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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Determine each of the following as being either true or false. If it is false, explain why.If the sine and cosine of an angle are both negative, then the angle must terminate in the third quadrant.
Express the given angle measurements in radian measure in terms of π.36°, 315°
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 = 21.2 cm,θ = 2.65, s = ?
Determine the sign of the given functions.tan 320°, sec 185°
Given that 3.572 is the measure of an angle, express the angle in degrees.
Express the given trigonometric function in terms of the same function of the reference angle.cos 190°, tan 290°
Solve the resulting triangles if the given changes are made in the indicated examples of this section.In Example 1, solve the triangle if the value of C is changed to 145°.Data from Example 1Solve
In Fig. 8.53, show that the area of a design label (a segment of a circle) intercepted by angle θ is A = 1/2r2 (θ − sinθ). Find the area if r = 4.00 cm and θ = 1.45. Fig. 8.53 LABEL
Find the necessary quantities if the given changes are made in the indicated examples of this section.In Example 2, find the resultant location if the 41.25° angle is changed to 31.25°.Data from
Find the component vectors if the given changes are made in the indicated examples of this section.In Example 2, change 126.0° to 216.0°.Data from Example 2A surveyor’s marker is located 14.4 m
By use of a diagram, find the vector sum 2A + B for the given vectors. A B
Find the resultant vectors if the given changes are made in the indicated examples of this section.In Example 2, find the resultant if θA is changed to 0°.Data from Example 2Find the resultant of
Solve the resulting triangles if the given changes are made in the indicated examples of this section.In Example 2, solve the triangle if the value of B is changed to 82.94°.Data from Example 2Solve
Find the component vectors if the given changes are made in the indicated examples of this section.In Example 3, change 205.32° to 295.32°.Data from Example 3Resolve vector A, of magnitude 375.4
Find the resultant vectors if the given changes are made in the indicated examples of this section.In Example 2, what is the resultant of the three vectors if the direction of vector A is
Solve the resulting triangles if the given changes are made in the indicated examples of this section.In Example 3, solve the triangle if 49.3 is changed to 54.3.Data from Example 3For a triangular
Find the necessary quantities if the given changes are made in the indicated examples of this section.In Example 3, find the resultant velocity if the wind is from the northwest, rather than
Determine each of the following as being either true or false.To add two vectors by use of a diagram, place the tail of the second at the head of the first, keeping magnitudes and directions. The sum
Find the resultant vectors if the given changes are made in the indicated examples of this section.In Example 4, find the resultant if 70° is changed to 20°.Data from Example 4Find the resultant of
For the triangle in which a = 22.5,B = 78.6°, and c = 30.9, find b.
Solve the resulting triangles if the given changes are made in the indicated examples of this section.In Example 4, solve the triangle if the value of b is changed to 70.0.Data from Example 4Solve
Find the component vectors if the given changes are made in the indicated examples of this section.In Example 3, change 205.32° to 270.00°.Data from Example 3Resolve vector A, of magnitude 375.4
Find the resultant vectors if the given changes are made in the indicated examples of this section.In Example 4, for vectors A and B, what is vector 2A + 3B?Data from Example 4For vectors A and B in
Solve the triangles with the given parts.a = 6.00, b = 7.56, C = 54.0°
Two hockey players strike the puck at the same time, hitting it with horizontal forces of 6.85 lb and 4.50 lb that are perpendicular to each other. Find the resultant of these forces.
A surveyor locates a tree 36.50 m to the northeast of a set position. The tree is 21.38 m north of a utility pole. What is the displacement of the utility pole from the set position?
Find the resultant vectors if the given changes are made in the indicated examples of this section.In Example 5, for vectors A and B, what is vector 2B − A?Data from Example 5For vectors A and B in
Determine each of the following as being either true or false.In adding vectors, the answer is the magnitude of the resultant.
Find the resultant vectors if the given changes are made in the indicated examples of this section.In Example 5, for vectors A and B, what is vector 2B − A?Data from Example 5For vectors A and B in
Vectors A and B are at right angles. Find the magnitude and direction (the angle from vector A) of the resultant.A = 14.7B = 19.2
Solve the triangles with the given parts.a = 45.7, A = 65.0°, B = 49.0°
Find the component vectors if the given changes are made in the indicated examples of this section.In Example 4, change 53.5° to 45.0°.Data from Example 4The tension T in a cable supporting the
Solve the triangles with the given parts.b = 87.3, c = 34.0, A = 130.0°
A jet is 115 mi east and 88.3 mi north of Niagara Falls. What is its displacement from Niagara Falls?
For the triangle in which A = 18.9°,B = 104.2°, and a = 426, find c.
Determine each of the following as being either true or false.The Law of Sines is used in solving a triangle for which two sides and the included angle are known.
Find the resultant vectors if the given changes are made in the indicated examples of this section.In Example 6, if 20° replaces 40°, what is the resultant force?Data from Example 6Two persons pull
Vectors A and B are at right angles. Find the magnitude and direction (the angle from vector A) of the resultant.A = 592B = 195
Solve the triangles with the given parts.b = 3.07, A = 26.0°, C = 120.0°
Find the horizontal and vertical components of the vectors shown in the given figures. In each, the magnitude of the vector is 750. 0 28.0° X
Solve the triangles with the given parts.a = 4530, b = 924, C = 98.0°
In lifting a heavy piece of equipment from the mud, a cable from a crane exerts a vertical force of 6520 N, and a cable from a truck exerts a force of 8280 N at 15.0° above the horizontal. Find the
Solve the triangle in which a = 9.84,b = 3.29, and c = 8.44.
Determine each of the following as being either true or false.The Law of Cosines is used in solving a triangle for which two sides and the angle opposite one of them are known.
Vectors A and B are at right angles. Find the magnitude and direction (the angle from vector A) of the resultant.A = 3.086B = 7.143
Solve the triangles with the given parts.c = 4380, A = 37.4°, B = 34.6°
Determine whether a scalar or a vector is described in (a) and (b). Explain your answers.(a) A soccer player runs 15 m from the center of the field.(b) A soccer player runs 15 m from the center of
Solve the triangles with the given parts.a = 0.0845, c = 0.116, B = 85.0°
Find the horizontal and vertical components of the vectors shown in the given figures. In each, the magnitude of the vector is 750. 0 У 105.0⁰ -Х X
At a point in the plane, two electric charges create an electric field (a vector quantity) of 25.9 kN/C at 10.8° above the horizontal to the right and 12.6 kN/C at 83.4 below the horizontal to the
For vector R, find R and standard position θ if Rx = − 235 and R = 152.
Determine each of the following as being either true or false.The ambiguous case occurs when two sides of a triangle and one of their opposite angles are given.
Find the horizontal and vertical components of the vectors shown in the given figures. In each, the magnitude of the vector is 750. y 242.3° 0 X
Vectors A and B are at right angles. Find the magnitude and direction (the angle from vector A) of the resultant.A = 1734B = 3297
Solve the triangles with the given parts.a = 932, B = 0.9°, C = 82.6°
Determine whether a scalar or a vector is described in (a) and (b). Explain your answers.(a) A small-craft warning reports 25 mi/h winds.(b) A small-craft warning reports 25 mi/h winds from the north.
Solve the triangles with the given parts.a = 395.3, b = 452.2, c = 671.5
A motorboat leaves a dock and travels 1580 ft due west; then it turns 35.0° to the south and travels another 1640 ft to a second dock. What is the displacement of the second dock from the first dock?
Find the horizontal and vertical components of the vectors shown in the given figures. In each, the magnitude of the vector is 750. 307.6° y X
Find the x-and y-components of the given vectors by use of the trigonometric functions. A = 72.0, θA = 24.0°
Find the horizontal and vertical components of a force of 871 kN that is directed at a standard-position angle of 284.3°.
With the given sets of components, find R and θ.Rx = 5.18, Ry = 8.56
Find the horizontal and vertical components of the vectors shown in the given figures. In each, the magnitude of the vector is 750. y 180° X
Solve the triangles with the given parts.a = 4.601, b = 3.107, A = 18.23°
Determine whether a scalar or a vector is described in (a) and (b). Explain your answers.(a) An arm of an industrial robot pushes with a 10-lb force downward on a part.(b) A part is being pushed with
Solve the triangles with the given parts.a = 2.331, b = 2.726, c = 2.917
Toronto is 650 km at 19.0° north of east from Chicago. Cincinnati is 390 km at 48.0° south of east from Chicago. What is the displacement of Cincinnati from Toronto?
Find the x-and y-components of the given vectors by use of the trigonometric functions. A = 8050, θA =149.0⁰
With the given sets of components, find R and θ.Rx = 89.6, Ry = −52.0
Solve the triangles with the given parts.b = 362.2, c = 294.6, B = 110.63°
A ship leaves a port and travels due west. At a certain point, it turns 31.5° north of west and travels an additional 42.0 mi to a point 63.0 mi on a direct line from the port. How far from the port
Determine whether a scalar or a vector is described in (a) and (b). Explain your answers.(a) A ballistics test shows that a bullet hit a wall at a speed of 400 ft/s.(b) A ballistics test shows that a
From a fixed point, a surveyor locates a pole at 215.6 ft due east and a building corner at 358.2 ft at 37.72° north of east. What is the displacement of the building from the pole?
Solve the triangles with the given parts.a = 385.4, b = 467.7, c = 800.9
Find the x-and y-components of the given vectors by use of the trigonometric functions. A = 5.716, θA = 215.59°
Find the horizontal and vertical components of the vectors shown in the given figures. In each, the magnitude of the vector is 750. 270⁰ y x
Add the given vectors by drawing the appropriate resultant.
Find the sum of the vectors for which A = 449, θA = 74.2°, B = 285, and θB = 208.9° by using components.
With the given sets of components, find R and θ.Rx = −0.982, Ry = 2.56
Solve the triangles with the given parts.b = 7751, c = 3642, B = 20.73°
Find the x-and y-components of the given vectors by use of the trigonometric functions.A = 657.1,θA = 343.74°
Solve the triangles with the given parts.a = 0.2433, b = 0.2635, c = 0.1538
A rocket is launched with a vertical component of velocity of 2840 km/h and a horizontal component of velocity of 1520 km/h. What is its resultant velocity?
Add the given vectors by drawing the appropriate resultant.
Solve the triangle for which a = 22.3,b = 29.6, and A = 36.5°.
Assuming the vectors in Fig. 9.93 are in equilibrium, find T1 and T2. Fig. 9.93 41.7° T₂ 185 N 35.6°
With the given sets of components, find R and θ.Rx = −729, Ry = −209
Solve the triangles with the given parts.a = 150.4, c = 250.9, C = 76.43°
Add the given vectors by drawing the appropriate resultant.
Solve the triangles with the given parts.a = 320, b = 847, C = 158.0°
In testing the behavior of a tire on ice, a force of 520 lb is exerted to the side, and a force of 780 lb is exerted to the front. What is the resultant force on the tire?
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.15.8 lb, θ = 76.0°
Vectors A and B are at right angles. Find the magnitude and direction (from A) of the resultant.A = 327B = 505
With the given sets of components, find R and θ.Rx = −646, Ry = 2030
Solve the triangles with the given parts.a = 63.8, B = 58.4°, C = 22.2°
Solve the triangles with the given parts.b = 18.3, c = 27.1, A = 8.7°
Add the given vectors by drawing the appropriate resultant.
To raise a crate, two ropes are attached to its top. If the force in one rope is 240 lb at 25° from the vertical, what must be the force in the second rope at 35° from the vertical in order to lift
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.9750 N, θ = 243.0°
Vectors A and B are at right angles. Find the magnitude and direction (from A) of the resultant.A = 6.8A = 2.9

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