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mathematics
basic technical mathematics
Questions and Answers of
Basic Technical Mathematics
Show that the side c of any triangle ABC is related to the perpendicular h from C to side AB by the equationc = h cot A + h cot B.
The signal from a radio station with two antennas d meters apart has a wavelength λ (in m). The intensity of the signal depends on the angle θ as shown in Fig. 4.26. An angle of minimum intensity
Two legs of a right triangle are 2.607 and 4.517. What is the smaller acute angle?
A submarine dives such that the horizontal distance h it moves and the vertical distance v it dives are related by v = h tanθ. Here, θ is the angle of the dive, as shown in Fig. 4.27. Find θ if h
Solve the right triangles with the given parts. Refer to Fig. 4.68.a = 0.721, b = 0.144 A C b Fig. 4.68 B a C
What is x if (3, 2) and (x, 7) are on the same terminal side of an acute angle?
Solve the right triangles with the given parts. Refer to Fig. 4.68.B = 4.38°, b = 5682 A C b Fig. 4.68 B a C
Explain why values of sinθ increase as θ increases from 0° to 90°.
Find the perimeter of a regular octagon (eight equal sides with equal interior angles) that is inscribed in a circle (all vertices of the octagon touch the circle) of radius 10.
A brace is used in the structure shown in Fig. 4.25. Its length is l = a(secθ + cscθ). Find l if a = 28.0cm and θ = 34.5°. a 1 0 Fig. 4.25 a
Solve the right triangles with the given parts. Refer to Fig. 4.68.B = 85.7°, b = 852.44 A C b Fig. 4.68 B a C
Solve the right triangles with the given parts. Refer to Fig. 4.68.b = 6.508, c = 7.642 A C b Fig. 4.68 B a C
Solve the right triangles with the given parts. Refer to Fig. 4.68.A = 37.5°, a = 12.0 A C b Fig. 4.68 B a C
If the backup camera on a car is mounted at a height h above the road and is angled downward (from the horizontal) at an angle θ, then the distance x along the road between the car and the point at
The sound produced by a jet engine was measured at a distance of 100 m in all directions. The loudness d of the sound (in decibels) was found to be d = 70.0 + 30.0 cosθ, where the 0° line was
Solve the right triangles with the given parts. Refer to Fig. 4.68.a = 106, c = 382 A C b Fig. 4.68 B a C
A windmill rotates 15.6 revolutions in a counterclockwise direction. By how many radians does it rotate?
According to Snell’s law, if a ray of light passes from air into water with an angle of incidence of 45.0°, then the angle of refraction θr is given by the equation sin 45.0° = 1.33 sin
A circular gear rotates clockwise by exactly 3.5 revolutions. By how many degrees does it rotate?
Find the values of the indicated trigonometric functions if θ is an acute angle.Find cscθ, given cosθ = 0.1063.
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(50, 20)
A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is 13.33°. The camera is 196.0 cm above the surface. How far from the camera is
The Willis Tower in Chicago can be seen from a point on the ground known to be 5200 ft from the base of the tower. The angle of elevation from the observer to the top of the tower is 16°. How high
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.a = 56.73, b = 44.09Data from Table
By means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest 0.01°. 0.838 rad
Find the values of the trigonometric functions. Round off results according to Table 4.1.csc 0.49°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.a = 9.908, c = 12.63Data from Table
By means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest 0.01°.4.447 rad
Find the values of the trigonometric functions. Round off results according to Table 4.1.sec 7.8°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.B = 37.5°, a = 0.862Data from
Express the given angles to the nearest minute.749.75°
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, the coordinates are approximate.(0.687, 0.943)
A rectangular piece of plywood 4.00 ft by 8.00 ft is cut from one corner to an opposite corner. What are the angles between edges of the resulting pieces?
By means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest 0.01°.−3.642 rad
To get a good view of a person in front of a teller’s window, it is determined that a surveillance camera at a bank should be directed at a point 15.5 ft to the right and 6.75 ft below the camera.
Find the values of the trigonometric functions. Round off results according to Table 4.1.cot 85.96°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Express the given angles to the nearest minute.126.05°
Sketch an appropriate figure, unless the figure is given.Find the angle of view θ of the camera lens (see Fig. 4.67), given the measurements shown in the figure. Film diagonal = 42.5 mm 375 mm Fig.
A guardrail is to be constructed around the top of a circular observation tower. The diameter of the observation area is 12.3 m. If the railing is constructed with 30 equal straight sections, what
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.A = 87.25°, b = 8.450Data from
Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest 0.01°.1.257 rad
Determine the trigonometric functions of the angles (in standard position) whose terminal side passes through the given points. Give answers in exact form.(24, 7)
Find the values of the indicated functions assuming θ is an acute angle. Give answers in exact form.Given cosθ = 12/13, find sinθ and cot θ.
The given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.435°, −270°
Explain why the given statements are true for an acute angle θ.sinθ is always between 0 and 1.
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.cot θ = 7.117
The given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.−5°, 265°
Explain why the given statements are true for an acute angle θ.tanθ can equal any positive real number.
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.secθ = 1.006
The given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.1 rad, 2 rad
Explain why the given statements are true for an acute angle θ.cosθ decreases in value as θ increases from 0° to 90°.
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.sinθ = 1.030
The given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.3 rad, −3π rad
Explain why the given statements are true for an acute angle θ.The value of secθ is never less than 1.
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.tanθ = 0.0052
The given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.4 rad, π/3 rad
Solve the given systems of equations by the method of elimination by substitution. y = 2x + 10 2x + y = -2
Find the slopes of the lines that pass through the given points.(2, 0), (4, −8)
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. y = x - 1 y = -x + 8
Use the rref feature on a calculator to find the three currents given in the following system of equations. Round answers to three significant digits. 3.001₁ 4.001₂ 1₁ + 1₂ - 4.001₂ +
Solve by determinants: 3x - 2y = 4 2x + 5y = -1
Evaluate the given third-order determinants. 9-68 -3 7 4 -2 225 2 5
Evaluate the given determinants. 83 41
Determine each of the following as being either true or false. If it is false, explain why.One method of finding the solution of the following system of equations would be to subtract the left side
Solve the given systems of equations. 2x + y z = 4 4x - 3y2z 8x - 2y3z = 3 -2
Evaluate the given third-order determinants. -2 4 -1 4 2 5 -1 4 -8
Determine whether or not the given equation is linear.2v + 3t2 = 60
Solve the given systems of equations by the method of elimination by substitution. x = 2y + 1 2x - 3y = 4
Evaluate the given determinants. -1 3 26
Determine whether or not the given pair of values is a solution of the given system of linear equations.2x + y = 8 x = − 1, y = 103x − y = − 13
Determine each of the following as being either true or false. If it is false, explain it why. 10 04-1 3 -1 7 0 = 0
Solve the given systems of equations. 51 +6w 41 7w 31+w7h = 1 3h = 6 2h = -3
By finding the slope and y-intercept, sketch the graph of 2x + y = 4.
Solve the given systems of equations by the method of elimination by substitution. P = V - 4 V + p = P 10
Determine whether or not the given equation is linear.2l + 3w = 4lw
Evaluate the given third-order determinants. -8 5 2 -4 -6 -1 0 10 10 -1
Evaluate the given determinants. 3-5 7-2
Determine whether or not the given pair of values is a solution of the given system of linear equations.A + 5B = −7 A = −2, B = 13A − 4B = −4
The perimeter of a rectangular ranch is 24 km, and the length is 6.0 km more than the width. Set up equations relating the length l and the width w, and then solve for l and w.
Solve the given systems of equations. 3r+st = 2 r+t2s=0 4rs + t = 3
Determine whether or not the given pair of values is a solution of the given system of linear equations. 3y - 6x = 4 x = 1, y = 2 4, зу 6x-3y = -4
Determine whether or not the given equation is linear.I1 + I3 = I2
Determine each of the following as being either true or false. If it is false, explain why.If the graphs of the equations in a linear system are parallel lines with different y-intercepts, the system
Evaluate the given third-order determinants. 10 2-7 -2 -3 6 65-2
Solve by addition or subtraction: 6N 2P 13 = = 4N3P-13
Solve the given systems of equations. 51 +6w 41 7w 31+w7h = 1 3h = 6 2h = -3
Evaluate the given determinants. 7 1-3 -4
Solve the given systems of equations by the method of elimination by substitution. x + y = -5 2x - y = 2
Evaluate the given determinants. -2 5 31
Evaluate the given third-order determinants. 4 -9 -3 -11 2 -2 01-5
Determine whether or not the given pair of values is a solution of the given system of linear equations. 1 2x - 5y = 0 x = 1, y = - 4x + 10y = 4
Determine whether or not the given pair of values is a solution to the given linear equation in two unknowns.2x + 3y = 9; (3, 1), (5, 1/3)
Evaluate the given determinants. 15 -9 12 0
Evaluate the given determinants. -20 -15 -8 -6
Evaluate the given determinants. 40 10 -20 -60
In testing an anticholesterol drug, it was found that each milligram of drug administered reduced a person’s blood cholesterol level by 2 units. Set up the function relating the cholesterol level C
Solve the given systems of equations. 2u2v + 3w = 0 3u + v + 4w = 21 -u - 3v + 7w = 15
Determine whether or not the given pair of values is a solution to the given linear equation in two unknowns.5x + 2y = 1; (0.2, −1), (1, −2)
Solve the following system of equations graphically. Determine the values of x and y to the nearest 0.1. 2x - 3y = 6 4x + y = 4
Solve the given systems of equations by the method of elimination by substitution. 3x + y = 1 2y = 3x - 16
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