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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Plot the graphs of the given functions on log-log paper.x3y = 8
Find the antilogarithm of each of the given logarithms by using a calculator.0.02436
Find the natural logarithms of the given number.6552
Plot the graphs of the given function.y = 0.25x
Determine the value of x.logx 8 = 0
Express each as a sum, difference, or multiple of logarithms. See Example 2.10 log5 √tData from Example 2(a) Using Eq. (13.7), we may express log4 15 as a sum of logarithms:(b) Using Eq. (13.8), we
Solve the given equation.3 log8 x = −2
Epress each as a sum, difference, or multiple of logarithms. See Example 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
Express the given equations in exponential form.log2 32 = 5
Plot the graphs of the given functions on log-log paper.x2y2 = 25
Find the antilogarithm of each of the given logarithms by using a calculator.3.30112
Express each as a sum, difference, or multiple of logarithms. See Example 2.log6(abc2)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
Find the natural logarithms of the given numbers.1.394
Plot the graphs of the given function.y = 4x
Determine the value of x.logx 10 = 1/3
Solve the given equation.8x = 4x2−1
Express the given equations in logarithmic form.(1/2)−3 = 8
Plot the graphs of the given functions on log-log paper.x2y3 = 16
Find the antilogarithm of each of the given logarithms by using a calculator.−6.9788
Find the natural logarithms of the given numbers.293
Evaluate the exponential function y = 4x for the given values of x.x = 5/2
Determine the value of x.logx (1/243) = 5
Solve the given equation.3x2+8 = 272x
Express the given equations in logarithmic form.(1/4)2 = 1/16
Plot the graphs of the given functions on log-log paper.xy = 40
Find the antilogarithm of each of the given logarithms by using a calculator.−1.2154
Express each as a sum, difference, or multiple of logarithms. See Example 2.2 log8 (n5)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
Find the natural logarithms of the given numbers.76.1
Evaluate the exponential function y = 4x for the given values of x.x = −3/2
Determine the value of x.logx 36 = 2
Determine the value of x.log9 27 = x
Solve the given equation.15.6x+2 = 23x
Express the given equations in logarithmic form.(81)3/4 = 27
Plot the graphs of the given functions on log-log paper.y = 8x0.25
Determine the value of x.log5 x = −1
Solve the given equation.6x+2 = 85
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.Focus (0, 8), major axis 34
Identify each of the equations as representing either a circle, a parabola, an ellipse, a hyperbola, or none of these.2x(x − y) = y(3 + y − 2x)
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Focus (0,−0.5)
Find the equation of each of the lines with the given properties. Sketch the graph of each line.Has a slope of −3 and passes through the intersection of the lines 5x − y = 6 and x + y = 12.
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.Conjugate axis = 48, vertex (0, 10)
Find the slopes of the lines through the points.(−12, 20) and (32,−13)
Transform each equation to a form without an xy-term by a rotation of axes. Then transform the equation to a standard form by a translation of axes. Identify and sketch each curve.16x2 − 24xy + 9y2
Find a set of polar coordinates for each of the points for which the rectangular coordinates are given. 2
Find the equation of the indicated curve, subject to the given conditions. Sketch each curve.Ellipse: vertex (10, 0), focus (8, 0), tangent to x = −10
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Focus (−2.5, 0)
Plot the curves of the given polar equations in polar coordinates.r2 = 2cos 3θ
Find the equation of each of the curves described by the given information.Hyperbola: foci (2, 1) and (8, 1), conjugate axis 6 units
Find the equation of each of the circles from the given information.Center at (−7, 1), tangent to y-axis
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.Vertex (0, 13), focus (0,−12)
Identify each of the equations as representing either a circle, a parabola, an ellipse, a hyperbola, or none of these.15x2 = x(x − 12) + 4y(y − 6)
Find the equation of each of the lines with the given properties. Sketch the graph of each line.Passes through the point of intersection of 2x + y − 3 = 0 and x − y − 3 = 0 and through the
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.Sum of lengths of transverse and conjugate axes 28, focus (10, 0)
Find the slopes of the lines through the points.(23,−9) and (−25, 11)
Transform each equation to a form without an xy-term by a rotation of axes. Then transform the equation to a standard form by a translation of axes. Identify and sketch each curve.73x2 − 72xy +
Find the equation of the indicated curve, subject to the given conditions. Sketch each curve.Ellipse: center (0, 0), passes through (0, 3) and (2, 1)
Find a set of polar coordinates for each of the points for which the rectangular coordinates are given.(−10, 8)
What curve does the value of B2 − 4AC indicate should result for the graph of 4x2 − 4xy + y2 = 0? Is this the actual curve?
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Directrix y = −0.16
Find the equation of each of the curves described by the given information.Hyperbola: vertices (2, 1) and (−4, 1), focus (−6, 1)
Plot the curves of the given polar equations in polar coordinates.r = 2θ (spiral)
Find the equation of each of the circles from the given information.Tangent to both axes and the lines y = 4 and x = −4
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.End of minor axis (0, 12), focus (8, 0)
Identify each of the equations as representing either a circle, a parabola, an ellipse, a hyperbola, or none of these.(x + 1)2 + (y + 1)2 = 2(x + y + 1)
Reduce the equations to slope-intercept form and find the slope and the y-intercept. Sketch each line.4x − y = 8
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.Passes through (2, 3), focus (2, 0)
Find the slopes of the lines through the points.(√32, √18) and (−√50, √8)
What curve does the value of B2 − 4AC indicate should result for the graph of 2x2 + xy + y2 = 0? Is this the actual curve?
Find the equation of the indicated curve, subject to the given conditions. Sketch each curve.Hyperbola: V(0, 13), C(0, 0), conj. axis of 24
Find a set of polar coordinates for each of the points for which the rectangular coordinates are given.(0, 4)
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Directrix x = 20
Plot the curves of the given polar equations in polar coordinates.r = 1.5−θ (spiral)
Find the equation of each of the curves described by the given information.Hyperbola: center (1,−4), focus (1, 1), transverse axis 8 units
Find the equation of each of the circles from the given information.Tangent to lines y = 2 and y = 8, center on line y = x
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.Sum of lengths of major and minor axes is 18, focus (3, 0)
Identify each of the equations as representing either a circle, a parabola, an ellipse, a hyperbola, or none of these.(2x + y)2 = 4x(y − 2) − 16
Reduce the equations to slope-intercept form and find the slope and the y-intercept. Sketch each line.2x − 3y − 6 = 0
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.Passes through (8, √3), vertex (4, 0)
Find the slopes of the lines through the points.(e,− π) and (−2e, −π)
Find the equation of the indicated curve, subject to the given conditions. Sketch each curve.Hyperbola: vertex (0, 8), asymptotes y = 2x, y = −2x
Find a set of polar coordinates for each of the points for which the rectangular coordinates are given.(−5, 0)
Plot the curves of the given polar equations in polar coordinates.r = |4 sin3θ|
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.x2 + 2x − 4y − 3 = 0
Find the equation of each of the circles from the given information.Center at the origin, tangent to the line x + y = 2
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Directrix x = −84
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.Vertex (8, 0), passes through (2, 3)
Identify each of the equations as representing either a circle, a parabola, an ellipse, a hyperbola, or none of these.x(y − x) = x2 + x(y + 1) − y2 + 1
Find the equation of each of the circles from the given information.Center at (5, 12), tangent to the line y = 2x − 3
Find the slopes of the lines with the given inclinations.176.2°
Plot the curves of the given polar equations in polar coordinates.(parabola) r 2 1 - cose
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.x2 + 4y2 = 32y
Determine the center and radius of each circle. Sketch each circle.(x − 2)2 + (y + 3)2 = 49
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Symmetric to x-axis, passes through (2,−1)
Identify each of the equations as representing either a circle, a parabola, an ellipse, a hyperbola, or none of these.4x(x − 1) = 2x2 − 2y2 + 3
Reduce the equations to slope-intercept form and find the slope and the y-intercept. Sketch each line.3x + 5y − 10 = 0
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.Passes through (5, 4) and (3, 4/5 √5)
Find the slopes of the lines through the points.(1.22,−3.45) and (−1.07,−5.16)
Find the x´y´ coordinates of the xy point (−2, 6) rotated through 60° .
Find the rectangular coordinates for each of the points for which the polar coordinates are given.(8, 4π/3)
Find the indicated quantities for each of the given equations. Sketch each curve.x2 + y2 + 6x − 7 = 0, center and radius

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