| Topic | Problem | Solution |
|---|---|---|
| None | Solve the system by the addition method. \[ \begi… | Given the system of equations: \[\begin{array}{l} 3 x=4 y+5 \\ 6 x=-1-5 y \end{array}\] |
| None | a. In 2000 , the population of a country was appr… | We are given that the population in 2000 (t=0) is 6.44 million, so \(A_{0} = 6.44\). We are also gi… |
| None | If $f(x)=3+\frac{6}{x}+\frac{2}{x^{2}}$, find $f^… | Given the function \(f(x) = 3 + \frac{6}{x} + \frac{2}{x^{2}}\) |
| None | Graph the function. \[ f(x)=2 \sqrt{x+4} \] Plot … | First, understand the function \(f(x)=2 \sqrt{x+4}\). This is a square root function that has been … |
| None | Given $h(x)=-5 x-1$, solve for $x$ when $h(x)=-6$. | We are given the function \(h(x)=-5 x-1\) and we are asked to solve for \(x\) when \(h(x)=-6\). Thi… |
| None | 2. Let $Q_{1}$ be the mean of $x, Q_{2}$ the samp… | Given the sequences x and y as follows: \[x: -48, -52, -89, 35, -18, -62, -96, -47, 84, -93, 98, 38… |
| None | Find a function $f(x)$ such that $f^{\prime}(x)=9… | Given that $f^{\prime}(x)=9 e^{x}-9 x$, we can integrate both sides with respect to $x$ to find $f(… |
| None | Find all points where the function has any relati… | First, we need to find the first order partial derivatives of the function. The partial derivative … |
| None | a. $\frac{-5}{6}+\frac{3}{6}=$ | Given the fractions \(-\frac{5}{6}\) and \(\frac{3}{6}\), we are asked to find their sum. |
| None | The surface area of a human (in square meters) ha… | Given the surface area of a human is approximated by \(A=0.024265 h^{0.3964} m^{0.5378}\), where \(… |
| None | Find $f_{x}(x, y)$ and $f_{y}(x, y)$. Then find $… | First, we need to find the partial derivatives $f_{x}(x, y)$ and $f_{y}(x, y)$ of the function $f(x… |
| None | Perform the indicated operation and simplify your… | Given the fractions \(\frac{11}{12}\) and \(\frac{5}{12}\), we are asked to subtract the second fra… |
| None | Solve the logarithmic equation. Be sure to reject… | Given the logarithmic equation \(7 \ln (3 x)=14\). |
| None | Solve the following exponential equation. Express… | Given the exponential equation \(e^{1-5x} = 2881\). |
| None | Find the compound amound for the deposit and the … | Given that the principal amount (P) is $318,000, the annual interest rate (r) is 5% or 0.05 in deci… |
| None | Use trigonometric identities and \&Agebraic metho… | The given equation is \(\sec ^{2}(x)+5=7\). Subtract 5 from both sides of the equation to isolate \… |
| None | Using a double-angle or half-angle formula to sim… | The double angle formula for cosine is \(\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)\). This me… |
| None | Consider the function $f(x)=3 x^{2}-6 x-1$ a. Det… | The given function is a quadratic function of the form \(f(x) = ax^2 + bx + c\). For such functions… |
| None | A microwaveable cup-of-soup package needs to be c… | Given that the volume of the soup the cylinder must hold is fixed at 250 cubic centimeters, we can … |
| None | $\lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}$ | This is a limit problem. The function is not defined at x=5, but we can simplify the function by fa… |
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