| Topic | Problem | Solution |
|---|---|---|
| None | The radius of a sphere is increasing at a rate of… | Given the rate of change of the radius (dr/dt) is 3 mm/s and the diameter is 40 mm, so the radius i… |
| None | The number of diagonals in a polygon, $d$, in ter… | Given the equation for the number of diagonals in terms of the number of sides: \(d=\frac{n(n-3)}{2… |
| None | 7. If $t_{3}=20$ and $t_{20}=122$ then the common… | Given the 3rd term (\(t_3\)) and the 20th term (\(t_{20}\)) of an arithmetic sequence, we can write… |
| None | center: $(-4,-5)$, area: $400 \pi$ | Given the area of the circle as \(400\pi\), we can use the formula for the area of a circle, \(A = … |
| None | Let $x$ and $y$ be real numbers and consider the … | Find the inner product of u and v: \(2*3 + x*(-4) + (-3)*(-y) = -5\) |
| None | A cylindrical tank with radius $7 \mathrm{~m}$ is… | Given the rate of volume increase $\frac{dV}{dt} = 4 \mathrm{~m}^3/\mathrm{min}$ and the radius of … |
| None | (1) If $f$ is a continuous function and $\lim _{x… | Find the value of f(1) given that \(\lim_{x \rightarrow 1}(3+f(x))=2\) |
| None | \#9. A $4 \mathrm{~m}$ ladder leans against a bui… | Use the Pythagorean theorem: \(4^2 = 1.3^2 + x^2\) |
| None | Here is a set of data. $\begin{array}{lllll}16 & … | Combine the two sets of data into one list: \(\{16, 46, 21, 5, 3, 3, 3, 16, 18, 46, 46, 46\}\) |
| None | Here are the masses, in grams, of some pencils. \… | Find the maximum and minimum values in the dataset: \(\text{data} = [13, 1, 4, 17, 49, 6, 3, 6, 35,… |
| None | In circle $S$ with $m \angle R S T=112^{\circ}$ a… | Find the base angle of triangle RST: \(\frac{180 - 112}{2} = 34^\circ\) |
| None | 20 Simplify each of the following. (a) $\frac{4 x… | Simplify expression (a): \(\frac{4 x^{2}}{18(x-3)^{2}} \times \frac{15(x-3)}{12 x^{4}}\) to \(\frac… |
| None | 21 Solve each of the following equations. (a) $4(… | (a) Distribute and combine like terms: \(4(x+1)-5(x+6)=3x+4\) becomes \(-x-26=3x+4\) |
| None | Two trains leave the station at the same time, on… | \(D = rt\) |
| None | Suppose we want to choose 2 letters, without repl… | \(a\) Calculate number of permutations: \(P(n,r) = \frac{n!}{(n-r)!}\) |
| None | The length of a rectangle is \( 3 \mathrm{~m} \) … | 1. Let width of rectangle be \( w \mathrm{~m} \), so length \( = (2w - 3) \mathrm{~m} \). |
| None | 5) Answer the question. lggy wants to purchase a … | Step 1: Find the price after instant rebate: \(15,690 - 3,500 = 12,190\) |
| None | If the column vector $\left[\begin{array}{l}-2 \\… | Given eigenvector \(v = \begin{bmatrix} -2 \\ -2 \end{bmatrix}\) and matrix \(A = \begin{bmatrix} a… |
| None | (1) Given: \( \begin{array}{l}p \vee q \\ r \righ… | 1. Apply Modus Tollens on second and third given expressions: \(\sim r \vee \sim \sim q \) |
| None | 6) Find the simple interest and balance for each … | \(I = P \times R \times T\) |
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