| Topic | Problem | Solution |
|---|---|---|
| None | Solve $\triangle A B C$ subject to the given cond… | We are given a triangle ABC with side lengths a, b and angle C. The given values are a=500, b=600, … |
| None | \( 7 x+19=11 x-89 \) | \(11x - 7x = 19 + 89\) |
| None | 3.1 Displacement, Velocity, and Acceleration A ca… | First, we need to find the position vector of the car after 2 seconds. We can do this by plugging i… |
| None | Use De Moivre's theorem to find the indicated pow… | Given the expression \(\left[4\left(\cos \frac{\pi}{36}+i \sin \frac{\pi}{36}\right)\right]^{6}\) |
| None | Given complex numbers $z_{1}$ and $z_{2}$, \[ z_{… | Given complex numbers $z_{1}$ and $z_{2}$, |
| None | Convert the complex number from polar form to rec… | Given the complex number in polar form is \(10\left(\cos \frac{5 \pi}{6}+i \sin \frac{5 \pi}{6}\rig… |
| None | Convert the complex number from polar form to rec… | Given the complex number in polar form is \(5.9\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\ri… |
| None | In order to estimate the height of a bridge over … | Let h(t) represent the height of the stone at time t. The equation for the height of the stone is g… |
| None | 19. A teacher records the amount of time it took … | Given the scores (x) and the time (y) as follows: x = [ 80, 75, 70, 90, 95, 100, 75, 60, 75, 95] an… |
| None | Current Attempt in Progress You step onto a hot b… | Given the distance of \(1.68\mathrm{~m}\) and the speed of \(190\mathrm{~m/s}\), we can use the for… |
| None | \( 4 x+8=60 \) | \(x = \frac{60 - 8}{4}\) |
| None | 30. The following data gives the retail price (pe… | Given the retail price and durability score for different types of laminate flooring, we are asked … |
| None | 43. A researcher in the field of sports biomechan… | The researcher has recorded the best 200m times for 12 high school track sprinters both before and … |
| None | Given $P(A)=0.51, P(B)=0.7$ and $P(A \cap B)=0.47… | Given \(P(A)=0.51\), \(P(B)=0.7\) and \(P(A \cap B)=0.477\), find the value of \(P(A \cup B)\), rou… |
| None | $t$ is inversely proportional to $w$. $t=9$ when … | Given that $t$ is inversely proportional to $w$, we can write the equation as $t = \frac{k}{w}$, wh… |
| None | Use synthetic division to rewrite the following f… | Given the fraction \(\frac{5 x^{5}-25 x^{4}+27 x^{3}-20 x^{2}-32 x}{x-4}\), we are asked to perform… |
| None | A shop normally sells hats for $£ 24.50$ each. Du… | Find the sale price of one hat: \(\frac{1}{2} \times £24.50 = £12.25\) |
| None | Consider the following polynomial function. \[ f(… | Consider the polynomial function \(f(x)=(x+2)(x-3)^{2}\). |
| None | \( 9 x-25=38 \) | \(9x - 25 = 38\) |
| None | $p$ is directly proportional to $t$. \[ p=48 \tex… | Given that p is directly proportional to t, we can write the equation as p = kt, where k is the con… |
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