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mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
Find the ninth term of the sequence (a + 2b), b,−a, . . . .
Find the first four terms of the expansion of (1 + x)−1 and then divide 1 + x into 1. Compare the results.
Solve the given problems by use of an appropriate sequence or series. All numbers are accurate to at least two significant digits.Approximate the value of (1.06)−6 by using three terms of the appropriate binomial series. Check using a calculator.
Solve the given problems by use of an appropriate sequence or series. All numbers are accurate to at least two significant digits.Approximate the value of 4√0.94 by using three terms of the appropriate binomial series. Check using a calculator.
Solve the given problems by use of an appropriate sequence or series. All numbers are accurate to at least two significant digits.If x, x + 2, x + 3 forms a geometric sequence, find x.
Solve the given problems by use of an appropriate sequence or series. All numbers are accurate to at least two significant digits.If x + 1, x2 − 2, 4x − 2 forms an arithmetic sequence, find x.
Solve the given problems by use of an appropriate sequence or series. All numbers are accurate to at least two significant digits.If x + x2 + x3 + . . . = 2, find x.
Each stroke of a pile driver moves a post 2 in. less than the previous stroke. If the first stroke moves the post 24 in., which stroke moves the post 4 in.?
Each 1.0 mm of a filter through which light passes reduces the intensity of the light by 12%. How thick should the filter be to reduce the intensity of the light to 20%?
A roof support with equally spaced vertical pieces is shown in Figure 19.13. Find the total length of the vertical pieces if the shortest one is 10.0 in. long. Fig. 19.13 10.0 in. 84.8°- 224.0 in.-
During each hour, an exhaust fan removes 15.0% of the carbon dioxide present in the air in a room at the beginning of the hour. What percent of the carbon dioxide remains after 10.0 h?
A pile of dirt and ten holes are in a straight line. It is 20 ft from the dirt pile to the nearest hole, and the holes are 8 ft apart. If a backhoe takes two trips to fill each hole, how far must it travel in filling all the holes if it starts and ends at the dirt pile?
During each microsecond, the current in an electric circuit decreases by 9.3%. If the initial current is 2.45 mA, how long does it take to reach 0.50 mA?
A machine that costs $8600 depreciates 1.0% in value each month. What is its value 5 years after it was purchased?
The level of chemical pollution in a lake is 4.50 ppb (parts per billion). If the level increases by 0.20 ppb in the following month and by 5.0% less each month thereafter, what will be the maximum level?
A piece of paper 0.0040 in. thick is cut in half. These two pieces are then placed one on the other and cut in half. If this is repeated such that the paper is cut in half 40 times, how high will the pile be?
After the power is turned off, an object on a nearly frictionless surface slows down such that it travels 99.9% as far during 1 s as during the previous second. If it travels 100 cm during the first second after the power is turned off, how far does it travel while sliding?
Under gravity, an object falls 16 ft during the first second, 48 ft during the second second, 80 ft during the third second, and so on. How far will it fall during the 20th second?
When new, an article cost $250. It was then sold at successive yard sales at 40% of the previous price. What was the price at the fourth yard sale?
A person invests $1000 each year at the beginning of the year. What is the total value of these investments after 20 years if they earn 3.5% annual interest, compounded semiannually?
An object suspended on a spring is oscillating up and down. If the first oscillation is 10.0 cm and each oscillation thereafter is 9/10 of the preceding one, find the total distance the object travels if it bounces indefinitely.
In hydrodynamics, while studying compressible fluid flow, the expressionarises. Find the first three terms of the expansion of this expression. a 1, (1+5 = m 2 m2 a/a1)
Each side of an equilateral triangle is 2 cm in length. The midpoints are joined to form a second equilateral triangle. The midpoints of the second triangle are joined to form a third equilateral triangle. Find the sum of all of the perimeters of the triangles if this process is continued
For the object in Exercise 77, what is the total distance fallen during the first 20 s?Data from Exercises 70Under gravity, an object falls 16 ft during the first second, 48 ft during the second second, 80 ft during the third second, and so on. How far will it fall during the 20th second?
During each oscillation, a pendulum swings through 85% of the distance of the previous oscillation. If the pendulum swings through 80.8 cm in the first oscillation, through what total distance does it move in 12 oscillations?
In finding the partial pressure PF of the fluorine gas under certain conditions, the equationis found. By using three terms of the expansion forapproximate the value of this expression. PE (1 + 2 x 10-10)√1+ 4 x 10-10 2 atm
A well driller charges $10.00 for drilling the first meter of a well and for each meter thereafter charges 0.20% more than for the preceding meter. How much is charged for drilling a 150m well?
In testing a type of insulation, the temperature in a room was made to fall to 2 3 of the initial temperature after 1.0 h, to 2 5 of the initial temperature after 2.0 h, to 2 7 of the initial temperature after 3.0 h, and so on. If the initial temperature was 50.0°C, what was the temperature after
Two competing businesses make the same item and sell it initially for $100. One increases the price by $8 each year for 5 years, and the other increases the price by 8% each year for 5 years. What is the difference in price after 5 years?
During 1 year a beach eroded 1.2 m to a line 48.3 m from the wall of a building. If the erosion is 0.1 m more each year than the previous year, when will the waterline reach the wall?
A wire hung between two poles is parabolic in shape. To find the length of wire between two points on the wire, the expressionis used. Find the first three terms of the binomial expansion of this expression. √1 +0.08x²
On a highway with a steep incline, the runaway truck ramp is constructed so that a vehicle that has lost its brakes can stop. The ramp is designed to slow a truck in succeeding 20-m distances by 10 km/h, 12 km/h, 14 km/h, . . . . If the ramp is 160 m long, will it stop a truck moving at 120 km/h
Each application of an insecticide destroys 75% of a certain insect. How many applications are needed to destroy at least 99.9% of the insects?
At the end of 2010 a house was valued at $375,000, and then increased in value by 5.00%, on average, each year 2011 through 2016. Its value did not change in 2017, but then decreased by 8.00%, on average, each year 2018 through 2021. What was its value at the end of 2021?
Oil pumped from a certain oil field decreases 10% each year. How long will it take for production to be 10% of the first year’s production?
Show that the middle term of a finite arithmetic sequence equals S/n, if n is odd.
The sum of three terms of a geometric sequence is −3, and the second is 6 more than the first. Find these terms.
Do the reciprocals of the terms of a geometric sequence form a geometric sequence? Explain.
The terms a, a + 12, a + 24 form an arithmetic sequence, and the terms a, a + 24, a + 12 form a geometric sequence. Find these sequences.
Derive a formula for the value V after 1 year of an amount A invested at r% (as a decimal) annual interest, compounded n times during the year. If A = $1000 and r = 0.04 (4%), write two or three paragraphs explaining why the amount of interest increases as n increases and stating your approach to
Determine if the given functions are exponential functions.(a) y = (√5)−x(b) y = −(√−5)x
Express each as a sum, difference, or multiple of logarithms. See Example 2.log5 33Data from Example 2(a) Using Eq. (13.7), we may express log4 15 as a sum of logarithms:(b) Using Eq. (13.8), we may express log4 (5/3) as the difference of logarithms:(c) Using Eq. (13.9), we may express log4 (t2) as
Express each as a sum, difference, or multiple of logarithms. See Example 2.log3 14Data from Example 2(a) Using Eq. (13.7), we may express log4 15 as a sum of logarithms:(b) Using Eq. (13.8), we may express log4 (5/3) as the difference of logarithms:(c) Using Eq. (13.9), we may express log4 (t2) as
Determine the value of x.log4 (sin x) = −0.5
Express the given equations in logarithmic form.3−2 = 1/9
Evaluate:2 ln 0.9523/log 6066.
Plot the graphs of the given functions on semilogarithmic paper.y = 4x3 + 2x2
Use logarithms to the base 10 to find the indicated logarithms.log2 86
Solve the given equations.5x−1 = 0.07
Find the common logarithm of each of the given numbers by using a calculator.tan 12.6
Express the given equations in logarithmic form.4−2 = 1/16
Determine the value of x.log8 32 = x + 1
Use logarithms to the base 10 to find the indicated logarithms.log100 3720
Find the antilogarithm of each of the given logarithms by using a calculator.0.929
Perform the indicated operations if the given changes are made in the indicated examples of this section.In Example 4(b), change the 1/2 to 5/2 and then make any other necessary changes.Data From Example 4(b)Given log4y = 1/2, in exponential form it becomes y = 41/2 , or y = 2.
Evaluate the exponential function y = 4x for the given values of x.x = −0.5
An equation used for a certain electric circuit is ln i − ln I = −t/RC. Solve for i.
Express each as a sum, difference, or multiple of logarithms. See Example 2.log2 (a3)Data from Example 2(a) Using Eq. (13.7), we may express log4 15 as a sum of logarithms:(b) Using Eq. (13.8), we may express log4 (5/3) as the difference of logarithms:(c) Using Eq. (13.9), we may express log4 (t2)
Express each as a sum, difference, or multiple of logarithms. See Example 2.log3 (2/11)Data from Example 2(a) Using Eq. (13.7), we may express log4 15 as a sum of logarithms:(b) Using Eq. (13.8), we may express log4 (5/3) as the difference of logarithms:(c) Using Eq. (13.9), we may express log4
Solve the given equations.0.6x = 2x2
Express the given equations in logarithmic form.81/3 = 2
Plot the graphs of the given functions on log-log paper.y = x2/3
Find the antilogarithm of each of the given logarithms by using a calculator.1.257
Use logarithms to the base 10 to find the indicated logarithms.log40 7.50 ×102
Evaluate the exponential function y = 4x for the given values of x.x = −2
Determine the value of x.log12 144 = x − 3
Express each as a sum, difference, or multiple of logarithms. See Example 2.log7 (9/2)Data from Example 2(a) Using Eq. (13.7), we may express log4 15 as a sum of logarithms:(b) Using Eq. (13.8), we may express log4 (5/3) as the difference of logarithms:(c) Using Eq. (13.9), we may express log4 (t2)
Solve the given equations.5(0.8x) = 2
Express the given equations in logarithmic form.(12)0 = 1
Plot the graphs of the given functions on log-log paper.y = √x
Find the common logarithm of each of the given numbers by using a calculator.log2 16
Use logarithms to the base 10 to find the indicated logarithms.log12 0.122
If A0 dollars are invested in a retirement account that earns 8%, compounded continuously for t years, the value A of the investment is given by A = A0e0.08t. Determine how long it takes for the investment to double in value.
Evaluate the exponential function y = 4x for the given values of x.x = 4
Determine the value of x.2 log1/2 8 = x
Solve the given equations.3(14x) = 400
Express the given equations in logarithmic form.2−6 = 1/64
Plot the graphs of the given functions on log-log paper.y = 0.01x4
Find the common logarithm of each of the given numbers by using a calculator.√274
Use logarithms to the base 10 to find the indicated logarithms.logπ 245
Evaluate it: log5 732
Evaluate the exponential function y = 4x for the given values of x.x = 0.5
Plot the graphs of the given functions on semilogarithmic paper.y = 2x3 + 6x
In a series ac circuit with a resistor, an inductor, and a capacitor, R = 6.50Ω, XC = 3.74Ω, and Z = 7.50Ω. Find XL.
Are 8j and −8j the solutions to the equation x2 + 64 = 0?
Determine if the given functions are exponential functions.(a) y = −7(−5)−x (b) y = −7(5−x)
Find the common logarithm of each of the given numbers by using a calculator.sin 45.2°
Use logarithms to the base 10 to find the indicated logarithms.log7 52
Determine the value of x.log9 x = 3
Solve the given equations.e−x = 17.54
Express the given equations in logarithmic form.27 = 128
Plot the graphs of the given functions on semilogarithmic paper.y = 2x4
Find the common logarithm of each of the given numbers by using a calculator.8.043 ×10−8
Use logarithms to the base 10 to find the natural logarithms of the given numbers.4.438 ×10−4
Perform the indicated operations on the resulting expressions if the given changes are made in the original expressions of the indicated examples of this section.In Example 5(c), change the 7’s to 5’s.Data from Example 5(c) log, √7 = log7 (71/2) = log,7 = 3
Perform the indicated operations on the resulting expressions if the given changes are made in the original expressions of the indicated examples of this section.In Example 7, change the 2 to 3.Data from Example 7Use the basic properties of logarithms to solve the following equation for y in terms
Solve for y in terms of x: 3 log7 x − log7 y = 2.
Determine if the given functions are exponential functions.(a) y = −7x (b) y = (−7)−x
Determine the value of x.log10 x = 4
Solve the given equations.3−x = 0.525
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