Elementary Technical Mathematics
11th Edition
ISBN: 9781285199191
Author: Dale Ewen, C. Robert Nelson
Publisher: Cengage Learning
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Chapter 7.3, Problem 54E
The number of people working on a project and the amount of work completed vary directly assuming all work at the same rate. If three painters can paint 12 motelrooms per day, how many painters are needed to paint 20 motel rooms per day?
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1. Abel's Theorem. The goal in this problem is to prove Abel's theorem by following a series of steps
(each step must be justified).
Theorem 0.1 (Abel's Theorem).
If y1 and y2 are solutions of the differential equation
y" + p(t) y′ + q(t) y = 0,
where p and q are continuous on an open interval, then the Wronskian is given by
W (¥1, v2)(t) = c exp(− [p(t) dt),
where C is a constant that does not depend on t. Moreover, either W (y1, y2)(t) = 0 for every t in I or
W (y1, y2)(t) = 0 for every t in I.
1. (a) From the two equations (which follow from the hypotheses),
show that
y" + p(t) y₁ + q(t) y₁ = 0 and y½ + p(t) y2 + q(t) y2 = 0,
2. (b) Observe that
Hence, conclude that
(YY2 - Y1 y2) + P(t) (y₁ Y2 - Y1 Y2) = 0.
W'(y1, y2)(t) = yY2 - Y1 y2-
W' + p(t) W = 0.
3. (c) Use the result from the previous step to complete the proof of the theorem.
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Support Department Cost Allocation—Reciprocal Services Method
Blue Africa Inc. produces laptops and desktop computers. The company’s production activities mainly occur in what the company calls its Laser and Forming departments. The Cafeteria and Security departments support the company’s production activities and allocate costs based on the number of employees and square feet, respectively. The total cost of the Security Department is $261,000. The total cost of the Cafeteria Department is $300,000. The number of employees and the square footage in each department are as follows:
Department
Employees
Square Feet
Security
10
570
Cafeteria
28
2,400
Laser
40
4,800
Forming
50
800
Using the reciprocal services method of support department cost allocation, determine the total costs from the Security Department that should be allocated to…
I need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)
Chapter 7 Solutions
Elementary Technical Mathematics
Ch. 7.1 - Express each ratio in lowest terms: 3 to 15Ch. 7.1 - Express each ratio in lowest terms: 6:12Ch. 7.1 - Express each ratio in lowest terms: 7:21Ch. 7.1 - Express each ratio in lowest terms: 422Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Express each ratio in lowest terms: 3 ft to 15 in.Ch. 7.1 - Express each ratio in lowest terms: 3 cm to 15 mmCh. 7.1 - Express each ratio in lowest terms: 1 in. to 8 ft
Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Express each ratio in lowest terms: 6 to 423Ch. 7.1 - Express each ratio in lowest terms: 513223Ch. 7.1 - Express each ratio in lowest terms: 1812214Ch. 7.1 - Express each ratio in lowest terms: 10 to 212Ch. 7.1 - Express each ratio in lowest terms: 78:916Ch. 7.1 - Express each ratio in lowest terms: 312 to 212Ch. 7.1 - Express each ratio in lowest terms: 223:334Ch. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Express each rate in lowest terms: 240mi8galCh. 7.1 - Express each rate in lowest terms: 360mi18acresCh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Express each rate in lowest terms: 625mi1212hCh. 7.1 - Prob. 30ECh. 7.1 - Express each rate in lowest terms: 214lb6galCh. 7.1 - Prob. 32ECh. 7.1 - A bearing bronze mix includes 96 lb of copper and...Ch. 7.1 - What is the alternator-to-engine drive ratio if...Ch. 7.1 - A technician measured an oil flow rate of 90 gal...Ch. 7.1 - A flywheel has 72 teeth, and a starter drive-gear...Ch. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - The resistance in ohms of a resistor is the ratio...Ch. 7.1 - A 150-bu wagon holds 2.7 tons of grain. Express...Ch. 7.1 - The total yield from a 55-acre field is 7425 bu....Ch. 7.1 - A 350-gal spray tank covers 14 acres. Find the...Ch. 7.1 - Suppose 12 gal of herbicide concentrate are used...Ch. 7.1 - A flower bed contains a mixture of 6 ft3 of...Ch. 7.1 - Prob. 46ECh. 7.1 - Suppose 16 ft of copper tubing costs $27.04. Find...Ch. 7.1 - A structure has 3290 ft2 of wall area (excluding...Ch. 7.1 - A 2150-ft2 home sells for $268,750. Find the ratio...Ch. 7.1 - You need 15 ft3 of cement to make 80 ft3 of...Ch. 7.1 - A welder has 9 pieces of 4-ft steel angle and 12...Ch. 7.1 - A welder grabs a handful of 6011 welding rods and...Ch. 7.1 - The total number of hours required for a private-...Ch. 7.1 - Two small window air conditioner units were...Ch. 7.1 - A 1-litre (1000 mL) IV bag of dextrose solution...Ch. 7.1 - Over a period of 5 h, 1200 mL of an IV solution...Ch. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - In tilapia fish farming, 5 tons of high-quality...Ch. 7.1 - Find the flow rate for each given IV (assume a...Ch. 7.1 - Prob. 62ECh. 7.1 - Find the flow rate for each given IV (assume a...Ch. 7.1 - Find the flow rate for each given IV (assume a...Ch. 7.1 - Find the length of time each IV should be...Ch. 7.1 - Prob. 66ECh. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.1 - Prob. 69ECh. 7.1 - Ann worked 6 hours and her pay was $54.60. What...Ch. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - A recipe calls for 1 gal of tomato paste and 3 qt...Ch. 7.1 - The soup of the day has water as 35% of its volume...Ch. 7.1 - Prob. 75ECh. 7.1 - 18 lb of potatoes are used in a recipe for 42...Ch. 7.2 - In each proportion, find a. the means, b. the...Ch. 7.2 - In each proportion, find a. the means, b. the...Ch. 7.2 - In each proportion, find a. the means, b. the...Ch. 7.2 - In each proportion, find a. the means, b. the...Ch. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Determine whether or not each pair of rations is...Ch. 7.2 - Determine whether or not each pair of rations is...Ch. 7.2 - Determine whether or not each pair of rations is...Ch. 7.2 - Determine whether or not each pair of rations is...Ch. 7.2 - Determine whether or not each pair of rations is...Ch. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Prob. 15ECh. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Solve each proportion (round each result to three...Ch. 7.2 - Prob. 42ECh. 7.2 - You need 234ft3 of sand to make 8 ft3 of concrete....Ch. 7.2 - Prob. 44ECh. 7.2 - A builder sells an 1800-ft2 home for $171,000....Ch. 7.2 - Suppose 826 bricks are used in constructing a wall...Ch. 7.2 - Prob. 47ECh. 7.2 - A salesperson is paid a commission of $75 for...Ch. 7.2 - A plane flies for 3 h and uses 25 gal of 100LL...Ch. 7.2 - Metal duct that is 6 in. in diameter costs $7.50...Ch. 7.2 - Suppose 20 gal of water and 3 lb of pesticide are...Ch. 7.2 - A farmer uses 150 lb of a chemical on a 40-acre...Ch. 7.2 - Suppose a yield of 100 bu of corn per acre removes...Ch. 7.2 - Prob. 54ECh. 7.2 - An orchard has 3 rows with 5 apple trees each. The...Ch. 7.2 - A 25-lb bag of fertilizer covers 1200 ft2 of lawn....Ch. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - If welding rods cost $75 per 50 lb, how much would...Ch. 7.2 - An engine with displacement of 2.0 L develops 270...Ch. 7.2 - Prob. 62ECh. 7.2 - An automobile uses 18 gal of fuel to go 560 mi....Ch. 7.2 - A fuel pump delivers 35 mL of fuel in 420 strokes....Ch. 7.2 - A label reads: 2.5 mL of solution for injection...Ch. 7.2 - Prob. 66ECh. 7.2 - You are to administer 150 mg of aminophylline from...Ch. 7.2 - Prob. 68ECh. 7.2 - When finding the percent, round to the nearest...Ch. 7.2 - When finding the percent, round to the nearest...Ch. 7.2 - Prob. 71ECh. 7.2 - When finding the percent, round to the nearest...Ch. 7.2 - When finding the percent, round to the nearest...Ch. 7.2 - Prob. 74ECh. 7.2 - When finding the percent, round to the nearest...Ch. 7.2 - Prob. 76ECh. 7.2 - When finding the percent, round to the nearest...Ch. 7.2 - Prob. 78ECh. 7.2 - Prob. 79ECh. 7.2 - Prob. 80ECh. 7.2 - Prob. 81ECh. 7.2 - Prob. 82ECh. 7.2 - Find the number of millilitres of pure ingredient...Ch. 7.2 - Prob. 84ECh. 7.2 - Prob. 85ECh. 7.2 - Prob. 86ECh. 7.2 - Prob. 87ECh. 7.2 - Prob. 88ECh. 7.2 - Prob. 89ECh. 7.2 - Prob. 90ECh. 7.2 - The ratio of beef to pork for meat loaf is 5:2....Ch. 7.2 - Prob. 92ECh. 7.2 - The following recipe is for sherry vinegar...Ch. 7.2 - Prob. 94ECh. 7.2 - The following recipe is for 16 crepes: 14 cup...Ch. 7.2 - Prob. 96ECh. 7.2 - Prob. 97ECh. 7.2 - Prob. 98ECh. 7.2 - The kitchen ratio of ingredients for tenderloin of...Ch. 7.2 - Prob. 100ECh. 7.3 - Use the map in Figure 7.2 (page 266) to find the...Ch. 7.3 - Prob. 2ECh. 7.3 - Use the map in Figure 7.2 (page 266) to find the...Ch. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Use the map in Figure 7.2 (page 266) to find the...Ch. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Use the scale drawing of a metal plate cover in...Ch. 7.3 - Use the scale drawing of a metal plate cover in...Ch. 7.3 - Use the scale drawing of a metal plate cover in...Ch. 7.3 - Use the scale drawing of a metal plate cover in...Ch. 7.3 - Use the scale drawing of a metal plate cover in...Ch. 7.3 - Use the scale drawing of a metal plate cover in...Ch. 7.3 - Use the scale drawing of a metal plate cover in...Ch. 7.3 - Use the scale drawing of a metal plate cover in...Ch. 7.3 - Use the scale drawing of a metal plate cover in...Ch. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Prob. 36ECh. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Prob. 39ECh. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Use the formulas for the hydraulic press to find...Ch. 7.3 - Distance and time vary directly when driving at a...Ch. 7.3 - Distance and the amount of gasoline used vary...Ch. 7.3 - The number of patio blocks varies directly with...Ch. 7.3 - The number of people working on a project and the...Ch. 7.4 - Fill in the blanks: Pulley A Pulley B Diameter rpm...Ch. 7.4 - Fill in the blanks: Pulley A Pulley B Diameter rpm...Ch. 7.4 - Prob. 3ECh. 7.4 - Fill in the blanks: Pulley A Pulley B Diameter Rpm...Ch. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Fill in the blanks: Pulley A Pulley B Diameter rpm...Ch. 7.4 - A small pulley is 13 in. in diameter, and a larger...Ch. 7.4 - A 21-in. pulley, rotating at 65 rpm, turns a...Ch. 7.4 - A large pulley turns at 48 rpm. A smaller pulley 8...Ch. 7.4 - Prob. 12ECh. 7.4 - A motor turning at 1870 rpm has a 4.0-in.-diameter...Ch. 7.4 - A hydraulic pump is driven with an electric motor...Ch. 7.4 - One pulley is 7 cm larger in diameter than a...Ch. 7.4 - One pulley is twice as large in diameter as a...Ch. 7.4 - Use Illustration 2 for Exercises 1718 ILLUSTRATION...Ch. 7.4 - Use Illustration 2 for Exercises 1718 ILLUSTRATION...Ch. 7.4 - Use Illustration 3 for Exercises 1920. Note:...Ch. 7.4 - Use Illustration 3 for Exercises 1920. Note:...Ch. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Fill in the blanks: Gear A Gear B Number of teeth...Ch. 7.4 - Fill in the blanks: Gear A Gear B Number of teeth...Ch. 7.4 - Prob. 26ECh. 7.4 - A small gear with 25 teeth turns a large gear with...Ch. 7.4 - A large gear with 180 teeth running at 600 rpm...Ch. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Complete the table F1 d1 F2 d2 18 lb 5 in. 9 lbCh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - In Exercises 3337, draw a sketch for each and...Ch. 7.4 - A block of steel weighing 1800 lb is to be raised...Ch. 7.4 - A rocker arm raises oil from an oil well. On each...Ch. 7.4 - A carpenter needs to raise one side of a building...Ch. 7.4 - A 1200-g mass is placed 72 cm from the fulcrum of...Ch. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - A piece of machinery weighs 3 tons. It is to be...Ch. 7.4 - The length and width vary inversely in a rectangle...Ch. 7.4 - The speed and time of travel vary inversely when...Ch. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7 - Write each ratio in lowest terms: 7 to 28Ch. 7 - Write each ratio in lowest terms: 60:40Ch. 7 - Write each ratio in lowest terms: 1 g to 500 mgCh. 7 - Write each ratio in lowest terms: 5ft6in.9ftCh. 7 - Prob. 5RCh. 7 - Prob. 6RCh. 7 - Prob. 7RCh. 7 - Prob. 8RCh. 7 - Prob. 9RCh. 7 - Prob. 10RCh. 7 - Prob. 11RCh. 7 - Prob. 12RCh. 7 - Prob. 13RCh. 7 - Prob. 14RCh. 7 - A piece of cable 180 ft long costs $67.50. How...Ch. 7 - A copper wire 750 ft long has a resistance of 1.89...Ch. 7 - A crew of electricians can wire 6 houses in 144 h....Ch. 7 - An automobile braking system has a 12-to-1 lever...Ch. 7 - Jones invests $6380 and Hernandez invests $4620 in...Ch. 7 - Prob. 20RCh. 7 - Prob. 21RCh. 7 - Prob. 22RCh. 7 - Prob. 23RCh. 7 - Prob. 24RCh. 7 - Prob. 25RCh. 7 - Prob. 26RCh. 7 - Prob. 27RCh. 7 - An object 9 ft from the fulcrum of a lever...Ch. 7 - Prob. 29RCh. 7 - The number of workers needed to complete a...Ch. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Write each ratio in lowest terms: 400 mL to 5 LCh. 7 - Prob. 4TCh. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - If 60 ft of fencing costs $138, how much does 80...Ch. 7 - Five quarts of pure antifreeze are added to 10...Ch. 7 - The scale on a map is 1 cm = 10 km. If two cities...Ch. 7 - A used automobile sells for $7500. The down...Ch. 7 - A small gear with 36 teeth turns a large gear with...Ch. 7 - A pulley is 20 cm in diameter and rotating at 150...Ch. 7 - Given the lever formula, F1d1=F2d2, and F1=800 lb,...Ch. 7 - A man who weighs 200 lb is to be raised by a lever...
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