The points A(-3, -4) and C(5, 4) are the ends of the diagonal of a rhombus ABCD. (a) Find the equation of the diagonal BD. (b) Given that the side BC has gradient $\frac{5}{3}$, find the coordinates of B and hence of D.

A restaurant offers a choice of four appetizers, four-teen entrees, six desserts, and five beverages. How many different meals are possible if a diner intends to order only three courses? (Consider the beverage to be a “course.”)

Find P(X < 2Y) if

$$f_{X, Y}(x, y)=x+y$$

for X and Y each defined over the unit interval.

Brass waveguides are often silver plated to reduce losses. If the thickness of silver $\left(\mu=\mu_{\mathrm{o}}, \varepsilon=\varepsilon_{\mathrm{o}}, \sigma=6.1 \times 10^{7} \mathrm{S} / \mathrm{m}\right)$ must be $5 \delta$, find the minimum thickness required for a waveguide operating at 12 GHz.

The sum of the infinite geometric series $1+r+r^{2}+\ldots$ is k times the sum of the series $1-r+r^{2}-\ldots$, where k > 0. Express r in terms of k.

Will the CountKeywords program work if lines 33–34 are changed to Set keywordSet = new LinkedHashSet<>(Arrays.asList(keywordString));

What are $A_{\text {mid }}$ in $\mathrm{dB}, f_{H}, f_{L}$, and the BW in Hz for the amplifier described by $A_{v}(s) = \frac{4 \pi^{2} \times 10^{14} s^{2}}{(s+20 \pi)(s+50 \pi)\left(s+2 \pi \times 10^{5}\right)\left(s+2 \pi \times 10^{6}\right)}$ What type of amplifier is this?

Which energy source does not originate from the Sun? (a) coal (b) solar (c) oil (d) nuclear

Suppose a Normal model is useful for describing weights of the yearling Angus steers. Remember, the mean and standard deviation of the weights were 1152 lbs and 84 lbs. Which would be more unusual, a steer weighing 1000 pounds or one weighing 1250 pounds?

What does the following statement do? for ( ; ; ) { // Do something }

Find the natural domain and corresponding range of each of the following functions. (a) $f: x \mapsto x^{2}$ (b) $\mathbf{f}: x \mapsto \cos x^{\circ}$ (c) $f: x \mapsto \sqrt{x-3}$ (d) $\mathrm{f}: x \mapsto x^{2}+5$ (e) $\mathrm{f}: x \mapsto \frac{1}{\sqrt{x}}$ (f) $f: x \mapsto x(4-x)$ (g) $f: x \mapsto \sqrt{x(4-x)}$ (h) $\mathrm{f}: x \mapsto x^{2}+4 x+10$ (i) $f: x \mapsto(1-\sqrt{x-3})^{2}$

Choose the best answer. Which is used to reduce the impact of timber harvesting? (a) tree plantations (b) selective cutting (c) prescribed burns (d) mechanized logging

The heat flow vector $\mathbf{H}=k \nabla T$, where T is the temperature and k is the thermal conductivity. Show that if $T=50 \sin \frac{\pi x}{2} \cosh \frac{\pi y}{2}$ then $\nabla \cdot \mathbf{H}=0$.

Dharmesh has a square garden with a perimeter of 132 feet. Is the area of the garden greater than $1,000$ square feet??

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