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mathematics
basic technical mathematics

Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions

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 rule, determine the volume of soil to be removed. Dist. (ft) Area (ft²) 0 560 250 500 750 1000 1250
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 center of the Earth to the end of the shadow due to the rays from the sun?
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. 2.145 4.75 ft
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 pier is 6.75 m, what is the volume of concrete in the pier?
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 increase in length causes a bend straight up in the middle of the track, how high is the top of the bend?
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 where it is attached. How long is the guy wire?
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 starting point. How far is she (on a straight line) from her starting point?
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 (not including any floor area).
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 cylinder, can you tell me the radius of each, if the radii are equal?”Data from Exercises 82An
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 is 1620 km. What area does the hurricane cover? Neglect the curvature of the Earth and any possible
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) 921 ft on a side, with a diagonal of length 1490 ft. Using these data, draw a sketch and write one or
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 same amount of pollutant after 5.0h as it had in 3.0h. Before the installation the exhaust contained
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 complex, an architect planned to use 34 energy-efficient ceiling lights using a total of 1000 W. Two
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 Example 3A medical researcher finds that a given sample of an experimental drug can be divided into 4
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 spacecraft maneuvers so that it may “capture” an already orbiting satellite that is 6000 km ahead. If the
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 Example 5A refinery has 7250 L of a gasoline-methanol blend that is 6.00% methanol. How much pure
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. Together a new model today and 6 years ago cost $64,000. What was the cost of each?
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 stream. In 1 h, 1.98 ×107ft3 flow into the lake from the two streams. What is the flow rate of each?
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. There were 500,000 more recycled the second year than the first year. How many are recycled each year?
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 the second day. If the total number of hits for both days was 495,000, find the number of hits 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 leases for $200 per acre, and the reminder for $300 per acre. How much is leased at each price?
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 be administered 660 mg more than another. How much should be administered to each?
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 = the first gear.”
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 more teeth than the first and the third has 15 more teeth than the second, how many teeth does each
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 increased his data plan, and his bill increased by $10 per month for the next 4 months. If he paid
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. Her monthly bill increased by $30 per month for the second and third years, and then another $20 for
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 zero. If the second current is twice the first and the third current is 9.2μA more than the
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, with five more trucks than the first, is used on daily routes of 6 h. Budget allotments allow for
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 km longer than the main pipeline. The total length of the four pipelines is 35.4 km. How long is
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 of 65% and 75%, they produce 530 MW. At 100% efficiency, what power would each produce?
(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 economy systems at $40 each, and 75 more econoplus systems at $80 each, than deluxe systems at $140
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 value of an account for which P = $1000, i = 2%, n = 2, and t = 3 years (values are exact).
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 taxes. The remainder was invested, partly for a 40% gain, and the rest for a 10% loss. How much was
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 traveling at 40mi/h in the opposite direction of train A on an adjacent track. How long does it take
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 slope at 150 m/min. If a round trip takes 24 min, how long is the slope?
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 $2.90/gal and B charges $2.70/gal. Each charges 0.2¢/gal per mile for delivery. Where on
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 starts 30.0s after a second car. The first car travels at 260ft/s, and the second car travels at
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 6100 chips of both types, 0.50% of one type and 0.80% of the other type were defective. If a total
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 mortgage payment, which is 23.0% of the monthly income. How much is the mortgage payment?
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 start at the same time into the tunnel. Find their speeds if the train from France travels 8.0 km/h
Evaluate the given expressions.(√7)2 − 3√8

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