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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Factor the given expressions completely. Each is from the technical area indicated.V2 − 2nBV + n2B2 (chemistry)
Factor the given expressions completely. Each is from the technical area indicated.a4 + 8a2π2f2 + 16π4f4 (periodic motion: energy)
Evaluate the given expressions by using factoring. The results may be checked with a calculator. 59 57 72 - 5²
Factor the given expressions completely. Each is from the technical area indicated.wx 4 − 5wLx 3 + 6wL2x2 (beam design)
Factor the given expressions completely. Each is from the technical area indicated.1 − 2r2 + r4 (lasers)
Factor the given expressions completely. Each is from the technical area indicated.3Adu2 − 4Aduv + Adv2 (water power)
Factor n2 + n, and then explain why it represents a positive even integer if n is a positive integer.
Factor the given expressions completely. Each is from the technical area indicated.k2A2 + 2kλA + λ2 − α2 (robotics)
Factor n3 − n, and then explain why it represents a multiple of 6 if n is an integer greater than 1.
Find the two integer values of k that make 4x2 + kx + 9 a perfect square trinomial.
Factor the expressions completely2Q2 + 2 (fire science)
Find the two integer values of k that make 16y2 + ky + 25 a perfect square trinomial.
Factor the expressions completely.4d2D2 − 4d3D − d4 (machine design)
Find six values of k such that x2 + kx + 18 can be factored.
Factor the expressions completely.81s − s3 (rocket path)
Explain why most students would find 24x2 − 23x − 12 more difficult to factor than 23x2 − 18x − 5.
Factor the expressions completely.12(4 − x2) − 2x(4 − x2) − (4 − x2)2 (container design)
Factor the expressions completely.rR2 − r3 (pipeline flow)
When an object is thrown upward with an initial velocity of v0 (in ft/s) from an initial height of s0 (in ft), its height after t seconds is given by −16t2 + v0t + s0. Find an expression for
When an object is thrown upward with an initial velocity of v0 (in ft/s) from an initial height of s0 (in ft), its height after t seconds is given by −16t2 + v0t + s0. Find an expression for
Factor the expressions completely.p1R2 – p1r2 – p2R2 + p2r2
Factor the expressions completely, it is necessary to set up the proper expression. Each expression comes from the technical area indicated.A square as large as possible is cut from a circular metal
Factor the expressions completely, it is necessary to set up the proper expression. Each expression comes from the technical area indicated.A pipe of outside diameter d is inserted into a pipe of
A spherical float has a volume of air within it of radius r1, and the outer radius of the float is r2. Express in factored form the difference in areas of the outer surface and the inner surface.
The kinetic energy of an object of mass m traveling at velocity v is given by 1/2mv2. Suppose a car of mass m0 equipped with a crash-avoidance system automatically applies the brakes to avoid a
Solve for the indicated variable. Each equation comes from the technical area indicated.i1R1 = (i2 − i1)R2, for i1 (electricity: ammeter)
Solve for the indicated variable. Each equation comes from the technical area indicated.(factor resulting denominator radiation) R = KT₂ - KT₁4, for k
Solve for the indicated variable. Each equation comes from the technical area indicated.nV + n1v = n1V, for n1 (acoustics)
Solve for the indicated variable. Each equation comes from the technical area indicated.3BY + 5Y = 9BS, for B (physics: elasticity)
Solve for the indicated variable. Each equation comes from the technical area indicated.Sq + Sp = Spq + p, for q (computer design)
Solve for the indicated variable. Each equation comes from the technical area indicated.ER = AtT0 − AtT1, for t (energy conservation)
Change the given angles to equal angles expressed to the nearest second.86.274°
Change the given angles to equal angles expressed to the nearest second.257.019°
Assume θ is an acute angle with the given trigonometric function value. Find the exact coordinates of the point where the terminal side of θ (in standard position) intersects the unit circle. sin
Explain why the given statements are true for an acute angle θ.sin θ + cos θ > 1, if θ is acute.
The given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.12 rad, −2 rad
Solve the right triangles with the given parts. Refer to Fig. 4.68.A = 17.0°, b = 6.00 A C b Fig. 4.68 B a C
Solve the right triangles with the given parts. Refer to Fig. 4.68.B = 68.1°, a = 1080 A C b Fig. 4.68 B a C
Explain why the given statements are true for an acute angle θ.If θ < 45°, sinθ < cosθ
Assume θ is an acute angle with the given trigonometric function value. Find the exact coordinates of the point where the terminal side of θ (in standard position) intersects the unit circle.tan θ
Change the given angles to equal angles expressed in decimal form to the nearest 0.001°.21°42´36"
Find the values of the indicated trigonometric functions if θ is an acute angle.Find sinθ, given tanθ = 1.936.
Change the given angles to equal angles expressed in decimal form to the nearest 0.001°.−107°16'23''
Find the values of the indicated trigonometric functions if θ is an acute angle.Find cosθ, given sinθ = 0.6725.
Find the values of the indicated trigonometric functions if θ is an acute angle.Find tan θ, given sec θ = 1.3698.
Solve the right triangles with the given parts. Refer to Fig. 4.68.a = 81.0, b = 64.5 A C b Fig. 4.68 B a C
Find the area of the patio shown in Fig. 4.77. 76.0⁰ 12.8 ft 28.0° Fig. 4.77
Answer the given questions about the indicated examples of this section.In the first line of Example 10, if − is changed to +, what changes occur in the graph?Data from Example 10Sketch the graph
Solve the given systems of equations. x + y − z = -3 x + z = 2 2xy + 2z = 3
In Example 8, by changing what one number in the first equation does the system become (a) Inconsistent? (b) Consistent?Data from Example 8Solve the system of equations x − 3y = 9 −2x +
Evaluate the given third-order determinants. -7 0 0 245 142
Solve by substitution: x + 2y = 5 4y = 3 - 2x
Determine each of the following as being either true or false. If it is false, explain why.One method of finding the solution of the system of equations 2x + 3y = 8, x − y = 3, would be by
In Example 5, change $700 to $830 and then solve for the values of the investments.Data from Example 5Two investments totaling $18,000 yield an annual income of $700. If the first investment has an
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 7, change 3 to 4 in the first equation and then find if there is any change in the
Determine whether or not the given equation is linear.8x − 3y = 12
Determine each of the following as being either true or false. If it is false, explain it why. 24 -1 3 1 = 2
Solve the given systems of equations. 2x + 3y + z = 2 -x + 2y + 3z = -1 -3x - 3y + z = 0
Determine whether or not the given pair of values is a solution of the given system of linear equations.x − y = 5 x = 4, y = − 12x + y = 7
Solve the given systems of equations by the method of elimination by substitution. x = y + 3 x 2y = 5
Solve the given systems of equations by use of determinants. 4x + y + z = 2 2x - y - z = 4 3y + z = 2
Evaluate the given determinants. 2 a+2 a-1 a
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. 3x + 2y = 6 x - 3y = 3
Solve the given systems of equations using the reduced row echelon form (rref) feature on a calculator. The decimals in are approximate. 1₂ = 1₁ + 13 8.001₁ + 10.01₂ 6.0013 10.01₂ 80.0 60.0
Solve the given systems of equations by use of determinants. x + y + z = 2 x -z = 1 x + y = 1
Evaluate the given determinants. x + y 2x y - x 2y
Find the slope and the y-intercepts of the lines with the given equations. Sketch the graphs. 2y = 3x - 3
Find the slope of the line that passes through the given points.(3, 1), (2, −7)
Solve the given systems of equations by the method of elimination by addition or subtraction. R - 4r = 4r + 3R 17 3
Solve the given systems of equations using the reduced row echelon form (rref) feature on a calculator. The decimals in are approximate. 1.21x + 1.32y + 1.20z 6.81 4.93x 1.25y + 3.65z = 22.0 2.85x +
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. 4R 3V -8 - = 6R+V = 6
Solve the given systems of equations by use of determinants. x + y -z = -3 x + z = 2 2xy + 2z = 3
Solve the given systems of equations by determinants. x + 2y = 5 x - 2y = 1
Solve each system of equations to the nearest 0.001 for each variable by using a calculator. y = 6x + 2 12x - 2y = -4
Solve the given systems of equations by determinants. All numbers are accurate to at least two significant digits.The forces acting on a link of an industrial robot are shown in Fig. 5.33. The
Find the slope of the line that passes through the given points.(−1, 2), (−4, 17)
Solve the given systems of equations by determinants. 4x + 3y = -4 y = 2x - 3
In planning a search pattern from an aircraft carrier, a pilot plans to fly at p mi/h relative to a wind that is blowing at w mi/h. Traveling with the wind, the ground speed would be 300 mi/h, and
Solve the given problems by determinants, set up appropriate systems of equations. All numbers are accurate to at least two significant digits.The increase L in length of a long metal rod is a
Solve the given problems by determinants, set up appropriate systems of equations. All numbers are accurate to at least two significant digits.An online retailer requires three different size
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.x + 2y = 4
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.5y − x = 5
Solve the given systems of equations by determinants. x + 2y + z = 2 3x6y + 2z = 2 2x z = 8
Solve the given systems of equations by the method of elimination by addition or subtraction. 2x - 3y = 4 2x + y = -4
Find the slope and the y-intercepts of the lines with the given equations. Sketch the graphs.y = −2x + 4
Find the slope of the line that passes through the given points.(1, 0), (3, 8)
Solve the given systems of equations by determinants. V + 2t = 7 2v + 4t = 9
Solve the given systems of equations by determinants. = 3x - y = 5 Зу 9х 3y - 9x = -15
Solve the given systems of equations by the method of elimination by addition or subtraction. 12t + 9y = 14 6t = 7y - 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. 2x - 5y = 10 3x + 4y = -12
Solve the given systems of equations by the method of elimination by addition or subtraction. 3x - y = 3 4x = 3y + 14
Solve the given systems of equations by use of determinants. 2x + 3y + z = 2 -x + 2y + 3z = -1 -3x - 3y + z = 0
Find the slope and the y-intercepts of the lines with the given equations. Sketch the graphs.8x − 2y = 5
Solve the given systems of equations by determinants. x + 3y = 7 2x + 3y = 5
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. -5x + 3y = 15 2x + 7y = 14
Find the function f(x) = ax2 + bx + c, if f(1) = 3, f(−2) = 15, f(1) = 3, f(−2) = 15, and f(3) = 5.
Solve the given systems of equations by determinants. 2x - 3y = 4 2x + y = -4
Solve the given systems of equations by use of determinants. 2x + y z = 4 4x3y2z = -2 8x2y3z = 3
Find the slope of the line that passes through the given points.(−1, −2), (6, 10)
Find the slope and the y-intercepts of the lines with the given equations. Sketch the graphs.6x = 16 + 6y

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