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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Find θ in degrees for 0° ≤ θ < 360°.sinθ = −0.9323
Find the radian measure of an angle at the center of a circle of radius 12 cm that intercepts an arc of 15 cm on the circle.
Find θ in degrees for 0° ≤ θ < 360°.cos θ = − 0.4730
Use a calculator (in radian mode) to evaluate the ratios (sinθ) θ and (tanθ)/θ for θ = 0.1, 0.01, 0.001, and 0.0001. From these values, explain why it is possible to say that sin θ = tan θ =
In calculating a back line of a lot, a surveyor discovers an error of 0.05° in an angle measurement. If the lot is 136.0 m deep, by how much is the back-line calculation in error? See Fig. 8.52. Use
Find the length of arc of a circle of radius 10 in. that is intercepted from the center of the circle by an angle of 3 radians.
Find θ in degrees for 0° ≤ θ < 360°.cotθ = 1.196
Using Eq. (8.12), evaluate tan 0.001°. Compare with a calculator value.Data from Eq. (8.12)sinθ = tanθ = θ
Using the fact that sin 0.3827, 8 π = find the value of cos 5π/8.
Find θ in radians for 0 ≤ θ < 2π.cosθ = 0.8387
An astronomer observes that a star 12.5 light-years away moves through an angle of 0.2" in 1 year. Assuming it moved in a straight line perpendicular to the initial line of observation, how many
Using the fact that tan 0.5774, 6 π = find the value of cot 5π/3.
Find θ in radians for 0 ≤ θ < 2π.cscθ = 9.569
Find θ in radians for 0 ≤ θ < 2π.sinθ = −0.8650
Express tan(π/2 + θ) in terms of cotθ(0 < θ < π/2).
Express cos(3π/2 + θ ) in terms of sinθ(0 < θ < π/2).
Find θ in radians for 0 ≤ θ < 2π.tanθ = 8.480
A flat plate of weight W oscillates as shown in Fig. 8.31. Its potential energy V is given by V = 1/2Wbθ2 where θ is measured in radians. Find V if W = 8.75 lb, b = 0.75 ft, and θ = 5.5°. Fig.
A unit of angle measurement used in artillery is the mil, which is defined as a central angle of a circle that intercepts an arc equal in length to 1 6400 of the circumference. How many mils are in a
Find θ in degrees for 0° ≤ θ < 360°.cosθ = −0.672, sinθ < 0
The electric intensity I (in Wm2) from the two radio antennas in Fig. 8.32 is a function of θ given by I = 0.023 cos2(π sin θ). Find I for θ = 40.0°. [cos2α = (cosα)2.] Antenna CIÓ Fig. 8.32
Through how many radians does the minute hand of a clock move in 25 min?
Find θ in degrees for 0° ≤ θ < 360°.tanθ = −1.683, cosθ < 0
After the brake was applied, a bicycle wheel went through 1.60 rotations. Through how many radians did a spoke rotate?
Find θ in degrees for 0° ≤ θ < 360°.cotθ = 0.4291, cosθ < 0
The London Eye is a Ferris wheel erected in London in 1999. It is 135 m high and has 32 air-conditioned passenger capsules, each able to hold 25 people. Through how many radians does it move after
The height h of a rocket launched 1200 m from an observer is found to bewhere t is the time after launch. Find h for t = 8.0 s. h 1200 tan 5t 3t + 10 for t < 10 s,
Find θ in degrees for 0° ≤ θ < 360°.sinθ = 0.2626, tanθ < 0
For an arc of length s, area of sector A, and central angle θ of circle of radius r, find the indicated quantity for the given values.s = 20.3 in., θ = 107.5°, r = ?
The charge q (in C) on a capacitor as a function of time is q = Asin ωt. If t is measured in seconds, in what units is ω measured? Explain.
For an arc of length s, area of sector A, and central angle θ of circle of radius r, find the indicated quantity for the given values.s = 5840 ft, r = 1060 ft, θ = ?
For an arc of length s, area of sector A, and central angle θ of circle of radius r, find the indicated quantity for the given values.A = 265 mm2, r = 12.8 mm, θ = ?
For an arc of length s, area of sector A, and central angle θ of circle of radius r, find the indicated quantity for the given values.A = 0.908 km2, θ = 234.5°, r = ?
For an arc of length s, area of sector A, and central angle θ of circle of radius r, find the indicated quantity for the given values.r = 4.62 m, A = 32.8 m2, s = ?
For an arc of length s, area of sector A, and central angle θ of circle of radius r, find the indicated quantity for the given values.θ = 98.5°, A = 0.493 ft2, s = ?
For an arc of length s, area of sector A, and central angle θ of circle of radius r, find the indicated quantity for the given values.θ = 0.85°, s = 7.94 in., A = ?
For an arc of length s, area of sector A, and central angle θ of circle of radius r, find the indicated quantity for the given values.r = 254 cm, s = 7.61 cm, A = ?
Without a calculator, evaluatetan 200° + 2 cot 110° + tan (−160°).
Without a calculator, evaluate 2 cos 40° + cos 140° + sin 230°.
The cross section of a tunnel is the major segment of a circle of radius 12.0 ft wide. The base of the tunnel is 20.0 ft wide. What is the area of the cross section? See Exercise 79.Data from
Find (a) The area and (b) The perimeter of the parcel of land shown in Fig. 8.54. Its shape is a right triangle attached to a circular sector. Fig. 8.54 20,0⁰ 40.0 m 30.0 m
The speedometer of a car is designed to be accurate with tires that are 14.0 in. in radius. If the tires are changed to 15.0 in. in radius, and the speedometer shows 55 mi/h, how fast is the car
The instantaneous power p (in W) input to a resistor in an alternating-current circuit is p = pm sin2 377t, m where pm is the maximum power input and t is the time (in s). Find p for pm = 0.120 W
A sector gear with a pitch radius of 8.25 in. and a 6.60-in. arc of contact is shown in Fig. 8.55. What is the sector angle θ? Fig. 8.55 0 8.25 in. -6.60-in. arc
The horizontal distance x through which a pendulum moves is given by x = a(θ + sinθ), where a is a constant and θ is the angle between the vertical and the pendulum. Find x for a = 45.0 cm and θ
Two pulleys have radii of 10.0 in. and 6.00 in., and their centers are 40.0 in. apart. If the pulley belt is uncrossed, what must be the length of the belt?
A special vehicle for traveling on glacial ice in Banff National Park in the Canadian Rockies has tires 4.8 ft in diameter. If the vehicle travels at 3.5 mi/h, what is the angular velocity (in r/min)
A rotating circular restaurant at the top of a hotel has a diameter of 32.5 m. If it completes one revolution in 24.0 min, what is the velocity of the outer surface?
Find the velocity (in mi/h) of the moon as it revolves about the Earth. Assume it takes 28 days for one revolution at a distance of 240,000 mi from the Earth.
The stopboard of a shot-put circle is a circular arc 1.22 m in length. The radius of the circle is 1.06 m. What is the central angle?
The longitude of Anchorage, Alaska, is 150° W, and the longitude of St. Petersburg, Russia, is 30° E. Both cities are at a latitude of 60° N. (a) Find the great circle distance (see page 254)
A piece of circular filter paper 15.0 cm in diameter is folded such that its effective filtering area is the same as that of a sector with central angle of 220°. What is the filtering area?
To produce an electric current, a circular loop of wire of diameter 25.0 cm is rotating about its diameter at 60.0 r/s in a magnetic field. What is the greatest linear velocity of any point on the
Find the area of the decorative glass panel shown in Fig. 8.56. The panel is made up of two equal circular sectors and an isosceles triangle. Fig. 8.56 2.00 ft 3.75 ft
A circular hood is to be used over a piece of machinery. It is to be made from a circular piece of sheet metal 3.25 ft in radius. A hole 0.75 ft in radius and a sector of central angle 80.0° are to
The chain on a chain saw is driven by a sprocket 7.50 cm in diameter. If the chain is 108 cm long and makes one revolution in 0.250 s, what is the angular velocity (in r/s) of the sprocket?
An ultracentrifuge, used to observe the sedimentation of particles such as proteins, may rotate as fast as 80,000 r/min. If it rotates at this rate and is 7.20 cm in diameter, what is the linear
A computer is programmed to shade in a sector of a pie chart 2.44 cm in radius. If the perimeter of the shaded sector is 7.32 cm, what is the central angle (in degrees) of the sector? See Fig. 8.57.
A Gothic arch, commonly used in medieval European structures, is formed by two circular arcs. In one type, each arc is one-sixth of a circle, with the center of each at the base on the end of the
The Trans-Alaska Pipeline was assembled in sections 40.0 ft long and 4.00 ft in diameter. If the depth of the oil in one horizontal section is 1.00 ft, what is the volume of oil in this section?
A laser beam is transmitted with a “width” of 0.0008° and makes a circular spot of radius 2.50 km on a distant object. How far is the object from the source of the laser beam? Use Eq.
The planet Venus subtends an angle of 15" to an observer on Earth. If the distance between Venus and Earth is 1.04 ×108mi, what is the diameter of Venus? Use Eq. (8.12)Eq. (8.12)sinθ = tanθ = θ
Write a paragraph explaining how you determine the units for the result of the following problem: An astronaut in a spacecraft circles the moon once each 1.95 h. If the altitude of the spacecraft is
In Exercise solve the given equations and check the results. 3N 8 3 N-4 2 34 ||
Determine each of the following as being either true or false. If it is false, explain it.x = −1 is a solution to the equation 1 x + 1 X 1 x² + x
Divide the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 28 44 (by 4)
Simplify the given expressions involving the indicated multiplications and divisions. 4x + 16 5y X y² 2x + 8
In Exercise solve the given equations and check the results. 2x - 7 3 +5=
Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. B-1 B+1 (by 1 B)
In problems perform indicated operations and simplify. 1 3 2x + 2 1 2 X 315 1
In Exercises perform the indicated operations and simplify. 3
If one riveter can do a job in 12 days, and a second riveter can do it in 16 days, how long would it take for them to do it together?
Simplify the given expressions involving the indicated multiplications and divisions. sr2 2t st 4
In Exercise solve the given equations and check the results. -3 8 ||
In problems perform indicated operations and simplify. x² + x 2-x x² x² - 4x + 4
Find the products by inspection. No intermediate steps should be necessary.−7xy(4x2 − 7y)
Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. a x - y (by x + y)
Simplify the given expressions involving the indicated multiplications and divisions. yz ab bz SE ay
Perform indicated operations and simplify. 2 4
Find the products by inspection. No intermediate steps should be necessary.3a(4x + 5a)
Solve the given quadratic equations by completing the square.10T − 5T2 = 4
Use a calculator to graph all three parabolas on the same coordinate system. Describe (a) the shifts of y = x2 that occur and (b) how each parabola opens.(a) y = x2 (b) y = (x − 2)2 +
Solve the given quadratic equations by using the quadratic formula.0.30R2 − 0.42R = 0.15
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.4x2 − 12x = 7
Solve the given quadratic equations by factoring.4x2 + 25 = 20x
Solve the given quadratic equations by completing the square.2 + 6v = 9v2
Use a calculator to graph all three parabolas on the same coordinate system. Describe (a) the shifts of y = x2 that occur and (b) how each parabola opens.(a) y = x2 (b) y = (x − 3)2 (c) y
Solve the given quadratic equations by using the quadratic formula.2.1x2 + 2.3x + 5.5 = 0
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.15 + 4z = 32z2
Solve the given quadratic equations by factoring.4x = 3 − 7x2
Solve the given quadratic equations by completing the square.2y2 − y − 2 = 0
Use a calculator to graph all three parabolas on the same coordinate system. Describe (a) the shifts of y = x2 that occur and (b) how each parabola opens.(a) y = x2 (b) y = x2 + 3 (c) y =
Solve the given quadratic equations by using the quadratic formula.2 − 7x = 5x2
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.37T = T2
Solve the given quadratic equations by factoring.A2 + 8A + 16 = 0
Solve the given quadratic equations by completing the square.3x2 = 3 − 4x
Use a calculator to solve the given equations. Round solutions to the nearest hundredth. If there are no real roots, state this.3x2 − 25 = 20x
Solve the given quadratic equations by using the quadratic formula.18s + 12 = 24s2
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.25y2 = 81
Solve the given quadratic equations by factoring.3x2 − 13x + 4 = 0

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