.25 and 51.75 minutes.… |
| None | Find the area of the shaded region. The graph to … | The question is asking for the area under the curve of a normal distribution, which is equivalent t… |
| None | The waiting times between a subway departure sche… | The waiting times between a subway departure schedule and the arrival of a passenger are uniformly … |
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