| Topic | Problem | Solution |
|---|---|---|
| None | Determine if $(3,-6,2)$ is a solution of the syst… | Substitute the values of the ordered triple $(3,-6,2)$ into the system of equations. |
| None | Solve the system. \[ \begin{array}{rr} -5 x-y= & … | Write the system of equations in matrix form. The matrix A is \[\begin{bmatrix} -5 & -1 & 0 \\ 0 & … |
| None | The first set of scales shows the mass of an empt… | Let the weight of the empty bowl be \(b\) grams and the weight of the sugar be \(s\) grams. |
| None | A spherical snowball is melting in such a way tha… | The volume of a sphere is given by the formula \(V = \frac{4}{3}\pi r^3\). |
| None | Let $A$ be the area of a circle with radius $r$. … | First, we know that the area of a circle is given by the formula \(A = \pi r^2\). |
| None | Question 2. Applications of Trig Substitution: An… | Given the equation of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\), we want to find th… |
| None | Find $f^{\prime \prime}(x)$ \[ f(x)=\left(x^{2}+8… | Given the function \(f(x)=(x^{2}+8)^{5}\), we are asked to find the second derivative \(f''(x)\). |
| None | a) $5 x+2 y=21$ | We are given the linear equation \(5x + 2y = 21\). |
| None | Alonso brings $\$ 21$ to the market to buy eggs a… | Alonso brings $21 to the market to buy eggs and avocados. He gets eggs that cost $2.50. Then, he no… |
| None | $\left\{\begin{array}{l}2 x+3 y=13 \\ 3 x-5 y=10\… | We are given the system of equations: \[\begin{cases} 2x + 3y = 13 \ 3x - 5y = 10 \end{cases}\] |
| None | Write an equation in vertex form of the parabola … | The vertex form of a parabola is given by \(f(x) = a(x-h)^2 + k\), where \((h,k)\) is the vertex of… |
| None | A electronic store lists an article for $\$ 978$ … | Calculate the final price of the article at the electronic store after applying all the discounts: … |
| None | Company A pays $\$ 25,000$ yearly with raises of … | \(\text{Company A's salary in year 10} = 25000 + 1600 \times (10 - 1) = 25000 + 1600 \times 9 = 250… |
| None | $x^{2}+6 x-5=0$ | Solve the quadratic equation $x^{2}+6 x-5=0$ using the quadratic formula: $x = \frac{-b \pm \sqrt{b… |
| None | Write the equation in standard form for the circl… | Write the equation in standard form: \((x - 0)^2 + (y + 9)^2 = 6^2\) |
| None | 41. A piece of wood burns completely in $1 \mathr… | Given that a piece of wood burns completely in 1 second at \(600^\circ\mathrm{C}\), and the time it… |
| None | Laila went for a $10 \mathrm{~km}$ run. She ran t… | Laila ran the first 5 km in 30 minutes, rested for 25 minutes, and then ran the remaining 5 km in 3… |
| None | Tobias is scared that the banks will close on him… | Tobias has \(\$4,300\) in frozen cash. |
| None | $x^{2}-3 x-5=0$ | Given the quadratic equation \(x^2 - 3x - 5 = 0\), we can use the quadratic formula to find the roo… |
| None | A rectangle is constructed with its base on the d… | Let the length of the rectangle be x and the width be y. The base of the rectangle is on the diamet… |
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