| Topic | Problem | Solution |
|---|---|---|
| None | If $f(x)=\frac{-3 x^{5}+7 x^{4}-7 x^{3}}{x^{4}}$,… | We are given the function \(f(x)=\frac{-3 x^{5}+7 x^{4}-7 x^{3}}{x^{4}}\) and asked to find its der… |
| None | Find all $x$-intercepts and $y$-intercepts of the… | Set the function equal to zero to find the x-intercepts: \(2x^3 - 2x^2 - 84x = 0\). |
| None | $\left\{\begin{array}{c}2 x+y+3 z=13 \\ x+2 y=11 … | We are given the system of linear equations: \[\begin{cases} 2x + y + 3z = 13 \\ x + 2y = 11 \\ 3x … |
| None | Solve the following exponential equation by expre… | Express both sides of the equation as powers of the same base. We know that 5 and 125 can both be e… |
| None | \[ \begin{array}{l} A=\left[\begin{array}{rrr} 2 … | First, we need to find the column space of matrix A, which is denoted as \(W = Col(A)\). The column… |
| None | In a certain country, the true probability of a b… | We are given that the probability of a baby being a girl in a certain country is 0.484. We are aske… |
| None | Find the probability that when a couple has three… | Given that the probability of having a boy or a girl is \(\frac{1}{2}\). |
| None | $\begin{array}{r}5 \\ +\quad 16\end{array}$ | Add 5 and 16 together: \(5 + 16\) |
| None | Does the point \( (-9,0) \) satisfy the equation … | Substitute \((-9,0)\) into equation: \( 0=4(-9)-9 \) |
| None | The population of a town with a 2016 population o… | Given that the population grows at a rate of 2.6% per year, this is equivalent to a growth factor o… |
| None | A certain drug is eliminated from the bloodstream… | The half-life of a substance undergoing exponential decay can be used to determine the decay consta… |
| None | the state in 2035 Let $y(t)$ be the population of… | Let \(y(t)\) be the population of the state, in millions, \(t\) years after the year 2000. The expo… |
| None | Assume that the amounts of weight that male colle… | First, we need to standardize the weights by subtracting the mean and dividing by the standard devi… |
| None | Write two numbers that multiply to the value on t… | Let's denote the two numbers as \(x\) and \(y\). According to the problem, we have two equations: \… |
| None | Find the relative rate of change of $f(x)$ at the… | Given the function \(f(x) = 282 - 3x\), we first need to find the derivative of the function. |
| None | Find the relative rate of change of $f(x)=21+3 e^… | Given the function \(f(x)=21+3 e^{-3 x}\), we are asked to find the relative rate of change. |
| None | 2. $\left(\S 3.5,5\right.$ pts each) Find the der… | First, we need to understand the problem. We are asked to find the derivative of the given equation… |
| None | Find the accumulated value of an investment of $\… | Given an initial investment (P) of $2000, an annual interest rate (r) of 10% or 0.10, the number of… |
| None | Solve the Cauchy-Euler equation. \[ x^{2} \frac{d… | Let y(x) = x^m, then \(y'(x) = m x^{m-1}\) and \(y''(x) = m(m-1)x^{m-2}\) |
| None | Assume that $x=x(t)$ and $y=y(t)$. Let $y=x^{3}+6… | Given that \(y=x^{3}+6\) and \(\frac{d x}{d t}=2\) when \(x=1\). |
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