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study help
mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
Answer the given questions.Where are all points whose x-coordinates are 1?
Find the domain of the given functions. g(x) = √x - 2 x - 3
Use a graphing calculator to solve the given equations to the nearest 0.001.x2 + x − 5 = 0
Evaluate the given functions. Values of the independent variable are approximate.f(x) = 8.07 − 2x; find f(5.87) and f(−4.29).
Evaluate the given functions.find H(4) and H((−0.4)2). H(q) = 8 + 2√√9; 9
Graph the given functions.y = x2 + 2x
Evaluate the given functions.g(t) = at2 − a2t; find g(1/3) and g(a).
Determine the quadrant in which the point (x, y) lies.x > 0 and y > 0
Find the indicated values by means of linear interpolation.In Exercise 7, find the rate for t = 10.0 years.Data from Exercises 7The time required for a sum of money to double in value, when compounded annually, is given as a function of the interest rate in the following table: Rate (%) Time
Evaluate the given functions.f(x) = 1 − 9x 2; find [f(x)]2 − f(x2).
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings.y = |4 − x2|+ 2
Graph the given functions.y = 2x2 + 1
Find the domain of the given functions. 1 f(D) = √D + D-2
Determine the quadrant in which the point (x, y) lies.x < 0 and y < 0
Evaluate the given functions.f(x) = 4 − 5x; find f(2x) − 2f(x).
Graph the given functions.y = 1/2x2 + 2
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings.y = 2 − |x2 − 4|
Find the domain of the given functions. f(n) n² 6 - 2n
Determine the quadrant in which the point (x, y) lies.x > 0 and y < 0
Evaluate the given functions.find ∅(2π) and ∅(−2). o(x) = 2 6-x² 2x
Find the indicated values by means of linear interpolation.In Exercise 6, find the temperature for s = 12 mi/h.Data from Exercises 6The temperatures felt by the body as a result of the wind-chill factor for an outside temperature of 20°F (as determined by the National Weather Service) are given in
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. y = x² √3-x
Evaluate the given functions. f(x) = - 3x² − 2x + 4; find f(x + h) − f(x) h
Find the domain of the given functions. Y(y) = y +1 √y-2
Find the indicated values by means of linear interpolation.In Exercise 5, find the inductance for d = 9.2 cm.Data from Exercises 5A changing electric current in a coil of wire will induce a voltage in a nearby coil. Important in the design of transformers, the effect is called mutual inductance.
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. y = 3 + 2 X
Use the following table, which gives the valve lift L (in mm) of a certain cam as a function of the angle θ (in degrees) through which the cam is turned. Plot the values. Find the indicated values by reading the graph.For L = 2.0 mm, find θ. 0(°) L (mm) 0 20 0 1.2 40 60 80 2.3 3.3 3.8 3.0 100
Graph the given functions.y = x2 − 3
Evaluate the given functions.f(T) = 7.2 − 2.5 |T|; find f(2.6) and f(−4).
Evaluate the given functions. φ(ν) 6v - 9. Iv + 11 find (-2) and o(v + 1).
Determine the quadrant in which the point (x, y) lies.x < 0 and y > 0
Evaluate the given functions.F(x) = x3 + 2x2 − 3x; find F(3 + h) − F(3).
Graph the given functions.y = 6 − 2x2
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. y = 3√√2x + 1
Evaluate the given functions.f(x) = 6; find f (−2) and f(0.4).
Evaluate the given functions. H(h)=√12h; find H(-4) and H(2h) + 2.
Find the domain and range of the given functions.y = x + |x|
Use the following table, which gives the valve lift L (in mm) of a certain cam as a function of the angle θ (in degrees) through which the cam is turned. Plot the values. Find the indicated values by reading the graph.(a) For θ = 25°, find L. (b) For θ = 96°, find L. 0(°) L (mm) 0 20 0
Find the indicated coordinates.P is the point (−4, 1). Locate point Q such that the line segment joining P and Q is bisected by the origin.
Graph the given functions.y = −2x2
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. y = x + √√√x + 3
Use the graph in Fig. 3.41, which relates the temperature of cooling steam and the time. Find the indicated values by reading the graph.For T = 133.5°C, find t. T (°C) 150 140 130 0 1 2 3 Fig. 3.41 4 5 t (min)
Evaluate the given functions.f(x) = −x2 − 9; find f(2) and f(−2).
Find the domain and range of the given functions.y = |x − 3|
From the table in Problem 11, find the voltage for i = 200 mA using linear interpolation.Data from Problem 11 Voltage (V) Current (mA) 10.0 20.0 30.0 145 188 40.0 50.0 285 220 255 60.0 315
Find the indicated coordinates.P is the point (3, 6). Locate point Q such that the x-axis is the perpendicular bisector of the line segment joining P and Q.
Find the domain and range of the given functions and explain your answer. f(x) = -6 √2-x
Graph the given functions.y = x2
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. y = 3 x² - 4
Evaluate the given functions.f(x) = 2x + 1; find f(3) and f(−5).
Find the indicated coordinates.Two vertices of an equilateral triangle are (7, 1) and (2, 1). What is the x-coordinate of the third vertex?
Use the graph in Fig. 3.41, which relates the temperature of cooling steam and the time. Find the indicated values by reading the graph.For T = 145.0°C, find t. T (°C) 150 140 130 0 1 2 3 Fig. 3.41 4 5 t (min)
Evaluate the given functions.g(I) = 8 − 3I ; = find g(1/6) and g(−4).
Graph the given functions.A = 6 -1/3r
Find the indicated functions.Express the area A of an equilateral triangle as a function of its side s.
The voltage V and current i (in mA) for a certain electrical experiment were measured as shown in the following table. Plot the graph of i = f(V) and estimate f(45.0) by reading the graph.
Find the domain and range of the given functions and explain your answer.H(h) = 2h + √h + 1
Find the indicated coordinates.Three vertices of a rectangle are (6, 3), (−1, 3), and (−1,−2). What are the coordinates of the fourth vertex?
Determine the appropriate function.A person invests x dollars at 2% APR (annual percentage rate) and y dollars at 1% APR. If the total annual income is $600, solve for y as a function of x.
Use the graph in Fig. 3.41, which relates the temperature of cooling steam and the time. Find the indicated values by reading the graph.For t = 4.3min, find T. T (°C) 150 140 130 0 1 2 3 Fig. 3.41 4 5 t (min)
Find the domain and range of the given functions. f(s) = √s-2
Plot the given points and then join these points, in the order given, by straight-line segments. Name the geometric figure formed.A(−2,−1), B(3,−1),C(3, 5), D(−2, 5), A(−2,−1)
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings.y = x4 − 2x3 − 5
Graph the given functions.s = 7 − 2t
Find the indicated functionsExpress the area A of a square as a function of its diagonal d; express the diagonal d of a square as a function of its area A.
If the function y = 2x2 − 3 is shifted right 1 and up 3, what is the resulting function?
Represent the data graphically.The torque T of an engine, as a function of the frequency f of rotation, was measured as follows: f(r/min) T (ft. lb) 500 1000 1500 2000 2500 3000 3500 175 90 62 45 34 31 27
Find the domain and range of the given functions. F(r) = √r + 4
Plot the given points and then join these points, in the order given, by straight-line segments. Name the geometric figure formed.A(0, 3), B(0,−1),C(4,−1), A(0, 3)
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. y = 2x x - 2
Use the graph in Fig. 3.41, which relates the temperature of cooling steam and the time. Find the indicated values by reading the graph.For t = 1.8min, find T. T (°C) 150 140 130 0 1 2 3 Fig. 3.41 4 5 t (min)
Evaluate the given functions.f(x) = 7x − 5; find f(3) and f(−6).
Find the indicated functions.A circle is inscribed in a square (the circle is tangent to each side of the square). Express the total area A of the four corner regions bounded by the circle and the square as a function of the radius r of the circle.
A window has the shape of a semicircle over a square, as shown in Fig. 3.47. Express the area of the window as a function of the radius of the circular part.
Find the domain and range of the given functions.T(t) = 2t4 + t2 − 1
Plot the given points and then join these points, in the order given, by straight-line segments. Name the geometric figure formed.A(−5,−2), B(4,−2),C(6, 3), D(−5, 3), A(−5,−2)
Use a graphing calculator to find the range of the function y x² + 2 2 x + 2
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings.y = x2 − 3x5 + 3
Determine the appropriate function.Fencing around a rectangular storage depot area costs twice as much along the front as along the other three sides. The back costs $10 per foot. Express the cost C of the fencing as a function of the width w if the length (along the front) is 20 ft longer than the
Graph the given functions.y = −3
Find the indicated functions.Express the perimeter p of a square as a function of its side s; express the side s of a square as a function of its perimeter p.
Represent the data graphically.The time required for a sum of money to double in value, when compounded annually, is given as a function of the interest rate in the following table: Rate (%) Time (years) 4 5 6 7 8 17.7 14.2 11.9 10.2 9.0 9 8.0 10 7.3
Find the domain and range of the given functions. G(R) = 3.2 R
Find the domain and the range of the function, f(x) = √6-x.
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. x. 5-2 - 9- 4 3 1
Display the graphs of the given functions on a graphing calculator. Use appropriate window settings.y = x4 − 6x2
Determine the appropriate function.A conical sheet-metal hood is to cover an area 6 m in diameter. Find the total surface area A of the hood as a function of its height h.
Graph the given functions.y = 4 − 3x
Find the indicated functionsExpress the edge e of a cube as a function of its surface area A.
Represent the data graphically.The temperatures felt by the body as a result of the wind-chill factor for an outside temperature of 20°F (as determined by the National Weather Service) are given in the following table: Wind speed (mi/h) Temp. felt (°F) 5 10 15 20 25 30 35 40 13 9 6 4 3 1 0 -1
Plot the given points and then join these points, in the order given, by straight-line segments. Name the geometric figure formed.A(−1, 4), B(3, 4),C(2,−2), A(−1, 4)
Determine the appropriate function.The radius of a circular water wave increases at the rate of 2 m/s. Express the area of the circle as a function of the time t (in s).
Graph the given functions.y = 2x − 4
Plot the given points A(3,1), B(-6,0), C(-2,-5), D(1, -3)
Find the indicated functions.Express the diameter d of a sphere as a function of its volume V.
Locate all points (x, y) for which x < 0 and y = 0.
Find the domain and range of the given functions.g(u) = 3 − 4u2
Determine each of the following as being either true or false. If it is false, explain why.The graph of y = f(x + 4) is the graph of y = f(x) shifted to the left 4 units.
Find the indicated functionsExpress the circumference c of a circle as a function of (a) Its radius r and(b) Its diameter d.
Plot graph of the function y = √4 + 2x.
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