Chapter 22

Find the angle of inclination, in decimal degrees to three significant digits, of a line passing through the given points. (6,3) and (-1,5)

What force would be needed to stretch a spring \((k=14.5 \mathrm{lb} / \mathrm{in.})\) from an unstretched length of 8.50 in. to a length of 12.50 in.?

Find the angle of inclination, in decimal degrees to three significant digits, of a line passing through the given points. \((x, 3)\) and \((x+5,8)\)

When a body moves with constant acceleration \(a\) (such as in free fall), its velocity \(v\) at any time \(t\) is given by \(v=v_{0}+a t,\) where \(v_{0}\) is the initial velocity. Note that this is the equation of a straight line. If a body has a constant acceleration of \(2.15 \mathrm{m} / \mathrm{s}^{2}\) and has a velocity of \(21.8 \mathrm{m} / \mathrm{s}\) at \(5.25 \mathrm{s}\), find (a) the initial velocity and (b) the velocity at \(25.0 \mathrm{s}\)

Slopes of Parallel and Perpendicular Lines Find the slopes of the lines parallel to, and perpendicular to, each line with the given slope. $$m=5$$

Slopes of Parallel and Perpendicular Lines Find the slopes of the lines parallel to, and perpendicular to, each line with the given slope. $$m=2$$

Slopes of Parallel and Perpendicular Lines Find the slopes of the lines parallel to, and perpendicular to, each line with the given slope. $$m=4.8$$

Slopes of Parallel and Perpendicular Lines Find the slopes of the lines parallel to, and perpendicular to, each line with the given slope. $$m=-1.85$$

Slopes of Parallel and Perpendicular Lines Find the slopes of the lines parallel to, and perpendicular to, each line with the given slope. $$m=-2.85$$

A steel pipe is \(21.50 \mathrm{m}\) long at \(0^{\circ} \mathrm{C} .\) Find its length at \(75.0^{\circ} \mathrm{C}\) if \(\alpha\) for steel is \(12.0 \times 10^{-6}\) per Celsius degree.

Slopes of Parallel and Perpendicular Lines Find the slopes of the lines parallel to, and perpendicular to, each line with the given slope. $$m=-5.372$$

The pressure at a point located at a depth \(x\) ft from the surface of a liquid varies directly as the depth. If the pressure at the surface is \(20.6 \mathrm{lb} / \mathrm{in.}^{2}\) and increases by \(0.432 \mathrm{lb} /\) in. \(^{2}\) for every foot of depth, write an equation for \(P\) as a function of the depth \(x\) (in feet). At what depth will the pressure be \(30.0 \mathrm{lb} / \mathrm{in.}^{2} ?\)

Angle Between Two Lines Find the angle of intersection between line \(L_{1}\) having a slope of 1 and line \(L_{2}\) having a slope of 6.

Angle Between Two Lines Find the angle of intersection between line \(L_{1}\) having a slope of 3 and line \(L_{2}\) having a slope of -2.

Angle Between Two Lines Find the angle of intersection between line \(L_{1}\) having an angle of inclination of \(35^{\circ}\) and line \(L_{2}\) having an angle of inclination of \(160^{\circ}\).

The increase in length of a wire in tension is directly proportional to the applied load \(P .\) Write an equation for the length \(L\) of a wire that has an initial length of \(3.00 \mathrm{m}\) and that stretches \(1.00 \mathrm{mm}\) for each \(12.5 \mathrm{N} .\) Find the length of the wire with a load of \(750 \mathrm{N}\)

Angle Between Two Lines Find the angle of intersection between line \(L_{1}\) having an angle of inclination of \(22^{\circ}\) and line \(L_{2}\) having an angle of inclination of \(86^{\circ} .\)

The freezing point of water is \(32^{\circ}\) Fahrenheit (F), or \(0^{\circ}\) Celsius (C). The boiling point of water is \(212^{\circ} \mathrm{F}\) or \(100^{\circ} \mathrm{C}\). The curve connecting these two point pairs is a straight line. Use the two-point form of the equation of a straight line to derive an equation connecting degrees Fahrenheit and degrees Celsius. (We use this equation to convert between Fahrenheit and Celsius.)

Applications The distance between two stakes on a slope is taped at 2055 ft, and the angle of the slope with the horizontal is \(12.3^{\circ} .\) Find the horizontal distance between the stakes.

Applications What is the angle of inclination with the horizontal of a roadbed that rises 15.0 ft in each \(250 \mathrm{ft}\), measured horizontally?

Applications How far apart must two stakes on a \(7^{\circ}\) slope be placed so that the horizontal distance between them is \(1250 \mathrm{m} ?\)

Applications A straight tunnel under a river is 755 ft long and descends \(12.0 \mathrm{ft}\) in this distance. What angle does the tunnel make with the horizontal?

Applications A straight driveway slopes downward from a house to a road and is \(28.0 \mathrm{m}\) in length. If the angle of inclination from the road to the house is \(3.60^{\circ},\) find the height of the house above the road.

Applications An escalator is built so as to rise \(2.00 \mathrm{m}\) for each \(3.00 \mathrm{m}\) of horizontal travel. Find its angle of inclination.

Applications A straight highway makes an angle of \(4.50^{\circ}\) with the horizontal. How much does the highway rise in a distance of \(2500 \mathrm{ft}\), measured along the road?