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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

To build a highway, it is necessary to cut through a hill. A surveyor measured the cross-sectional areas at 250-ft intervals through the cut as shown in the following table. Using the trapezoidal
The roof of the Louisiana Superdome in New Orleans is supported by a circular steel tension ring 651 m in circumference. Find the area covered by the roof.
The diameter of the sun is 1.38 ×106 km, the diameter of the Earth is 1.27 ×104 km, and the distance from the Earth to the sun (center to center) is 1.50 ×108 km. What is the distance from the
The Hubble space telescope is within a cylinder 4.3 m in diameter and 13 m long. What is the volume within this cylinder?
A hot-water tank is in the shape of a right circular cylinder surmounted by a hemisphere as shown in Fig. 2.145. How many gallons does the tank hold? (1.00 ft 3 contains 7.48 gal.) 2.50 ft Fig.
A horizontal cross section of a concrete bridge pier is a regular hexagon (six sides, all equal in length, and all internal angles are equal), each side of which is 2.50 m long. If the height of the
A railroad track 1000.00 ft long expands 0.20 ft (2.4 in.) during the afternoon (due to an increase in temperature of about 30°F). Assuming that the track cannot move at either end and that the
On level ground a straight guy wire is attached to a vertical antenna. The guy wire is anchored in the ground 15.6 ft from the base of the antenna, and is 4.0 ft longer than the distance up the pole
On a straight east-west road, a man walks 1500 m to the east and a woman walks 600 m to the west until they meet. They turn south and walk to a point that is 1700 m (on a straight line) from his
A basketball court is 44 ft longer than it is wide. If the perimeter is 288 ft, what are the length and width?
A tent is in the shape of a regular pyramid surmounted on a cube. If the edge of the cube is 2.50 m and the total height of the tent is 3.25 m, find the area of the material used in making the tent
The diagonal of a TV screen is 152 cm. If the ratio of the width of the screen to the height of the screen is 16 to 9, what are the width and height?
An avid math student wrote to a friend, “My sailboat has a right triangular sail with edges (in ft) of 3k − 1, 4k + 3, and 5k + 2. Can you tell me the area of the sail if k > 1?”
The friend in Exercise 82 replied, “Yes, and I have two cups that hold exactly the same amount of water, one of which is cylindrical and the other is hemispherical. If I tell you the height of the
A satellite is 1590 km directly above the center of the eye of a circular (approximately) hurricane that has formed in the Atlantic Ocean. The distance from the satellite to the edge of the hurricane
The Pentagon, headquarters of the U.S. Department of Defense, is the world’s largest office building. It is a regular pentagon (five sides, all equal in length, and all interior angles are equal)
Make the indicated conversions.18.4 in. to meters
Make the indicated conversions.65 km/h to ft/s
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.After installing a pollution control device, a car’s exhaust contained the
Change numbers in ordinary notation to scientific notation or change numbers in scientific notation to ordinary notation.An optical coating on glass to reduce reflections is about 0.00000015 m thick.
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 2, in the first line, change 34 to 31.Data from Example 2In designing an office
Evaluate the given expressions. √9+16
Evaluate the given expressions (7)(-3)(-2) (-6)(0)
Evaluate the given expressions, the numbers are approximate. 3.372 x 10-3 7.526 x 10¹2
Determine each of the following as being either true or false. If it is false, explain why.The absolute value of any real number is positive.
Evaluate the given expressions. (+6)(-2) 3(-1) 12 - 51
Determine each of the following as being either true or false. If it is false, explain why.16 − 4 ÷ 2 = 14
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 3, in the second line, change “4 more slides” to “3 more slides.”Data from
Evaluate the given expressions, the numbers are approximate. 346.4 - 23.5 287.7 0.9443 (3.46)(0.109)
Determine each of the following as being either true or false. If it is false, explain why.For approximate numbers, 26.7 − 15 = 11.7.
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 4, in the second line, change 27,000km/h to 27,100km/h.Data from Example 4A
Determine each of the following as being either true or false. If it is false, explain why.2a3 = 8a3
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 5, change “pure methanol” to “of a blend with 50.0% methanol.”Data from
Determine each of the following as being either true or false. If it is false, explain why.0.237 = 2.37 ×10−1
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A certain new car costs $5000 more than the same model new car cost 6 years ago.
Perform the indicated operations and simplify. When exponents are used, use only positive exponents in the result. 8a³x² - 4a²x4 -2ax²
Perform the indicated operations and simplify. When exponents are used, use only positive exponents in the result.(2a0b−2c3)−3
Determine each of the following as being either true or false. If it is false, explain why.−√−4 = 2
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.The flow of one stream into a lake is 1700ft3/s more than the flow of a second
Perform the indicated operations and simplify. When exponents are used, use only positive exponents in the result.(2x + 3)2
Determine each of the following as being either true or false. If it is false, explain why. 3x = 2 7 + x9
Determine each of the following as being either true or false. If it is false, explain why.4x − (2x + 3) = 2x + 3
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.Approximately 6.9 million wrecked cars are recycled in two consecutive years.
Perform the indicated operations and simplify. When exponents are used, use only positive exponents in the result.3m2 (am − 2m3)
Perform the indicated operations and simplify. When exponents are used, use only positive exponents in the result. 6x2 13x +7 2x 1 -
Determine each of the following as being either true or false. If it is false, explain why.(x − 7)2 = 49 − 14x + x2
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A business website had twice as many hits on the first day of a promotion as on
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.Petroleum rights to 140 acres of land are leased for $37,000. Part of the land
Determine each of the following as being either true or false. If it is false, explain why.If 5x − 4 = 0, x = 5/4
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A vial contains 2000 mg, which is to be used for two dosages. One patient is to
Perform the indicated operations and simplify. When exponents are used, use only positive exponents in the result.(2x − 3)(x + 7)
Determine each of the following as being either true or false. If it is false, explain why.If a − bc = d, c = (d − a)/b
Perform the indicated operations and simplify. When exponents are used, use only positive exponents in the result.3x − [4x − (3 − 2x)]
Determine each of the following as being either true or false. If it is false, explain why.In setting up the solution to a word problem involving numbers of gears, it would be sufficient to “let x
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.Three meshed spur gears have a total of 107 teeth. If the second gear has 13
Solve for y: 5y − 2(y − 4) = 7
Evaluate the given expressions. (-5)(6)(-4) (-2)(3)
Evaluate the given expressions.−2 + (−5) − 3
Evaluate the given expressions. -5-12(-6)1 + -15 3
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A cell phone subscriber paid x dollars per month for the first 6 months. He then
Solve for x: 3(x − 3) = x − (2 − 3d)
Evaluate the given expressions. (-9)(-12)(-4) 24
Evaluate the given expressions.6 − 8 − (−4)
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A satellite television subscriber paid x dollars per month for the first year.
Convert 245 lb/ft3 to kg/L.
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.The sum of three electric currents that come together at a point in a circuit is
Evaluate the given expressions. 3-51-3-21- -4
Express 0.0000036 in scientific notation
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A delivery firm uses one fleet of trucks on daily routes of 8 h. A second fleet,
List the numbers −3, |−4|, −π, 2, and 0.3 in numerical order.
Evaluate the given expressions. 18 3-5 (-4)²
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A natural gas pipeline feeds into three smaller pipelines, each of which is 2.6
What fundamental law is illustrated by 3(5 + 8) = 3(5) + 3(8)?
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.At 100% efficiency two generators would produce 750 MW of power. At efficiencies
(a) How many significant digits are in the number 3.0450?(b) Round it off to two significant digits.
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A wholesaler sells three types of GPS systems. A dealer orders twice as many
Evaluate the given expressions. -(-3)² -8 (-2) 1-41
If P dollars is deposited in a bank that compounds interest n times a year, the value of the account after t years is found by evaluating P(1 + i/n)nt, where i is the annual interest rate. Find the
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A person won a state lottery prize of $20,000, from which 25% was deducted for
Evaluate the given expressions.√16 − √64
Perform the indicated operations.6LC − (3 − LC)
In finding the illuminance from a light source, the expression 8(100 − x)2 + x2 is used. Simplify this expression.
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.Train A is 520 ft long and traveling at 60.0mi/h. Train B is 440 ft long and
Evaluate the given expressions. -√81 +144
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A ski lift takes a skier up a slope at 50 m/min. The skier then skis down the
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.Two gasoline distributors, A and B, are 228 mi apart on Interstate 80. A charges
The equation L0 = L [1 + α(t2 − t1)] is used when studying thermal expansion. Solve for t2.
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.One lap at the Indianapolis Speedway is 2.50mi. In a race, a car stalls and then
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A computer chip manufacturer produces two types of chips. In testing a total of
An alloy weighing 20 lb is 30% copper. How many pounds of another alloy, which is 80% copper, must be added for the final alloy to be 60% copper?
Simplify the given expressions. Where appropriate, express results with positive exponents only. -16N-²(NT²) -2NºT-1
Simplify the given expressions. Where appropriate, express results with positive exponents only. √9 + 36
Simplify the given expressions. Where appropriate, express results with positive exponents only.√45
Simplify the given expressions. Where appropriate, express results with positive exponents only.(3a0b−2)3
Simplify the given expressions. Where appropriate, express results with positive exponents only. -35x-¹y(x²y) 5xy-1
Simplify the given expressions. Where appropriate, express results with positive exponents only. 15p¹q²r 5pq³r
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.A family has $3850 remaining of its monthly income after making the monthly
Evaluate the given expressions, all numbers are approximate. √0.1958 2.844 3.142(65)²
Set up an appropriate equation and solve. Data are accurate to two significant digits unless greater accuracy is given.Trains at each end of the 50.0-km-long Eurotunnel under the English Channel
Evaluate the given expressions.(√7)2 − 3√8

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