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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

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.
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
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
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 =
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 2x + 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
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
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
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
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
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
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
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
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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