| Topic | Problem | Solution |
|---|---|---|
| None | Assume that the weights of ripe watermelons grown… | The problem is asking for the number of watermelons that weigh less than 30.63 pounds. This is a pr… |
| None | Of all the numbers whose difference is 34 , find … | The problem is asking for two numbers whose difference is 34 and that have the minimum product. |
| None | The total sales, $S$, of a one-product firm are g… | The problem is a constrained optimization problem. We need to find the maximum value of the functio… |
| None | The temperature at a point on a metal plate is gi… | First, we need to find the partial derivatives of the function \(T(x, y)=\frac{x}{x^{2}+y^{2}}\) wi… |
| None | For the curve defined by \[ \vec{r}(t)=2 \cos (t)… | First, we need to find the derivative of the given vector function. The derivative of \(\vec{r}(t)\… |
| None | Find the length of the curve $\vec{r}(t)=\langle … | First, we need to find the derivative of the vector function \(\vec{r}(t)\). The derivative of \(\v… |
| None | A chemist has three different acid solutions. The… | Let's denote the amount of the $25\%$ solution as $x$, the amount of the $45\%$ solution as $y$, an… |
| None | Maria's Coffee Shop makes a blend that is a mixtu… | Let's denote the number of pounds of type A coffee as 'a' and the number of pounds of type B coffee… |
| None | 22. The angle of elevation to the top of a buildi… | The problem involves trigonometry. Specifically, it involves the tangent of the angle of elevation,… |
| None | The curve above is the graph of a sinusoidal func… | The given points $(-12,0)$ and $(2,0)$ are the x-intercepts of the sinusoidal function. The distanc… |
| None | Kaitlin takes classes at both Westside Community … | Kaitlin is taking classes at both Westside Community College and Pinewood Community College. At Wes… |
| None | Find the domain of the function. \[ h(x)=\sqrt{x-… | The domain of a function is the set of all possible input values (often the 'x' variable), which pr… |
| None | Two trains leave stations 288 miles apart at the … | Given that two trains leave stations 288 miles apart at the same time and travel toward each other.… |
| None | Let $f(x, y)=x^{2}-y^{3}-30 x y$ List the critica… | Define the function \(f(x, y)=x^{2}-y^{3}-30 x y\). |
| None | Solve the system of equations. If the system has … | The system of equations is a linear system. The second equation is a multiple of the first one. Thi… |
| None | If $\tan (\theta)=\frac{24}{7}, 0 \leq \theta \le… | We are given that \(\tan (\theta)=\frac{24}{7}\). We know that \(\tan (\theta)=\frac{\sin (\theta)}… |
| None | Find a plane containing the line $\bar{r}(t)=<3,-… | The given line can be represented in parametric form as: \(x = 3 + 7t\), \(y = -4 - 4t\), \(z = -3 … |
| None | Write an equation in slope-intercept form for the… | The slope-intercept form of a line is given by \(y = mx + b\), where \(m\) is the slope and \(b\) i… |
| None | You have the choice of receiving $\$ 80,000$ now … | We are given two options: receiving $80,000 now or receiving $38,000 now and another $56,000 six ye… |
| None | A company determines that its marginal cost, in d… | The company's marginal cost for producing x units of a product is given by \(C'(x) = 3200x^{-1.8}\)… |
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