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mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(√2a − √b)(√2a + 3√b)
Express each radical in simplest form, rationalize denominators, and perform the indicated operations. √2RI + √8/13
In Exercises express each expression in simplest form with only positive exponents.(x3 − y−3)1/3
Use a calculator to evaluate each expression.4.0187−4/9
Perform the indicated operations, expressing answers in simplest form with rationalized denominators.(2√mn + 3√n)2
Express each expression in simplest form with only positive exponents.(27a3)2/3 (a−2 + 1)1/2
Use a calculator to evaluate each expression.0.1863−7/6
Express each of the given expressions in simplest form with only positive exponents.(a + b)−1
Find the required horizontal and vertical components of the given vectors. A water skier is pulled up the ramp shown in Fig. 9.19 at 28 ft/s. How fast is the skier rising when leaving the ramp? Fig. 9.19 SESE 9.5 ft- 2.5 ft
Determine each of the following as being either true or false. For vector A, in standard position at angle θ, of magnitude A, the magnitude of the x-component is Ax = Asinθ
Refer to the wave in the string described in Exercise 37 of Section 10.3. For a point on the string, the displacement y is given by We see that each point on the string moves with simple harmonic motion. Sketch two cycles of y as a function of t for the given valuesA = 0.350 in., T = 0.250 s,
View at least two cycles of the graphs of the given functions on a calculator.y = 2 cot 3x
Sketch the curves of the given trigonometric functions. Check each using a calculator.y = 3 sin(−0.5x)
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator.y = −2 sin(2πx − π)
Find the amplitude and period of each function and then sketch its graph.y = −25 sin 0.4x
Display the graphs of the given functions on a calculator.y = sinπx − cos2x
View at least two cycles of the graphs of the given functions on a calculator. y = 18 csc (3x)
Plot the Lissajous figures.x = sinπt, y = 2 cos 2πt
Graph the given functions. Use the equations for negative angles in Section 8.2 to first rewrite the function with a positive angle, and then graph the resulting function.y = −5 cos(−4πx)
Sketch the curves of the given trigonometric functions. Check each using a calculator.y = 1/4 sec x
What conclusion do you draw from the calculator graphs of Y₁ = 7) and y₂ = -2cos[-(3x 2cos (3x + 2) + 4)]?
Sketch the curves of the given trigonometric functions. Check each using a calculator.y = −5 cotπx
View at least two cycles of the graphs of the given functions on a calculator.y = 1/2 sec 3x
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. y = 0.08 cos(4x ES ㅠ
Give the amplitude and sketch the graphs of the given functions. Check each using a calculator.y = −1500 sin x
Sketch the curves of the given trigonometric functions. Check each using a calculator.y = sinπx
Find the amplitude and period of each function and then sketch its graph.y = −1/2 cos 2/3x
The air pressure within a plastic container changes above and below the external atmospheric pressure by p = p0 sin 2πft. 0 Sketch two cycles of p = f(t) for the given values.p0 = 2.80 lb in.2 , f = 2.30 Hz
Give the amplitude and sketch the graphs of the given functions. Check each using a calculator.y = −0.2 sin x
View at least two cycles of the graphs of the given functions on a calculator.y = −0.4 csc 2x
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. y = 25 cos(3x + 푸) 4
Sketch the curves of the given trigonometric functions. Check each using a calculator.y = 36 sin 4πx
Find the amplitude and period of each function and then sketch its graph.y = 1/3 cos 0.75x
Display the graphs of the given functions on a calculator. = 2 sin(2x − 2) + cos(2x + 5) 6 3 y -
The air pressure within a plastic container changes above and below the external atmospheric pressure by p = p0 sin 2πft. 0 Sketch two cycles of p = f(t) for the given values.p0 = 45.0 kPa, f = 0.450 Hz
View at least two cycles of the graphs of the given functions on a calculator. y = -2 cot (2x + 4) 6
Give the amplitude and sketch the graphs of the given functions. Check each using a calculator.y = −4cos x
Sketch the curves of the given trigonometric functions. Check each using a calculator. y = 5 cos (4)
View at least two cycles of the graphs of the given functions on a calculator. tan (3) 3x -3) y tan
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator.y = −0.6 sin(2πx − 1)
Find the amplitude and period of each function and then sketch its graph.y = 0.4 sin 2πx/9
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. y = 1.8 sin TX + (3) 13
The vertical position y (in m) of the tip of a high speed fan blade is given by y = 0.10 cos360t , where t is in seconds. Use a calculator to graph two complete cycles of this function.
Display the graphs of the given functions on a calculator.y = 3 cos 2 x + sinπ/2x
Give the amplitude and sketch the graphs of the given functions. Check each using a calculator.y = −8 cos x
Sketch the curves of the given trigonometric functions. Check each using a calculator.y = −cos6πx
Sketch the curves of the given trigonometric functions. Check each using a calculator. y = -0.5 sin(-)
Find the amplitude and period of each function and then sketch its graph.y = 15cos πx/10
A study found that, when breathing normally, the increase in volume V (in L) of air in a person’s lungs as a function of the time t(in s) is V = 0.30 sin 0.50πt. Sketch two cycles.
Plot the Lissajous figures.x = 8 cos t, y = 5 sin t
Give the amplitude and sketch the graphs of the given functions. Check each using a calculator.y = −50 cos x
View at least two cycles of the graphs of the given functions on a calculator. y = 12 sec (2x + 4)
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator.y = 40 cos(3πx + 1)
Sketch the curves of the given trigonometric functions. Check each using a calculator. y = 8 sinx 4
Find the amplitude and period of each function and then sketch its graph.y = 3.3 cos π2x
Sketch two cycles of the radio signal e = 0.014 cos(2πft + π/4 ) (e in volts, f in hertz, and t in seconds) for a station broadcasting with f = 950 kHz (“95” on the AM radio dial).
Give the amplitude and sketch the graphs of the given functions. Check each using a calculator.y = −0.4 cos x
Plot the Lissajous figures.x = 5 cos t + 2, y = 5 sin t − 3
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator.y = 360 cos(6πx − 3)
View at least two cycles of the graphs of the given functions on a calculator. y = 75 tan (0.5x-1 π 16/
Find the amplitude and period of each function and then sketch its graph.y = −12.5 sin 2x/π
Sketch the curves of the given trigonometric functions. Check each using a calculator. _y = 12 sin(3x . 크
Sketch two cycles of the acoustical intensity I of the sound wave for which I = A cos(2πft − ∅), given that t is in seconds, A = 0.027 W cm2 , f = 240 Hz, and ∅ = 0.80.
Plot the Lissajous figures.x = 2 sin t, y = 3 sin t
Although units of π are convenient, we must remember that π is only a number. Numbers that are not multiples of π may be used. In Exercises plot the indicated graphs by finding the values of y that correspond to values of x of 0, 1, 2, 3, 4, 5, 6, and 7 on a calculator. (Remember, the numbers 0,
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator.y = sin(π2x − π)
The rotating beacon of a parked police car is 12 m from a straight wall. (a) Sketch the graph of the length L of the light beam, where L = 12 sec πt, for 0 ≤ t ≤ 2.0 s. (b) Which part(s) of the graph show meaningful values? Explain.
The period is given for a function of the form y = sin bx. Write the function corresponding to the given period.π/3
Plot the Lissajous figures.x = 2 cos t, y = cos(t + 4)
Although units of π are convenient, we must remember that π is only a number. Numbers that are not multiples of π may be used. In Exercises plot the indicated graphs by finding the values of y that correspond to values of x of 0, 1, 2, 3, 4, 5, 6, and 7 on a calculator. (Remember, the numbers 0,
View at least two cycles of the graphs of the given functions on a calculator. y = 0.5 sec (0.2x + 5) 25
Sketch the curves of the given trigonometric functions. Check each using a calculator. n ( 121 + 7/7) y = 3 sin (
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. 1 = --sin (2x - 1)
The motion of a piston of a car engine approximates simple harmonic motion. Given that the stroke (twice the amplitude) is 0.100 m, the engine runs at 2800 r/min, and the piston starts by moving upward from the middle of its stroke, find the equation for the displacement d as a function of t (in
Plot the Lissajous figures. = cos(t +), ) , y = sin 2 x = cos
The period is given for a function of the form y = sin bx. Write the function corresponding to the given period.5π/2
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. y 3 -COS (TX + ²) cos 2 6
Although units of π are convenient, we must remember that π is only a number. Numbers that are not multiples of π may be used. In Exercises plot the indicated graphs by finding the values of y that correspond to values of x of 0, 1, 2, 3, 4, 5, 6, and 7 on a calculator. (Remember, the numbers 0,
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. y cos (1/2 x + 1) ㅠ = TT COS
Using the graph of y = tan x, explain what happens to tan x as x gets closer to π/2 (a) From the left (b) From the right.
Sketch the curves of the given trigonometric functions. Check each using a calculator.y = −2 cos(4x + π)
Sketch the curves of the given trigonometric functions. Check each using a calculator. cos(-/-)) 6 y = 0.8 cos
The period is given for a function of the form y = sin bx. Write the function corresponding to the given period.1/3
A riverboat’s paddle has a 12-ft radius and rotates at 18 r/min. Find the equation of motion of the vertical displacement (from the center of the wheel) y of the end of a paddle as a function of the time t (in min) if the paddle is initially horizontal and moves upward when the wheel begins to
Although units of π are convenient, we must remember that π is only a number. Numbers that are not multiples of π may be used. In Exercises plot the indicated graphs by finding the values of y that correspond to values of x of 0, 1, 2, 3, 4, 5, 6, and 7 on a calculator. (Remember, the numbers 0,
Use a calculator to display the Lissajous figures defined by the given parametric equations. 08 T ( 1 + 1) ₁ Y X = COS T = 2 sin t
Using a calculator, graph y = sin x and y = csc x in the same window. When sin x reaches a maximum or minimum, explain what happens to csc x.
Sketch the curves of the given trigonometric functions. Check each using a calculator. y = -sinπx + 프6
The period is given for a function of the form y = sin bx. Write the function corresponding to the given period.6
The sinusoidal electromagnetic wave emitted by an antenna in a cellular phone system has a frequency of 7.5 × 109 Hz and an amplitude of 0.045 V/m. Find the equation representing the wave if it starts at the origin. Sketch two cycles.
Find the function and graph it for a function of the form y = a sin x that passes through (π/2, −2).
Write the equation of a secant function with zero displacement, a period of 4π, and that passes through (0, −3).
Write the equation for the given function with the given amplitude, period, and displacement, respectively.sine, 4, 3π,−π/4
Graph the given functions. Use the equations for negative angles in Section 8.2 to first rewrite the function with a positive angle, and then graph the resulting function.y = 3 sin(−2x)
Use a calculator to display the Lissajous figures defined by the given parametric equations.x = sin2πt, y = cosπt
Find the function and graph it for a function of the form y = a sin x that passes through (3π/2, −2).
Use a graphing calculator to show that sin x < tan x for 0 < x < π/2, although sin x and tan x are nearly equal for the values near zero.
Sketch the curves of the given trigonometric functions. Check each using a calculator.y = 250 sin(3πx − π)
Write the equation for the given function with the given amplitude, period, and displacement, respectively.cosine, 8, 2π/3,π/3
Sketch the curves of the given trigonometric functions. Check each using a calculator. y = 8 cos(4x -3)
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