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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Solve the indicated or given systems of equations by an appropriate algebraic method.Find the function f (x) = ax + b, if f (2) = 1 and f (−1) = −5.
Chains support a crate, as shown in Fig. 5.23. The equations relating tensions T1 and T2 are given below. Determine the tensions to the nearest 1 N from the graph. 0.8T, 0.6T₁ 0.67₂ = 12 68 +
Solve the given problems by determinants, set up appropriate systems of equations. All numbers are accurate to at least two significant digits.A company budgets $750,000 in salaries, hardware, and
Solve the indicated or given systems of equations by an appropriate algebraic method.Find the function f(x) = ax + b, if f (6) = −1 and f (−6) = 11.
Solve the given systems of equations by determinants. 7x = 2y 6 7y = 12 - 4x
Solve the given problems by determinants, set up appropriate systems of equations. All numbers are accurate to at least two significant digits.A person spent 1.10 h in a car going to an airport, 1.95
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.A new development has
Find the x- and y-intercepts of the line with the given equation. Sketch the line using the intercepts. A calculator can be used to check the graph.y = 3x + 6
Solve the indicated or given systems of equations by an appropriate algebraic method.Solve the following system of equations by (a) Solving the first equation for x and substituting,
Graphically solve the given problems. A calculator may be used.An architect designing a parking lot has a row 202 ft wide to divide into spaces for compact cars and full-size cars. The architect
Solve the given systems of equations by determinants. 3R = 8 - 51 61 = 8R + 11
Solve the indicated or given systems of equations by an appropriate algebraic method.Solve for x and y: 5 2 x + y x - y 20 2 x + y x - y + 3 نیا 2
Solve the given problems by determinants, set up appropriate systems of equations. All numbers are accurate to at least two significant digits.An intravenous aqueous solution is made from three
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.Two joggers are 2.0 mi
Find the x- and y-intercepts of the line with the given equation. Sketch the line using the intercepts. A calculator can be used to check the graph.y = −2x − 4
Graphically solve the given problems. A calculator may be used.The equations relating the currents i1 and i2 shown in Fig. 5.25 are given below. Find the currents to the nearest 0.1 A. 2i₁ + 6(i₁
Solve the given systems of equations by determinants. 90x110y = 40 30x - 15y = 25
Solve the indicated or given systems of equations by an appropriate algebraic method.Find the voltages V1 and V2 of the batteries shown in Fig. 5.28. The terminals are aligned in the same direction
Solve the given systems of equations by determinants. 0.42x0.56y= 1.26 0.98x 1.40y = -0.28
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.A shipment of 320 cell
Solve the indicated or given systems of equations by an appropriate algebraic method.A spring of length L is stretched x cm for each newton of weight hung from it. Weights of 3 N and then 5 N are
Graphically solve the given problems. A calculator may be used.A small plane can fly 780 km with a tailwind in 3 h. If the tailwind is 50% stronger, it can fly 700 km in 2 h 30 min. Find the speed p
Find the x- and y-intercepts of the line with the given equation. Sketch the line using the intercepts. A calculator can be used to check the graph.12x + y = 30
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.Two types of
Solve the indicated or given systems of equations by an appropriate algebraic method.Two grades of gasoline are mixed to make a blend with 1.50% of a special additive. Combining x liters of a grade
Find the equation of the regression line for the given data. Then use this equation to make the indicated estimate. Round decimals in the regression equation to three decimal places. Round estimates
Find the x- and y-intercepts of the line with the given equation. Sketch the line using the intercepts. A calculator can be used to check the graph.y = 0.25x + 4.5
Explain your answers, choose an exercise from among Exercises 39–48 that you think is most easily solved by the indicated method.SubstitutionData from Exercises 48Solve the given systems of
Graphically solve the given problems. A calculator may be used.A construction company placed two orders, at the same prices, with a lumber retailer. The first order was for 8 sheets of plywood and 40
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.Since ancient times, a
Find the equation of the regression line for the given data. Then use this equation to make the indicated estimate. Round decimals in the regression equation to three decimal places. Round estimates
Find the equation of the regression line for the given data. Then use this equation to make the indicated estimate. Round decimals in the regression equation to three decimal places. Round estimates
Solve the indicated or given systems of equations by an appropriate algebraic method.A 6.0% solution and a 15.0% solution of a drug are added to 200 mL of a 20.0% solution to make 1200 mL of a 12.0%
Explain your answers, choose an exercise from among Exercises 39–48 that you think is most easily solved by the indicated method.DeterminantsData from Exercises 48Solve the given systems of
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.The ratio of males to
Graphically solve the given problems. A calculator may be used.A certain car gets 21 mi/gal in city driving and 28 mi/gal in highway driving. If 18 gal of gas are used in traveling 448 mi, how many
Find the equation of the regression line for the given data. Then use this equation to make the indicated estimate. Round decimals in the regression equation to three decimal places. Round estimates
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.A machinery sales
Find the required values.Determine the values of m and b that make the following system have no solution:y = 3x - 7y = mx + b
Find the intercepts of the line X a b = 1.
Evaluate the given determinants. 4 - 1 - 1 2 8 6-2 1 - 1
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.A person’s email for a day contained a total of 78
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.The weight Wf supported by the front wheels of a
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.A boat carrying illegal
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.A moving walkway at an
Find the required values. What, if any, value(s) of m and b result in the following system having (a) One solution, (b) An unlimited number of solutions?y = -3x + by = mx + 8
Considering the slope m and the y-intercept b, explain how to determine if there is (a) A unique solution, (b) An inconsistent solution, or (c) A dependent solution.
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.A 150-m cable is cut into two pieces such that one
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.Sterling silver is 92.5%
Find the intercepts of the line y = mx + b.
The diameter of the large end, d (in in.), of a certain type of machine tool can be found from the equation d = 0.2l + 1.2, where l is the length of the tool. Sketch d as a function of l, for values
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.The torque of a force is the product of the force and
Solve the given systems of equations algebraically. 2x + y + 2 = 4 x - 2y - z = 3 3x + 3y - 2z = 1
Evaluate the given determinants. 30 22 - 12 44 -27 0 -34 -41 35
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.There are two types of offices in an office building,
Evaluate the given determinants. -2.24.1 7.0 1.2 6.4 -3.5 -7.2 2.4 -1.0
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.A surveyor measures the
Evaluate the given determinants. -500 0-500 100 200 250 300 -300 200
The points (−2, 5) and (3, 7) are on the same straight line.(a) Find another point on the line for which x = −12.(b) Find another point on the line for which y = −3.
Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.The velocity of sound in
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.In a test of a heat-seeking rocket, a first rocket is
Do the points (1, −2), (3, −3), (5, −4), (7, −6), and (11, −7) lie on the same straight line?
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.A sprinkler system is used to water two areas. If the
Write one or two paragraphs giving reasons for choosing a particular method of solving the following problem. If a first pump is used for 2.2 h and a second pump is used for 2.7 h, 1100 ft3 can
Solve for x. Here, we see that we can solve an equation in which the unknown is an element of a determinant. 12-1 -2 3 -1 2-2 X = -3
Solve the given systems of equations algebraically. 2r + s + 2t = 8 3r2s 4t = 5 -2r + 3s + 4t = -3
For the dependent system of Example 8 on page 150, both equations can be written as y = 1/3x − 3. The solution for the system can then be shown in terms of a general point on the graph as (x, =
Solve the given systems of equations by determinants. 4u 4v 2w = -4 + - 20u15v 24u 12v + 10w = -10 9w 39
Solve the given systems of equations using the rref feature on a calculator. x + y + z = 80 2x3y = -20 2x + 3z = 115
Solve the given systems of equations by determinants, the numbers are approximate. 32t+24u+63v = 32 19v 3lu +42t = 132 - 48t + 12u + 11v = 0 =
Solve the given systems of equations algebraically. 4u + 4v 2w = -4 20u15v + 10w = 24u 12v = -10 9w = 39
Solve the given systems of equations algebraically, the numbers are approximate. 3.6x + 5.2yz = -2.2 3.2x 4.8y + 3.9z = 6.4x + 4.1y + 2.3z 8.1 5.1
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.An underwater (but near the surface) explosion is
Solve the given systems of equations using the rref feature on a calculator. 5x + y - 4z 3x-5y = -5 - 6z = -20 x-3y + 82 = -27 8z
Solve the given systems of equations algebraically, the numbers are approximate. 32t + 24u+63v = 32 19v 3lu +42t = 132 48t 12u + 11v = 0
Solve the given systems of equations algebraically. x + 2y + z = 2 3x - 6y + 2z = 2 2x z = 8 -
Find the equation of the regression line for the given data. Then use this equation to make the indicated estimate. Round decimals in the regression equation to three decimal places. Round estimates
Solve the given systems of equations by determinants, the numbers are approximate. 3.6x + 5.2yz = -2.2 3.2x 4.8y + 3.9z = 8.1 6.4x + 4.1y+2.3z = 5.1
For the dependent system of Example 8 on page 150, write the form for the solution with arbitrary y. See Exercise 67.Data from Exercises 67For the dependent system of Example 8 on page 150, both
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.A small isolated farm uses a windmill and a gas
Sketch the indicated lines.In 2010, it was estimated that about 4.4 billion text messages were sent each day in the United States, and in 2020 it was estimated that this number was 6.8 billion.
Sketch the indicated lines.A straight ski run declines 80 m over a horizontal distance of 480 m. Find the equation for the height h of a skier above the bottom as a function of the horizontal
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.In an election, candidate A defeated candidate B by
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.What conclusion can you draw from a sales report that
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.In mixing a weed-killing chemical, a 40% solution of
A plane cruising at an altitude of 2.5 km starts descending so that its altitude decreases at the rate 150 m/min. Find the equation for its altitude h (in m) as a function of time t and sketch the
Sketch the indicated lines.Two electric currents, I1 and I2 (in mA), in part of a circuit in a computer are related by the equation 4I1 − 5I2 = 2. Sketch I2 as a function of I1. These
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.An airplane flies into a headwind with an effective
Sketch the indicated lines.In mixing 85-octane gasoline and 93-octane gasoline to produce 91-octane gasoline, the equation 0.85x + 0.93y = 910 is used. Sketch the graph.
What conditions must be placed on the constants of the system of equations in Exercise 65 such that the system is (a) Inconsistent?(b) Dependent?Data from Exercises 65What condition(s) must be
Solve the given systems of equations by determinants. 2x + y + z = 4 x - 2y z = 3 - 3x + 3y - 2z = 1
Solve the given systems of equations by determinants. 2r + s + 2t = 8 3r 2s 4t = 5 -2r + 3s + 4t = -3
Solve for x. Here, we see that we can solve an equation in which the unknown is an element of a determinant. 12 0-1 3 -2 2 1 X || 5
Solve for x. Here, we see that we can solve an equation in which the unknown is an element of a determinant. 지 -1 x 34 7
Solve for x. Here, we see that we can solve an equation in which the unknown is an element of a determinant. 25 1 X 3
Set up appropriate systems of two linear equations and solve the systems algebraically. All data are accurate to at least two significant digits.Regarding the forces on a truss, a report stated that
Find the equation of the regression line for the given data. Then use this equation to make the indicated estimate. Round decimals in the regression equation to three decimal places. Round estimates
Determine the value of k that makes the system dependent. 3x - ky = 6 x + 2y = 2
Determine the value of k that makes the system dependent. 5x + 20y = 15 2x + ky = 6
Determine the value of k that makes the system inconsistent. 2x - 5y = 7 kx + 10y = 2

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