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Distance and Bearing of a Ship A ship leaves port on a bearing of $34.0^{\circ}$ and travels $10.4 \mathrm{mi} .$ The ship then turns due east and travels $4.6 \mathrm{mi}$. How far is the ship from port, and what is its bearing from port?

Distance and Bearing of a Ship A ship leaves port on a bearing of $34.0^{\circ}$ and travels $10.4 \mathrm{mi} .$ The ship then turns due east and travels $4.6 \mathrm{mi}$. How far is the ship from port, and what is its bearing from port?

Precalculus Student Solutions Manual 5th

Applications of Trigonometry

Applications of Vectors
Solve each problem. See Examples $1-4$. A person in a plane flying straight north observes a mountain at a bearing of $24.1^{\circ} .$ At that time, the plane is $7.92 \mathrm{km}$ from the mountain. A short time later, the bearing to the mountain becomes $32.7^{\circ} .$ How far is the airplane from the mountain when the second bearing is taken?

Solve each problem. See Examples $1-4$. A person in a plane flying straight north observes a mountain at a bearing of $24.1^{\circ} .$ At that time, the plane is $7.92 \mathrm{km}$ from the mountain. A short time later, the bearing to the mountain becomes $32.7^{\circ} .$ How far is the airplane from the mountain when the second bearing is taken?

Precalculus

Applications of Trigonometry

The Law of Cosines
Given three noncollinear points, we can find an equation of the form.$$x=a y^{2}+b y+c$$ of the horizontal parabola joining them by solving a system of equations. Work Exercises $59-62$ in order, to find the equation of the horizontal parabola containing the points$$(-5,1), \quad(-14,-2), \quad \text { and } \quad(-10,2)$$. Does the horizontal parabola open to the left or to the right? Why?

Given three noncollinear points, we can find an equation of the form.$$x=a y^{2}+b y+c$$ of the horizontal parabola joining them by solving a system of equations. Work Exercises $59-62$ in order, to find the equation of the horizontal parabola containing the points$$(-5,1), \quad(-14,-2), \quad \text { and } \quad(-10,2)$$. Does the horizontal parabola open to the left or to the right? Why?

Precalculus

Analytic Geometry

Parabolas

Given three noncollinear points, we can find an equation of the form.$$x=a y^{2}+b y+c$$ of the horizontal parabola joining them by solving a system of equations. Work Exercises $59-62$ in order, to find the equation of the horizontal parabola containing the points$$(-5,1), \quad(-14,-2), \quad \text { and } \quad(-10,2)$$. Write the equation of the horizontal parabola.

Given three noncollinear points, we can find an equation of the form.$$x=a y^{2}+b y+c$$ of the horizontal parabola joining them by solving a system of equations. Work Exercises $59-62$ in order, to find the equation of the horizontal parabola containing the points$$(-5,1), \quad(-14,-2), \quad \text { and } \quad(-10,2)$$. Write the equation of the horizontal parabola.

Precalculus

Analytic Geometry

Parabolas

Questions asked

INSTANT ANSWER

A piece of artillery at G is to fire at an invisible target T. An observer at B can see both G and T; with instruments he measures BT, BG and their azimuths. BG = 2080 yards, azimuth = 38 deg 20 mins, BT = 5380 yards, azimuth = 285 deg 50 min. Find the azimuth of T from G.

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Danielle Fairburn verified

Numerade educator

A manufacturer can sell “X” items per week at a price P = 300 - 0.015 X centavos and that it costs Y = 75 x + 30,000 centavos to produce the “X” items. (a) What is the production level for maximum profits?

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ANSWERED

Ivan Kochetkov verified

Numerade educator

If the natural length of a helical spring is 10 inches, and if it takes a force of 3 pounds to keep it extended 2 inches, find the work done in stretching the spring from its natural length to a length of 15 inches.

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ANSWERED

Ivan Kochetkov verified

Numerade educator

It is desired to make an open top can from a square piece of 0.025 aluminum sheet whose side is “a”, by cutting equal squares out of the corners and then folding up the aluminum sheet to form the slides. (a) What should be the length of a side of the squares cut out? (b) What is the maximum volume?

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Daniel Carr verified

Numerade educator

An aircraft navigator observes the angle of depression of a geographical landmark directly below the aircraft’s line of flight to be 35°. A minute later, its angle of depression is 50°. If the aircraft is flying straight and level at the rate of 240 kph, solve for: a. the altitude at which he is flying. b. the aircraft’s horizontal distance from the geographic landmark at the first point of observation.

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Willis James verified

Numerade educator

A point moves such that the difference between the slopes of the line joining it to the origin and the line joining points (2, 5) and (1, -3) is always 1. Solve for the equation of the locus.

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ANSWERED

Ivan Kochetkov verified

Numerade educator

The passenger airplanes leave an airport, one flying due North and the other flying due south. Both are flying at the same altitude of 10,000 feet. After 9 hours of flight, they are 3,500 miles apart. If one airplane travels 48 kilometers per hour faster than the other, find the velocity of each in kilometers per hour.

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Sheryl Ezze verified

Numerade educator

A tank is a right circular cylinder 3 ft. in radius and 8 ft. tall. It is standing upright on one end and has 5 ft. of water in it. How much work is required to lift the water to a point that is 1 ft. above the tank? Weight of the water is 62.5 lb. per cu. ft.

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ANSWERED

Ivan Kochetkov verified

Numerade educator

A sling shot is used to throw a piece of stone with a velocity of 160 ft./sec. in a direction 45 degrees above the horizontal. Find how far away the stone strikes the ground and its greatest height.

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ANSWERED

Brandy Heflin verified

Numerade educator

A small experimental rocket is launched vertically at the rate of 50 m/sec. by an observer on the ground 100 meters away. How fast is the rocket receding from the observer after 5 seconds?

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