91Ó°ÊÓ

Graph the complex number and find its absolute value. $$-5-2 i$$

Solve the triangle, if possible. $$A=126.5^{\circ}, a=17.2, c=13.5$$

Solve the triangle, if possible. (triangle can't copy) $$C=28^{\circ} 43^{\prime}, a=6 \mathrm{mm}, b=9 \mathrm{mm}$$

The magnitudes of vectors u and v and the angle \(\theta\) between the vectors are given. Find the sum of \(\mathbf{u}+\mathbf{v} .\) Give the magnitude to the nearest tenth and give the direction by specifying to the nearest degree the angle that the resultant makes with \(\mathbf{u}\). $$|\mathbf{u}|=45,|\mathbf{v}|=35, \theta=90^{\circ}$$

The magnitudes of vectors u and v and the angle \(\theta\) between the vectors are given. Find the sum of \(\mathbf{u}+\mathbf{v} .\) Give the magnitude to the nearest tenth and give the direction by specifying to the nearest degree the angle that the resultant makes with \(\mathbf{u}\). $$|\mathbf{u}|=20, \quad|\mathbf{v}|=20, \theta=117^{\circ}$$

A new homeowner has a triangular-shaped back yard. Two of the three sides measure \(53 \mathrm{ft}\) and \(42 \mathrm{ft}\) and form an included angle of \(135^{\circ} .\) To determine the amount of fertilizer and grass seed to be purchased, the owner must know, or at least approximate, the area of the yard. Find the area of the yard to the nearest square foot.

Amusement Park Ride. A teacup ride for children at an amusement park consists of five teacups equally spaced around a circle. Each cup holds 6 passengers and is at the end of an arm \(20 \mathrm{ft}\) long. Find the linear distance between a pair of adjacent cups. Round the length to the nearest tenth of a foot.

Shark Pool. Feeding and observing sharks has become a popular attraction at water parks. The floor of a newly constructed shark pool in the shape of a parallelogram has sides that measure 38 ft and \(57 \mathrm{ft}\). To meet the minimum required length for the shortest diagonal, the angles must be \(80^{\circ}\) and \(100^{\circ} .\) Find the lengths of the diagonals of the pool. Round the lengths to the nearest foot.

Fish Attractor. Each year at Cedar Resort, discarded Christmas trees are collected and sunk in the lake to form a fish attractor. Visitors are told that it is \(253 \mathrm{ft}\) from the pier to the fish attractor and \(415 \mathrm{ft}\) to another pier across the lake. Using a compass, a fisherman finds that the attractor's azimuth (the direction measured as an angle from north) is \(340^{\circ}\) and that of the other pier is \(35^{\circ} .\) What is the distance between the fish attractor and the pier across the lake?

Classify the function as linear, quadratic, cubic, quartic, rational, exponential, logarithmic, or trigonometric. $$f(x)=-\frac{3}{4} x^{4}[4.1]$$