| Topic | Problem | Solution |
|---|---|---|
| None | What is the average rate of change of $f(x)$ from… | Given the function \(f(x)=\sqrt{-7 x+2}\), we are asked to find the average rate of change from \(x… |
| None | What is the average rate of change of $f(x)$ from… | Given the function \(f(x)=-2 x-5\), we are asked to find the average rate of change from \(x_{1}=-9… |
| None | A note card company has found that the marginal c… | The total cost of producing $x$ cards is the integral of the marginal cost function from 0 to $x$. … |
| None | The rate at which a machine operator's efficiency… | The given equation is a differential equation. To find \(E(t)\), we need to integrate the given equ… |
| None | Find $M_{n}$ to three decimal places for the defi… | We are given a definite integral \(\int_{2}^{4} \frac{2}{x} dx\) and we are asked to find the Midpo… |
| None | The rates of change in population for two cities … | The population model for Alphaville is \(P(t)=45t+5000\). |
| None | $\lim _{x \rightarrow-\infty} \frac{\sqrt{x^{2}+2… | A questão está pedindo o limite de uma função à medida que x se aproxima do infinito negativo. Isso… |
| None | The shape of a wall in a museum is shown to the r… | The question is asking for the best approximation for the area of the wall. The area of the wall ca… |
| None | Use logarithmic differentiation to find $y^{\prim… | Given the function \(y = \frac{\sqrt{7 - 5x}(x^{2} + 1)^{2}}{x^{2} + 5x + 7}\) |
| None | $y=15 \sqrt[25]{2 x^{-1}}$ | Rewrite the equation using exponents: $y = 15(2x^{-1})^{0.04}$ |
| None | Of all numbers that add to 54 , find the pair tha… | The problem is asking to find two numbers that add up to 54 and have the maximum product. This is a… |
| None | A bakery works out a demand function for its choc… | The price elasticity of demand is a measure of the responsiveness of the quantity demanded to a cha… |
| None | Suppose that $y$ is proportional to the $4^{\text… | The problem states that \(y\) is proportional to the \(4^{\text{th}}\) power of \(x\). This means t… |
| None | Pierce Manufacturing determines that the daily re… | Substitute $x=80$ into the revenue function $R(x)=0.007 x^{3}+0.03 x^{2}+0.3 x$ to find the current… |
| None | The average cost for a company to produce $x$ uni… | The average cost for a company to produce \(x\) units of a product is given by the function \(A(x)=… |
| None | Assume that $C(x)$ is in dollars and $x$ is the n… | Given the total-cost function $C(x)=0.01 x^{2}+0.6 x+40$, we are asked to find the change in cost (… |
| None | Pierce Manufacturing determines that the daily re… | The revenue function, R(x), is given by \(R(x)=0.006 x^{3}+0.04 x^{2}+0.3 x\). This function gives … |
| None | A preformed piece of coal weighs $100 \mathrm{~g}… | Find the minimum and maximum weight of each piece of coal: \(min = 95g\), \(max = 105g\) |
| None | Find a formula for the $n$th term of the sequence… | The sequence is a nested radical sequence. The first term is \(\sqrt{6}\), the second term is \(\sq… |
| None | The largest fish Mandy caught last year weighed $… | Find the upper limit of the range that would round to 11 kg: \(11 + 0.5 = 11.5\) |
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