| Topic | Problem | Solution |
|---|---|---|
| None | What is the radius of a sphere with a volume of $… | Given the volume of the sphere, \(V = 802 \mathrm{~m}^{3}\) |
| None | $5^{2 x}-(\sqrt{5}+25) \cdot 5^{x}+25 \sqrt{5}=0$ | Substitute $y = 5^x$ and rewrite the equation in terms of $y$: $y^2 - (sqrt{5} + 25)y + 25sqrt{5} =… |
| None | (2) $3 \frac{3}{4} \div 5=$ | Convert the mixed number $3 \frac{3}{4}$ to an improper fraction: $\frac{3 \times 4 + 3}{4} = \frac… |
| None | 9. Determine whether each equation models a linea… | \(h=3t\) can be written in the form \(y = mx + b\), with \(m = 3\) and \(b = 0\). Therefore, it is … |
| None | (a) If $f(x)=x^{4}+5 x$, find $f^{\prime}(x)$ \[ … | Given the function \(f(x) = x^4 + 5x\), we want to find its derivative \(f'(x)\). |
| None | Solve for a: \[ \sqrt{4+\sqrt{16+16 a}}+\sqrt{1+\… | Square both sides of the equation: \(\left(\sqrt{4+\sqrt{16+16a}}+\sqrt{1+\sqrt{1+a}}\right)^2 = 6^… |
| None | In $\triangle \mathrm{NOP}, p=490$ inches, $m \an… | Find angle P: \(180 - 57 - 55 = 68^\circ\) |
| None | What is the volume of a hemisphere with a diamete… | Given diameter = 4.4 ft, find the radius: \(r = \frac{d}{2} = \frac{4.4}{2} = 2.2\) ft |
| None | Find the volume of a pyramid with a square base, … | Find the side length of the square base: \(side\_length = \frac{perimeter}{4} = \frac{4.1}{4} = 1.0… |
| None | A rectangular prism has a length of $6 \mathrm{~c… | Find the volume of the rectangular prism: \(V = l \times w \times h\) |
| None | IV- (6 points) In an orthonormal system of axes( … | 1) A(2;0), B(0;4), E(-4;0) |
| None | Solve by using the percent proportion. 72 is what… | \(\frac{x}{100} = \frac{72}{500}\) |
| None | \( \frac{3}{5}+\frac{2}{8} \) | \( \text{lcm}(5, 8) = 40 \) |
| None | The attendance at a high school homecoming game w… | \text{Initial Attendance: }550 |
| None | If 3 is increased to 9 , the increase is what per… | \(\text{Increase} = 9 - 3 = 6\) |
| None | Use the percent formula \( A=P B, A \) is \( P \)… | A = PB |
| None | Use similar triangles to solve. A person who is 6… | We are given that a person who is 6 feet tall is standing 168 feet from the base of a tree, and the… |
| None | Solve the system by the addition method. \[ \begi… | We are given the system of equations: \[\begin{array}{c} x+3 y=9 \\ 3 x+2 y=-1 \end{array}\] |
| None | to calculate a seller's rating, \( R \), based on… | \( R = \frac{F}{F + N} \) |
| None | \( D \) is the portion of the solid cone \( z=\sq… | \(\nabla \cdot \mathbf{F} = 2y^{2} + \frac{21}{16}x^{2} \) |
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