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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Determine whether or not the given pair of values is a solution of the given system of linear equations. 1- = ܕi = 1, i 5 = ܕI + 61 - 3 — 4i, = -
Evaluate the given determinants. -18-33 -21 44
Evaluate the given third-order determinants. 9-20 3-6 -4-6-2 -1
Evaluate the given determinants. -20 110 -70-80
Determine whether or not the given pair of values is a solution of the given system of linear equations. 3x - 2y = 2.2 5x + y = 2.8 x = 0.6, y = -0.2
Evaluate the given determinants. -6.5 12.2 -15.5 34.6
Solve the given systems of equations. 3x - 7y + 3z = 6 3x + 3y + 6z = 1 5x - 5y + 2z = 5 =
Solve the given systems of equations by the method of elimination by substitution. 2x + 3y = 7 6x - y = 1
Evaluate the given determinants. 0.91 -1.2 0.73 -5.0
Evaluate the given third-order determinants. 20 18-50 -15 24-12 -20 55 -22
Solve the given systems of equations. 18x + 24y + 4z = 46 63x + 6y - 15z = -75 -90x + 30y 20z = -55
Determine whether or not the given pair of values is a solution to the given linear equation in two unknowns.−3x + 5y = 13; (−1, 2), (4, 5)
Solve the given systems of equations by the method of elimination by substitution. 6s+ 6 = 3 4s - 2t = 17
Determine whether or not the given pair of values is a solution of the given system of linear equations. 7t - s = 2s + t = 3.2 2.5 S = -1.1, t = 0.3
Determine whether or not the given pair of values is a solution to the given linear equation in two unknowns.4y − x = −10; (2, −2), (2, 2)
Solve the given systems of equations. 10x + 15y 25z = 35 - 40x - 30y 20z = 10 16x - 2y + 8z = 6
Evaluate the given third-order determinants. 20 -4 0-15 1 40 30 6 -1
Evaluate the given determinants. 0.75 -1.32 0.15 1.18
Solve for y by determinants: 3x + 2y 2xy z = 4 + 3z = -2 x + 4z = 5
Solve the given systems of equations by the method of elimination by substitution. 33x + 2y = 34 40y = 9x + 11
By volume, one alloy is 60% copper, 30% zinc, and 10% nickel. A second alloy has percents of 50, 30, and 20, respectively. A third alloy is 30% copper and 70% nickel. How much of each alloy is needed
Evaluate the given determinants. 0.20 -0.05 0.28 0.09
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. y = -x + 4 y = x - 2
For each given value of x, determine the value of y that gives a solution to the given linear equation in two unknowns.3x − 2y = 12; x = 2, x = −3
Evaluate the given third-order determinants. 0.1 -0.5 -2 -0.2 1 0.8 0 0.4 2
Solve the given systems of equations. 2i₁ 41₂ 413 = 3 - 3i₁ +8₂ +213 = -11 4i₁ + 61₂ 13 = -8 -
Evaluate the given determinants. -8-4 -32 16
Solve the given systems of equations by the method of elimination by substitution. 3A 3B-1 5A6B-1
For each given value of x, determine the value of y that gives a solution to the given linear equation in two unknowns.6y − 5x = 60; x = −10, x = 8
Evaluate the given third-order determinants. 0.25 -0.54 -0.42 1.20 0.35 0.28 -0.50 0.12 -0.44
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. y = 2x - 6 y = -x + 1
Find the slopes of the lines that pass through the given points.(−1, −5), (−4, 4)
Solve the given systems of equations by use of determinants. 2x + 3y + z = 4 3x -z = -3 x - 2y + 2z -5
Solve the given systems of equations by the method of elimination by addition or subtraction. x + 2y = 5 x - 2y = 1
Solve the given systems of equations using the reduced row echelon form (rref) feature on a calculator. -x + 3y2z = 7 3x + 4y - 7z = -8 x + 2y + z = 2
Find the slopes of the lines that pass through the given points. (-6, 1), (1,-)
For each given value of x, determine the value of y that gives a solution to the given linear equation in two unknowns.x − 4y = 2; x = 3, x = −0.4
Evaluate the given determinants. 43 - 81 -7 16
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. 2y = x - 8 y = 2x + 2
Find the slopes of the lines that pass through the given points.(40, −20), (−30, −40)
Solve the given systems of equations by the method of elimination by addition or subtraction. x + 3y = 7 2x + 3y = 5
For each given value of x, determine the value of y that gives a solution to the given linear equation in two unknowns.3x - 2y = 9; x = 2/3, x = -3
Solve the given systems of equations using the reduced row echelon form (rref) feature on a calculator. 3a + 2b + c = 20 4a 10c-10 -a - 2b + 2c 2b 2c = -1
Use a calculator to solve the given equations to the nearest 0.1. 5 3 V = v + 4 V
The distance p (in m) from a camera with a 50-mm lens to the object being photographed is a function of the magnification m of the camera, given byPlot the graph for positive values of m up to 0.50.
The pressure loss L (in lb/in.2) of a fire hose as a function of its flow rate Q (in 100 gal/min) is L = 1.2Q2 + 1.5Q. Find L for Q = 450 gal/min.
A land developer is considering several options of dividing a large tract into rectangular building lots, many of which would have perimeters of 200 m. For these, the minimum width would be 30 m and
Solve the indicated equations graphically. Assume all data are accurate to two significant digits unless greater accuracy is given.Two cubical coolers together hold 40.0 L (40, 000 cm3). If the
In Example 3, change 53´ to 35´ and then find the decimal form.Data from Example 3(a) We change 17°53´ to decimal form by using the fact that 1° = 6´. This means that 53 = (53/60)° = 0.88°
Describe the values of x and y for which (1,−2), (−1,−2), and (x, y) are on the same straight line.
Make the given changes in the indicated examples of this section and then find the indicated values.In Example 6, change 0.354 to 0.345 and then find the angle.Data from Example 6To find the value of
Solve the indicated equations graphically. Assume all data are accurate to two significant digits unless greater accuracy is given.The height h (in ft) of a rocket as a function of time t (in s) of
Sketch the graph of a function for which the domain is 0 ≤ x ≤ 4 and the range is −5 ≤ y ≤ −2.
In Example 4, find another standard-position angle that has the same terminal side as the angle in Fig. 4.8(c).Data from Example 4(c)A third-quadrant angle of 225° is shown in Fig. 4.8(c).
Solve the indicated equations graphically. Assume all data are accurate to two significant digits unless greater accuracy is given.The length of a rectangular solar panel is 32 in. more than its
Make the given changes in the indicated examples of this section and then find the indicated values.In Example 7, change sinθ to tanθ and then find the value.Data from Example 7Find sinθ if secθ
Find the value of tan 73.8°.
In Example 4, find another standard-position angle that has the same terminal side as the angle in Fig. 4.8(e).Data from Example 4(e)A standard-position angle of −120° is shown in Fig. 4.8(e).
Determine each of the following as being either true or false.cscθ and sin−1θ are the same.
A straight 120̅ -ft culvert is built down a hillside that makes an angle of 25.0° with the horizontal. Find the height of the hill.
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.B = 64.3°, b = 0.652Data from
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(6, 8)
Draw appropriate figures and verify through observation that only one triangle may contain the given parts (that is, any others which may be drawn will be congruent).A 60° angle included between
Express the given angles in decimal form.574°45´
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(√3, 2)
Find the values of the trigonometric functions. Round off results according to Table 4.1.cot 57.86°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
As a fighter jet was coming in for a landing, it was 325 ft above ground when it was directly above the end of the landing strip. If it then came in at a constant angle of 6.5° with the landing
Determine one positive and one negative coterminal angle for each angle given.278.1°
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.b = 82.0, c = 881Data from Table
Determine the trigonometric functions of an angle in standard position if its terminal side passes through (5, 2). Give answers in exact and decimal forms.
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.a = 5920, b = 4110Data from Table
Express the given angles in decimal form.−83°21´
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(7, 7)
Find the values of the trigonometric functions. Round off results according to Table 4.1.csc 22.81°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
From a point on the South Rim of the Grand Canyon, it is found that the angle of elevation of a point on the North Rim is 1.2°. If the horizontal distance between the points is 9.8 mi, how much
A surveyor sights two points directly ahead. Both are at an elevation 18.525 m lower than the observation point. How far apart are the points if the angles of depression are 13.500° and 21.375°,
Determine one positive and one negative coterminal angle for each angle given.−197.6°
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.A = 32.10°, c = 56.85Data from
The loading ramp at the back of a truck is 9.50 ft long, and the top of the ramp is 2.50 ft above the ground. How much longer should the ramp be to reduce the angle it makes with the ground to 4.50°?
Express the given angles in decimal form.321°27´
Find the values of the trigonometric functions. Round off results according to Table 4.1.sec 80.4°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(840, 130)
Sketch an appropriate figure, unless the figure is given.What is the steepest angle between the surface of a board 3.50 cm thick and a nail 5.00 cm long if the nail is hammered into the board such
By means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest 0.01°.0.675 rad
Express the given angles to the nearest minute.17.5°
Explain your answers, choose an exercise from among Exercises 39–48 that you think is most easily solved by the indicated method.Addition or subtractionData from Exercises 48Solve the given systems
In order to make the coefficients easier to work with, first multiply each term of the equation or divide each term of the equation by a number selected by inspection. Then proceed with the solution
Solve the given systems of equations by determinants. r = -3s - 2 - 2r9s = 2
Solve the given systems of equations by determinants. All numbers are accurate to at least two significant digits.The area of a quadrilateral iswhere (x0, y0), (x1 , y1), (x2, y2), and (x3, y3) are
The forces acting on part of a structure are shown in Fig. 5.22. An analysis of the forces leads to the equationsAre the forces F1 = 45 and F2 = 28 N? 0.80F, +0.50F₂ 0.60F₁ 50 - 0.87F₂ = 12
Solve the given systems of equations by determinants. All numbers are accurate to at least two significant digits.An airplane begins a flight with a total of 36.0 gal of fuel stored in two separate
In order to make the coefficients easier to work with, first multiply each term of the equation or divide each term of the equation by a number selected by inspection. Then proceed with the solution
The electric resistance R of a certain resistor is a function of the temperature T given by the equation R = aT + b, where a and b are constants. If R = 1200Ω when T = 10.0°C and R = 1280Ω when T
Solve the given systems of equations by determinants. 27v 29 69 10i 40i + 33v =
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.3x + y = 3
Solve the given systems of equations by determinants. All numbers are accurate to at least two significant digits.In applying Kirchhoff’s laws (see the chapter introduction; the equations can be
A student earned $4000 during the summer and decided to put half into an IRA (Individual Retirement Account). If the IRA was invested in two accounts earning 4.0% and 5.0%, the total income for the
Solve the given problems by determinants, set up appropriate systems of equations. All numbers are accurate to at least two significant digits.An alloy used in electrical transformers contains nickel
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.4x − 3y = 12
Solve the given systems of equations by determinants. 3x - бу = 5 2y + 7x = 4

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