Elementary Technical Mathematics
11th Edition
ISBN: 9781285199191
Author: Dale Ewen, C. Robert Nelson
Publisher: Cengage Learning
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Chapter 3.2, Problem 12E
To determine
To fill: The blank in the statement, “
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3. (i) Let A, B, C, D, E be positive constants. Find the limit
n³ D
lim A(BC)³ +1 en 4+E.
n→∞
[6 Marks]
(ii) Let X be a random variable with the standard normal distribution,
i.e. X has the probability density function
Let
1
f(x)
√2π
n3x2
Xn = 100(50 +X6) en³4, n = 1, 2,...,
3+1
(a) Find the limit lim∞ Xn, verify your answer.
Y = 100(50 +X) 22.
[6 Marks]
(b) Is Xn≤Y? Verify your answer.
[6 Marks]
(c) Is EY∞o? Verify your answer.
[6 Marks]
(d) Does lim∞ EXn
(e) Find lim∞ EXn.
Elim Xn? Why?
[6 Marks]
[3 Marks]
Set up a free RStudio account at posit.cloud. At the start of your R session, you should enter the following commands.
set.seed(1)
e<-rnorm(n = 100,mean = 0,sd = 80)
x<-seq(1,100,1)
y<-10+15*x + e
Follow the examples in the Panopto Videos to use R to obtain the values requested below. (As always, if you round your answers, make sure you do so correctly and keep at least
three decimal places.)
(a) The smallest value of y =
(b) The largest value of y =
(c) The standard deviation of y =
(d) The mean of y =
(e) The median of y =
(f) The correlation between x and y =
:
(g) Using the variable e as data, the p-value for a test of Hoμ = 0 vs. HA μ0 is
3. (i) Using the definition of the line integral of a vector field, calculate the
line integral
L³
F.dy
of the vector field F: R² → R² given by
F(x, y) = (y, x),
and where the curve & is the unit semi-circle centred at the origin, located in
the upper half-plane and oriented in the anticlockwise direction.
Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9
in the Notes).
[20 Marks]
(ii) Calculate the same integral using Green's Theorem.
[10 Marks]
Chapter 3 Solutions
Elementary Technical Mathematics
Ch. 3.1 - Give the metric prefix for each value: 1000Ch. 3.1 - Give the metric prefix for each value: 100Ch. 3.1 - Give the metric prefix for each value: 0.01Ch. 3.1 - Give the metric prefix for each value: 0.1Ch. 3.1 - Give the metric prefix for each value: 0.001Ch. 3.1 - Give the metric prefix for each value: 10Ch. 3.1 - Give the metric prefix for each value: 1,000,000Ch. 3.1 - Give the metric prefix for each value: 0.000001Ch. 3.1 - Give the SI symbol for each prefix: hectoCh. 3.1 - Give the SI symbol for each prefix: kilo
Ch. 3.1 - Give the SI symbol for each prefix: deciCh. 3.1 - Give the SI symbol for each prefix: milliCh. 3.1 - Give the SI symbol for each prefix: centiCh. 3.1 - Prob. 14ECh. 3.1 - Give the SI symbol for each prefix: microCh. 3.1 - Give the SI symbol for each prefix: megaCh. 3.1 - Write the abbreviation for each quantity: 65...Ch. 3.1 - Write the abbreviation for each quantity: 125...Ch. 3.1 - Write the abbreviation for each quantity: 82...Ch. 3.1 - Write the abbreviation for each quantity: 205...Ch. 3.1 - Write the abbreviation for each quantity: 36...Ch. 3.1 - Write the abbreviation for each quantity: 75...Ch. 3.1 - Write the abbreviation for each quantity: 19...Ch. 3.1 - Write the abbreviation for each quantity: 5...Ch. 3.1 - Prob. 25ECh. 3.1 - Write the SI unit for each abbreviation: 15 LCh. 3.1 - Write the SI unit for each abbreviation: 36 kgCh. 3.1 - Write the SI unit for each abbreviation: 85 mmCh. 3.1 - Prob. 29ECh. 3.1 - Write the SI unit for each abbreviation: 9damCh. 3.1 - Write the SI unit for each abbreviation: 135 mLCh. 3.1 - Prob. 32ECh. 3.1 - Write the SI unit for each abbreviation: 45 mACh. 3.1 - Write the SI unit for each abbreviation: 75 MWCh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - The basic SI unit of electric current is ____.Ch. 3.1 - Prob. 38ECh. 3.1 - The common SI units of volume are ____ and ____.Ch. 3.1 - Prob. 40ECh. 3.2 - Which is longer? 1metreor1millimetreCh. 3.2 - Prob. 2ECh. 3.2 - Which is longer? 1metreor1kilometreCh. 3.2 - Prob. 4ECh. 3.2 - Which is longer? 1centimetreor1millimetreCh. 3.2 - Which is longer? 1killometreor1centimetreCh. 3.2 - Fill in each blank: 1m=mmCh. 3.2 - Fill in each blank: 1km=mCh. 3.2 - Fill in each blank: 1cm=mCh. 3.2 - Fill in each blank: 1m=cmCh. 3.2 - Fill in each blank: 1m=kmCh. 3.2 - Prob. 12ECh. 3.2 - Fill in each blank: 1mm=mCh. 3.2 - Prob. 14ECh. 3.2 - Fill in each blank: 1cm=mmCh. 3.2 - Fill in each blank: 1mm=cmCh. 3.2 - Fill in each blank: 1dam=dmCh. 3.2 - Prob. 18ECh. 3.2 - Which metric unit (km,m,cm,ormm ) should you use...Ch. 3.2 - Which metric unit (km,m,cm,ormm ) should you use...Ch. 3.2 - Prob. 21ECh. 3.2 - Which metric unit (km,m,cm,ormm ) should you use...Ch. 3.2 - Which metric unit (km,m,cm,ormm ) should you use...Ch. 3.2 - Which metric unit (km,m,cm,ormm ) should you use...Ch. 3.2 - Which metric unit (km,m,cm,ormm ) should you use...Ch. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Fill in each blank with the most reasonable unit...Ch. 3.2 - Prob. 31ECh. 3.2 - Fill in each blank with the most reasonable unit...Ch. 3.2 - Prob. 33ECh. 3.2 - Fill in each blank with the most reasonable unit...Ch. 3.2 - Prob. 35ECh. 3.2 - Fill in each blank with the most reasonable unit...Ch. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Read the measurements indicated by the letters on...Ch. 3.2 - Use a metric ruler to measure each line segment....Ch. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Change 675 m to km.Ch. 3.2 - Change 450 cm to m.Ch. 3.2 - Change 1540 mm to m.Ch. 3.2 - Change 3.2 km to m.Ch. 3.2 - Change 65 cm to m.Ch. 3.2 - Change 1.4 m to mm.Ch. 3.2 - Chagne7.3 m to cm.Ch. 3.2 - Change 0.25 km to m.Ch. 3.2 - Change 1250 m to km.Ch. 3.2 - Change 4.5 m to cm.Ch. 3.2 - Change 275 mm to cm.Ch. 3.2 - Change 48 cm to mm.Ch. 3.2 - Change 125 mm to cm.Ch. 3.2 - Change 0.75 m to m.Ch. 3.2 - Prob. 63ECh. 3.3 - Which is larger? 1 gram or 1 milligramCh. 3.3 - Which is larger? 1 gram or 1 kilogramCh. 3.3 - Which is larger? 1 milligram or 1 kilogramCh. 3.3 - Which is larger? 1 metric ton or 1 kilogramCh. 3.3 - Which is larger? 1 milligram or 1 microgramCh. 3.3 - Which is larger? 1 kilogram or 1 microgramCh. 3.3 - Fill in each blank: 1g=mgCh. 3.3 - Fill in each blank: 1kg=gCh. 3.3 - Fill in each blank: 1cg=gCh. 3.3 - Fill in each blank: 1mg=gCh. 3.3 - Fill in each blank: 1metricton=kgCh. 3.3 - Fill in each blank: 1g=cgCh. 3.3 - Fill in each blank: 1mg=gCh. 3.3 - Fill in each blank: 1g=mgCh. 3.3 - Which metric unit (kg, g, mg, or metric ton)...Ch. 3.3 - Which metric unit (kg, g, mg, or metric ton)...Ch. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Which metric unit (kg, g, mg, or metric ton)...Ch. 3.3 - Prob. 20ECh. 3.3 - Which metric unit (kg, g, mg, or metric ton)...Ch. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Which metric unit (kg, g, mg, or metric ton)...Ch. 3.3 - Prob. 25ECh. 3.3 - Fill in each blank with the most reasonable unit...Ch. 3.3 - Prob. 27ECh. 3.3 - Fill in each blank with the most reasonable unit...Ch. 3.3 - Prob. 29ECh. 3.3 - Fill in each blank with the most reasonable unit...Ch. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Change 875 g to kg.Ch. 3.3 - Change 127 mg to g.Ch. 3.3 - Change 85 g to mg.Ch. 3.3 - Change 1.5 kg to g.Ch. 3.3 - Change 3.6 kg to g.Ch. 3.3 - Change 430 g to mg.Ch. 3.3 - Change 270 mg to g.Ch. 3.3 - Change 1350 g to kg.Ch. 3.3 - Change 885 g to mg.Ch. 3.3 - Change 18 mg to g.Ch. 3.3 - Change 375 g to mg.Ch. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.4 - Which is larger? 1 litre or 1 millilitreCh. 3.4 - Which is larger? 1 millilitre or 1 kilolitreCh. 3.4 - Which is larger? 1 cubic millimeter or 1 cubic...Ch. 3.4 - Which is larger? 1 cubic metre or 1 litreCh. 3.4 - Which is larger? 1 square kilometer or 1 hectreCh. 3.4 - Which is larger? 1 square centimeter or 1 square...Ch. 3.4 - Fill in each blank: 1L=mLCh. 3.4 - Fill in each blank: 1mL=LCh. 3.4 - Fill in each blank: 1m3=cm3Ch. 3.4 - Fill in each blank: 1mm3=cm3Ch. 3.4 - Fill in each blank: 1cm2=mm2Ch. 3.4 - Fill in each blank: 1km2=haCh. 3.4 - Fill in each blank: 1m3=LCh. 3.4 - Prob. 14ECh. 3.4 - Which metric unit (m3,L,mL,m2,cm2,orha) should you...Ch. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Which metric unit (m3,L,mL,m2,cm2,orha) should you...Ch. 3.4 - Prob. 19ECh. 3.4 - Which metric unit (m3,L,mL,m2,cm2,orha) should you...Ch. 3.4 - Which metric unit (m3,L,mL,m2,cm2,orha) should you...Ch. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Which metric unit (m3,L,mL,m2,cm2,orha) should you...Ch. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Fill in each blank with the most reasonable unit...Ch. 3.4 - Fill in each blank with the most reasonable unit...Ch. 3.4 - Prob. 29ECh. 3.4 - Fill in each blank with the most reasonable unit...Ch. 3.4 - Prob. 31ECh. 3.4 - Fill in each blank with the most reasonable unit...Ch. 3.4 - Prob. 33ECh. 3.4 - Fill in each blank with the most reasonable unit...Ch. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Fill in each blank with the most reasonable unit...Ch. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Change 0.60 L to mL.Ch. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Change 85 cm3 to mL.Ch. 3.4 - Change 650 L to m3.Ch. 3.4 - Prob. 45ECh. 3.4 - Change 18 m2 to cm2.Ch. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - What is mass of 500 mL of water?Ch. 3.4 - Prob. 50ECh. 3.4 - How many hectares are contained in a rectangular...Ch. 3.4 - How many hectares are contained in a rectangular...Ch. 3.5 - Which is larger? 1 amp or 1 milliampCh. 3.5 - Which is larger? 1 microsecond or 1 picosecondCh. 3.5 - Prob. 3ECh. 3.5 - Which is larger? 1 megawatt or 1 milliwattCh. 3.5 - Which is larger? 1 kilovolt or 1 megavoltCh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Write the abbreviation for each unit: 7 millivoltsCh. 3.5 - Write the abbreviation for each unit: 17...Ch. 3.5 - Write the abbreviation for each unit: 1.2 amperesCh. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - Write the abbreviation for each unit: 540 ohmsCh. 3.5 - Write the abbreviation for each unit: 70...Ch. 3.5 - Prob. 15ECh. 3.5 - Fill in each blank: 1mA=ACh. 3.5 - Fill in each blank: 1ns=sCh. 3.5 - Fill in each blank: 1day=sCh. 3.5 - Fill in each blank: 1A=ACh. 3.5 - Fill in each blank: 1F=FCh. 3.5 - Fill in each blank: 1V=MVCh. 3.5 - Fill in each blank: 1Hz=kHzCh. 3.5 - Prob. 23ECh. 3.5 - Change 18 kW to W.Ch. 3.5 - Change 350 ms to s.Ch. 3.5 - Change 1 h 25 min 16 s to s.Ch. 3.5 - Prob. 27ECh. 3.5 - Change 15 MV to kV.Ch. 3.5 - Change 175 F to mF.Ch. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Use figure 3.14 to choose the most reasonable...Ch. 3.6 - Fill in each blank: 77F=CCh. 3.6 - Fill in each blank: 45C=FCh. 3.6 - Fill in each blank: 325C=FCh. 3.6 - Fill in each blank: 140F=CCh. 3.6 - Fill in each blank: 16C=FCh. 3.6 - Fill in each blank: 5F=CCh. 3.6 - Fill in each blank: 16F=CCh. 3.6 - Fill in each blank: 40C=FCh. 3.6 - Fill in each blank: 78C=FCh. 3.6 - Fill in each blank: 10F=CCh. 3.7 - Fill in each blank, rounding each result to three...Ch. 3.7 - Fill in each blank, rounding each result to three...Ch. 3.7 - Fill in each blank, rounding each result to three...Ch. 3.7 - Fill in each blank, rounding each result to three...Ch. 3.7 - Fill in each blank, rounding each result to three...Ch. 3.7 - Prob. 6ECh. 3.7 - Prob. 7ECh. 3.7 - Fill in each blank, rounding each result to three...Ch. 3.7 - Fill in each blank, rounding each result to three...Ch. 3.7 - Prob. 10ECh. 3.7 - Prob. 11ECh. 3.7 - A hole is 35 mm wide. How many inches wide is it?Ch. 3.7 - The diameter of a bolt is 0.425 in. Express this...Ch. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - How many pounds does a 150-kg satellite weigh?Ch. 3.7 - An iron bar weighs 2 lb 6 oz. Express its weight...Ch. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - A micro wheel weighs 0.045 oz. What is its weight...Ch. 3.7 - A hole is to be drilled in a metal plate 5 in. in...Ch. 3.7 - A can contains 15 oz of tomato sauce. How many...Ch. 3.7 - Prob. 23ECh. 3.7 - Prob. 24ECh. 3.7 - How many ft2arein140yd2?Ch. 3.7 - How many m2arein15yd2?Ch. 3.7 - Prob. 27ECh. 3.7 - How many ft2 are in rectangle 12.6 yd long and 8.6...Ch. 3.7 - How many ft2 are in a rectangle 12.6 m long and...Ch. 3.7 - Prob. 30ECh. 3.7 - Prob. 31ECh. 3.7 - Change5473in3tocm3.Ch. 3.7 - howmanymm3areinin3?Ch. 3.7 - Howmanyin3arein25cm3?Ch. 3.7 - Prob. 35ECh. 3.7 - Prob. 36ECh. 3.7 - A commercial space 60 ft wide and 90 ft deep rents...Ch. 3.7 - A concrete sidewalk is to be built (as shown in...Ch. 3.7 - How many acres are in a rectangular field that...Ch. 3.7 - How many acres are in a rectangular field that...Ch. 3.7 - How many hectares are in the field in Exercise 39?Ch. 3.7 - Prob. 42ECh. 3.7 - A house lot measures 145 ft by 186 ft. What part...Ch. 3.7 - How many acres are in 14mi2?Ch. 3.7 - Prob. 45ECh. 3.7 - How many acres are in 520 square rods?Ch. 3.7 - A corn yield of 10,550 kg/ha is equivalent to how...Ch. 3.7 - A soybean yield of 45 by/acre is equivalent to how...Ch. 3.7 - How many acres are in eight 30-in. rows 440 yards...Ch. 3.7 - a. How many rows 30 in. apart can be planted in a...Ch. 3.7 - For Octoberfest, a vender purchased 15 kg of...Ch. 3.7 - Prob. 52ECh. 3.7 - Change25.6kg/cm2tolb/in2.Ch. 3.7 - Prob. 54ECh. 3.7 - Prob. 55ECh. 3.7 - Change415lb/ft3tog/cm3.Ch. 3 - Given the metric prefix for each value: 0.001Ch. 3 - Given the metric prefix for each value: 1000Ch. 3 - Prob. 3RCh. 3 - Give the SI abbreviation for each prefix: microCh. 3 - Prob. 5RCh. 3 - Write the SI abbreviation for each quantity: 8.3...Ch. 3 - Prob. 7RCh. 3 - Prob. 8RCh. 3 - Prob. 9RCh. 3 - Prob. 10RCh. 3 - Prob. 11RCh. 3 - Prob. 12RCh. 3 - Prob. 13RCh. 3 - Prob. 14RCh. 3 - Prob. 15RCh. 3 - Fill in each blank: 6.1kg=gCh. 3 - Prob. 17RCh. 3 - Prob. 18RCh. 3 - Prob. 19RCh. 3 - Prob. 20RCh. 3 - Prob. 21RCh. 3 - Prob. 22RCh. 3 - Prob. 23RCh. 3 - Prob. 24RCh. 3 - Prob. 25RCh. 3 - Prob. 26RCh. 3 - Prob. 27RCh. 3 - Prob. 28RCh. 3 - Prob. 29RCh. 3 - Prob. 30RCh. 3 - Prob. 31RCh. 3 - Prob. 32RCh. 3 - Prob. 33RCh. 3 - Prob. 34RCh. 3 - Prob. 35RCh. 3 - Prob. 36RCh. 3 - Prob. 37RCh. 3 - Prob. 38RCh. 3 - Prob. 39RCh. 3 - Prob. 40RCh. 3 - Prob. 41RCh. 3 - Complete the following table of metric system...Ch. 3 - Prob. 1TCh. 3 - Give the metric prefix for 0.01.Ch. 3 - Prob. 3TCh. 3 - Write the SI unit for the abbreviations 240 L.Ch. 3 - Write the abbreviation for 30 hectograms.Ch. 3 - Which is longer, 1 km or 25 cm?Ch. 3 - Prob. 7TCh. 3 - Fill in each blank: 7.28mm=mCh. 3 - Prob. 9TCh. 3 - Fill in each blank: 256hm=cmCh. 3 - Prob. 11TCh. 3 - Fill in each blank: 16.2g=mgCh. 3 - Prob. 13TCh. 3 - Fill in each blank: 310g=cgCh. 3 - Prob. 15TCh. 3 - Fill in each blank: 1.52dL=LCh. 3 - Fill in each blank: 175L=m3Ch. 3 - Prob. 18TCh. 3 - Prob. 19TCh. 3 - Fill in each blank: 0.2L=mLCh. 3 - Prob. 21TCh. 3 - Prob. 22TCh. 3 - Prob. 23TCh. 3 - Fill in each blank: 13.9mA=ACh. 3 - Prob. 25TCh. 3 - What is the basic SI unit for temperature?Ch. 3 - What is the freezing temperature of water on the...Ch. 3 - Fill in each blank, rounding each result of three...Ch. 3 - Prob. 29TCh. 3 - Fill in each blank, rounding each result of three...Ch. 3 - Prob. 31TCh. 3 - Fill in each blank, rounding each result of three...Ch. 3 - Prob. 33TCh. 3 - Fill in each blank, rounding each result of three...Ch. 3 - Prob. 35T
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