| Topic | Problem | Solution |
|---|---|---|
| None | Find the inverse, if it exists, for the given mat… | We are given the matrix A = \(\begin{bmatrix} -3 & -1 \\ -2 & -1 \end{bmatrix}\) |
| None | Suppose that the functions $u$ and $w$ are define… | Define the functions $u$ and $w$ as $u(x)=x^{2}+1$ and $w(x)=\sqrt{x+6}$ respectively. |
| None | $3+3 \times 3-3+3=$ | First, we need to follow the order of operations (PEMDAS/BODMAS) to solve this expression. So, we'l… |
| None | Solve the proportion. \[ \frac{99}{v}=\frac{11}{2… | Cross-multiply: \(99 \times 2 = v \times 11\) |
| None | Use the simplex method to solve the following lin… | The problem is a linear programming problem and can be solved using the simplex method. The simplex… |
| None | Write an equation that expresses the following re… | The question is asking for an equation that expresses a relationship where $p$ varies directly with… |
| None | The equation of a line is given below. \[ -x+4 y=… | The equation of the line is given by \(-x+4y=8\). |
| None | Suppose that the weight (in pounds) of an airplan… | Let's denote the weight of the airplane as \(y\) and the amount of fuel as \(x\). The relationship … |
| None | Find the position vector for a particle with acce… | Given the acceleration vector \(\vec{a}(t)=\langle 3 t, 4 \sin (t), \cos (5 t)\rangle\), the initia… |
| None | In 2004 , an art collector paid $\$ 84,053,000$ f… | Given that the initial value of the painting in 1950, denoted as \(P_0\), is $30,000, the value of … |
| None | An investment of $\$ 4000.05$ earns interest at 2… | Given that the principal amount (P) is $4000.05, the annual interest rate for the first 3 years (r1… |
| None | A $\$ 5222.39$ investment matures in 5 years, 10 … | Given that the principal amount (P) is $5222.39, the annual interest rate (r) is 2.8\%, the number … |
| None | Show that the limit that follows does not exist b… | Given the function \(f = \frac{x^{2}y}{x^{4} + y^{2}}\), we are asked to show that the limit as (x,… |
| None | If $f(x)=8 x-7$ for $x \leq 3$ and $f(x)=4 g(x)$ … | Split the integral of \(f(x)\) from 0 to 15 into two integrals: from 0 to 3 and from 3 to 15. |
| None | Study the pattern in these examples. \[ \begin{ar… | Observe the given equations: \(a^{2} \# a^{5}=a^{12}\), \(a^{6} \# a^{4}=a^{26}\), and \(a^{5} \# a… |
| None | A circle is drawn with 9 points on its circumfere… | A circle is drawn with 9 points on its circumference. A student creates polygons with 3 or more sid… |
| None | Which of the following statements is true? A. If … | Analyze each option: |
| None | Mary is going to rent a truck for one day. There … | Mary is considering renting a truck for one day from either Company A or Company B. Company A charg… |
| None | What is the value of $x$ in $\left(4^{x}\right)^{… | Given the equation: \(\left(4^{x}\right)^{3}=4^{36}\) |
| None | the minimum and maximum values of the objective f… | First, we need to graph the constraints to find the feasible region. The constraints are \(x \geq 0… |
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