| Topic | Problem | Solution |
|---|---|---|
| None | Find $\frac{d y}{d x}$ \[ e^{4 x}=\sin (x+2 y) \] | Differentiate both sides of the equation with respect to x. The derivative of \(e^{4x}\) with respe… |
| None | Evaluate the function at the given value of the v… | To find the value of the function at a specific point, we need to substitute the given value into t… |
| None | Find the area under the graph of $f$ over the int… | The function is defined piecewise, so we need to split the interval into two parts: [1,2] and (2,3]. |
| None | a. A rectangular pen is built with one side again… | Let the sides perpendicular to the barn be of length \(x\). Notice that there are a total of \(100\… |
| None | Find the second derivative of the function. 6) $s… | Given the function \(s=\frac{t^{8}+9 t+8}{t^{2}}\), we are asked to find the second derivative. |
| None | Find an equation for the tangent to the curve at … | Given the function \(f(x) = 10 \sqrt{x} - x + 7\) and the point \((100,7)\). |
| None | Find dy/dt. 3) $y=t^{4}\left(t^{5}+3\right)^{4}$ | We are given the function \(y=t^{4}(t^{5}+3)^{4}\) and we are asked to find \(\frac{dy}{dt}\). |
| None | Solve the following system by the substitution me… | First, we can express \(x\) in terms of \(y\) from the first equation: \(x = 3 - y\). |
| None | Most railroad cars are owned by individual railro… | We can model the situation as a Markov Chain with two states: 'Home' and 'Pool'. Each month, 7% of … |
| None | A 6000 -seat theater has tickets for sale at $\$ … | Let's denote the number of tickets sold at $28 as x and the number of tickets sold at $40 as y. We … |
| None | Solve the system of equations by the substitution… | The system of equations is given by: \(x = 3y + 3\) and \(x = 8y - 7\). |
| None | The functions $u$ and $w$ are defined as follows.… | Define the functions \(u(x) = -x - 1\) and \(w(x) = x^2 + 2\) |
| None | QUESTION 1 Quadratic Equation Choose one $\cdot 5… | Given the quadratic equation \(x^{2}+4 x-5=0\) |
| None | The cost function for a certain commodity is \[ C… | Given the cost function \(C(q)=88+0.19 q-0.007 q^{2}+0.0008 q^{3}\) |
| None | Graphs of the velocity functions of two particles… | Given the velocity function of a particle, we need to find when the particle is speeding up or slow… |
| None | Express the following number in scientific notati… | The given number is \(850 imes 10^{6}\). |
| None | Find the greatest common divisor of the numbers. … | First, we need to find the prime factorization of both numbers. For 105, we have \(105 = 3^1 \cdot … |
| None | $2 \sqrt{x}-14=\frac{288}{\sqrt{x}}$ | Given the equation \(2 \sqrt{x}-14=\frac{288}{\sqrt{x}}\) |
| None | Find the greatest common divisor of 66 and 30 . T… | Define the problem: Find the greatest common divisor of 66 and 30. |
| None | If a single card is drawn from a standard 52-card… | A standard deck of 52 cards contains 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13… |
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