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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

A block of ice slides down a (frictionless) ramp with an acceleration of 5.3 m/s2. If the ramp makes an angle of 32.7° with the horizontal, find g, the acceleration due to gravity. See Fig. 9.43.
Find the indicated vector sums and differences with the given vectors by means of diagrams.D + E A B C D E
Use the law of cosines to solve the given problems.Write the form of the law of cosines, given sides a and b, and angle C = 90°.
Add the given vectors by components.A = 21.9,θA = 236.2° B = 96.7, θB = 11.5°C = 62.9, θC = 143.4°
Set up equations (do not solve) to solve the triangle in Fig. 9.73 by the law of cosines. Why is the law of sines easier to use? Fig. 9.73 A 10 30 a 20°
A boat followed a triangular route going from dock A, to dock B, to dock C, and back to dock A. The angles turned were 135° at B and 125° at C. If B is 875 m from A, how far is it from B to C?
Add the given vectors by using components.S = 8120, θS = 141.9°T = 1540, θT = 165.2°U = 3470, θU = 296.0°
Assuming the vectors in Fig. 9.42 are in equilibrium, find T1 and T2. T₁ Fig. 9.42 255 N 58.3° 37.2° T₂
Find the required horizontal and vertical components of the given vectors.A wind-blown fire with a speed of 18 ft/s is moving toward a highway at an angle of 66° with the highway. What is the
Find the required horizontal and vertical components of the given vectors. A nuclear submarine approaches the surface of the ocean at 25.0 km/h and at an angle of 17.3° with the surface. What are
Add the given vectors by components.E = 1653, θE = 36.37°F = 9807, θF = 253.06°
A small island is approximately a triangle in shape. If the longest side of the island is 520 m, and two of the angles are 45° and 55°, what is the length of the shortest side?
Add the given vectors by using components.A = 0.750, θA = 15.0°B = 0.265, θB = 192.4°C = 0.548, θC = 344.7°
An iRobot Roomba vacuum cleaner travels 12.5 ft across the floor where it then hits a wall and turns on a 47.0° corner. If it travels 15.0 ft in this new direction, how far is it from its starting
Find the indicated vector sums and differences with the given vectors by means of diagrams.C + D A B C D E
Add the given vectors by components.A = 9.821,θA = 34.27°B = 17.45, θB =752.50°
Add the given vectors by components.A = 6.89, θA = 123.0°B = 29.0, θB = 260.0°
Find the indicated vector sums and differences with the given vectors by means of diagrams.B + C A B C D E
A plane flies at 550 km/h into a head wind of 60 km/h at 78° with the direction of the plane. Find the resultant velocity of the plane with respect to the ground. See Fig. 9.41. Fig. 9.41 Wind 60
Solve the triangles with the given parts.a = 20, c = 10, C = 30°
Add the given vectors by using components.A = 7.031, θA = 122.54°B = 3.029, θB = 214.82°
A ship’s navigator determines that the ship is moving through the water at 17.5 mi/h with a heading of 26.3° north of east, but that the ship is actually moving at 19.3 mi/h in a direction of
Find the indicated vector sums and differences with the given vectors by means of diagrams.A + B A B C D E
Find the x-and y-components of the given vectors by use of the trigonometric functions. The magnitude is shown first, followed by the direction as an angle in standard position.509.4 m, θ = 360.0°
Solve the triangles with the given parts.a = 17, b = 24, c = 42. Explain your answer.
Add the given vectors by components.C = 5650, θC = 76.0°D = 1280, θD = 160.0°
Solve the triangles with the given parts.a = 450, b = 1260, A = 64.8°
Add the given vectors by using components.Y = 51.33, θY = 12.25°Z = 42.61, θZ = 0z 291.77°
Find the x-and y-components of the given vectors by use of the trigonometric functions. The magnitude is shown first, followed by the direction as an angle in standard position.38.47 ft, θ = 145.82°
Solve the triangles with the given parts.a = 1500, A = 15°, B = 140°
Add the given vectors by components.A = 30.7, θA = 18.2°B = 45.2, θB = 251.0°
Solve the triangles with the given parts.a = 0.841, b = 0.965, A = 57.1°
Two perpendicular forces act on a ring at the end of a chain that passes over a pulley and holds an automobile engine. If the forces have the values shown in Fig. 9.40, what is the weight of the
Add the given vectors by using components.A = 18,760, θA = 110.43°B = 4835, θB = 350.20⁰
Find the x-and y-components of the given vectors by use of the trigonometric functions. The magnitude is shown first, followed by the direction as an angle in standard position.6.78 lb, θ = 22.5°
Solve the triangles with the given parts.a = 1.78, b = 6.04, c = 4.80
Draw the given vectors and find their sum graphically. The magnitude is shown first, followed by the direction as an angle in standard position.7.5 cm, 240°; 2.3 cm, 30°
Solve the triangles with the given parts.b = 2880, c = 3650, B = 31.4°
Add the given vectors by components.A = 368, θA = 235.3°B = 227, θB = 295.0°
Add the given vectors by using components.A = 22.51, θA = 130.16°B = 7.604, θB = 200.09⁰
Find the x-and y-components of the given vectors by use of the trigonometric functions. The magnitude is shown first, followed by the direction as an angle in standard position.2.65 mN, θ = 197.3°
Solve the triangles with the given parts.a = 723, b = 598, c = 158
Draw the given vectors and find their sum graphically. The magnitude is shown first, followed by the direction as an angle in standard position.6.0 cm, 150°; 1.8 cm, 315°
Solve the triangles with the given parts.a = 89.45, c = 37.36, C = 15.62°
Add the given vectors by components.F = 154, θF = 90.0°T = 128, θT = 43.0°
Add the given vectors by using components.J = 0.0120, θJ = 370.5° K = 0.00781, θK, = 260.0⁰
Find the x-and y-components of the given vectors by use of the trigonometric functions. The magnitude is shown first, followed by the direction as an angle in standard position.16.4 cm/s2, θ =
In an accident, a truck with momentum (a vector quantity) of 22,100 kg · m/s strikes a car with momentum of 17,800 kg · m/s from the rear. The angle between their directions of motion is 25.0°.
Solve the triangles with the given parts.a = 49.32, b = 54.55, B = 114.36°
Draw the given vectors and find their sum graphically. The magnitude is shown first, followed by the direction as an angle in standard position.2.3 cm, 45°; 5.2 cm, 120°
Solve the triangles with the given parts.a = 5.240, b = 4.446, B = 48.13°
Add the given vectors by components.A = 18.0, θA = 0.0° B = 12.0, θB = 27.0°
Add the given vectors by using components.A = 780,θA = 28.0° B = 346,θB = 320.0⁰
Find the x- and y-components of the given vectors by use of the trigonometric functions. The magnitude is shown first, followed by the direction as an angle in standard position.8.17 ft/s2, θ =
The acceleration (a vector quantity) of gravity on a sky diver is 9.8 m/s2. If the force of the wind also causes an acceleration of 1.2 m/s2 at an angle of 15° above the horizontal, what is the
Add the given vectors by drawing the appropriate resultant.
Solve the triangles with the given parts.b = 103.7, c = 159.1, C = 104.67°
Draw the given vectors and find their sum graphically. The magnitude is shown first, followed by the direction as an angle in standard position.3.6 cm, 0°; 4.3 cm, 90°
Solve the triangles with the given parts.b = 283.2, B = 13.79°, C = 103.62°
With the given sets of components, find R and θ.Rx = 7.627, Ry = −6.353
Vectors A and B are at right angles. Find the magnitude and direction (from A) of the resultant.A = 26.52B = 89.86
Find the x-and y-components of the given vectors by use of the trigonometric functions. The magnitude is shown first, followed by the direction as an angle in standard position.0.0998 ft/s, θ =
Change 150° to radians in terms of π.
Find the exact value of x that is defined in terms of the continuing fraction at the right (the pattern continues endlessly). Explain your method of solution. x=2+ 2+ 1 2+ 1 1 2+..
The width of a rectangular LED television screen is 22.9 in. longer than the height. If the diagonal is 60.0 in., find the dimensions of the screen. See Fig. 7.21. Fig. 7.21 60.0 in. h+22.9 h
An architect is designing a Norman window (a semicircular part over a rectangular part) as shown in Fig. 7.22. If the area of the window is to be 16.0 ft2 and the height of the rectangular part is
A compact disc (CD) is made such that it is 53.0 mm from the edge of the center hole to the edge of the disc. Find the radius of the hole if 1.36% of the disc is removed in making the hole. See Fig.
A military jet flies directly over and at right angles to the straight course of a commercial jet. The military jet is flying at 200 mi/h faster than four times the speed of the commercial jet. How
An electronics student is asked to solve the equationWrite one or two paragraphs explaining your procedure for the solution, including a discussion of what methods of the chapter may be used in
An electric utility company is placing utility poles along a road. It is determined that five fewer poles per kilometer would be necessary if the distance between poles were increased by 10 m. How
A testing station found p parts per million (ppm) of sulfur dioxide in the air as a function of the hour h of the day to be p = 0.00174(10 + 24h − h2). Sketch the graph of p = f (h) and, from the
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 3(b), change 3.80 to 2.80.Data From Example 3(b)Because no units are shown for 1.05
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 1, change π/6 to π/4.Data from Example 1Find the length of arc on a circle of
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 2, add 40° to each angle, express in terms of the same function of a positive acute
Determine each of the following as being either true or false. If it is false, explain why.If θ is a fourth-quadrant angle, then cosθ > 0.
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 7, change cos to sin.Data from Example 7Find θ in radians, such that cos θ = 0.8829
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 3(a), change 17.5% to 18.5%.Data from Example3(a)Showing that 17.5% of high school
Answer the given questions about the indicated examples of this section.In Example 6, if the point (−1, √3) is replaced with the point (1,− √3), what are the resulting values?Data from
Answer the given questions about the indicated examples of this section.In Example 4, if 90° is added to each angle, what is the sign of each resulting function?Data from Example 4(a) The following
Determine each of the following as being either true or false. If it is false, explain why.sin 40° = −sin 220°
Determine the sign of (a) sec 285°, (b) sin 245°, (c) cot 265°.
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 7, change the − to + and then find θ.Data from Example 7Given that cos θ =
Determine each of the following as being either true or false. If it is false, explain why.For 0° < θ < 360°, sin θ > 0, and tan θ < 0, then sec θ > 0.
Express the given angle measurements in radian measure in terms of π.15°, 120°
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 4, change 90.0 m to 115 m.Data from Example 4A person on a hang glider is moving in
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 6, change 2.00 s to 2.50s.Data from Example 6A pulley belt 10.0 ft long takes 2.00 s
Determine the sign of the given functions.tan 135°, sec 50°
Express sin 205° in terms of the sine of the reference angle. Do not evaluate.
Express the given trigonometric function in terms of the same function of the reference angle.sin 155°, cos 220°
Determine each of the following as being either true or false. If it is false, explain why.To convert an angle measured in radians to an angle measured in degrees, multiply the number of radians by
Express the given angle measurements in radian measure in terms of π.12°, 225°
Determine the sign of the given functions.sin 240°, cos 300°
Find sin θ and sec θ if θ is in standard position and the terminal side passes through (−9, 12).
Express the given trigonometric function in terms of the same function of the reference angle.tan 91°, sec 345°
Determine each of the following as being either true or false. If it is false, explain why.The length of arc s of a circular arc of radius r and central angle θ (in radians) is s = 1/2θr.
Express the given angle measurements in radian measure in terms of π.75°, 330°
For an arc length s, area of sector A, and central angle θ of a circle of radius r, find the indicated quantity for the given values.r = 5.70 in., θ = π/4, s = ?
Determine the sign of the given functions.sin 290°, cos 200°
An airplane propeller blade is 2.80 ft long and rotates at 2200 r/min. What is the linear velocity of a point on the tip of the blade?
Express the given trigonometric function in terms of the same function of the reference angle.tan 105°, csc 328°

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