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mathematics
basic technical mathematics

Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions

Make the given changes in the indicated examples of this section and then find the indicated values.In Example 4, change 56.82 to 65.82 and then solve the triangle.Data from Example 4Solve the right triangle with b = 56.82 and c = 79.55.We sketch the right triangle as shown in Fig. 4.35. Because
Determine each of the following as being either true or false.In Example 2 of Section 4.2, if the terminal side passes through (6, 8) the values of the trigonometric functions are the same as those shown.
A jet is traveling directly between Calgary, Alberta and Portland, Oregon, which are 550 mi apart. At any given time, x represents the jet’s distance (in mi) from Calgary and y represents its distance from Portland. Find the domain and range of y = f(x).
The length L (in ft) of a cable hanging between equal supports 100 ft apart is L = 100(1 + 0.0003s2), where s is the sag (in ft) in the middle of the cable. Because L = f (s), find f(15).
Use a calculator to solve the given equations to the nearest 0.1.5 − x3 = 4x2
The resistance R (inΩ) of a resistor as a function of the temperature T (in °C) is given by R = 250(1 + 0.0032T). Plot R as a function of T.
A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator.y = 2/x , left 4
The electric power P (in W) dissipated in a resistor of resistance R (inΩ) is given by the functionBecause P = f (R), find f (R + 10) and f(10R). P = 200R (100+ R)²
Using a piecewise-defined function, express the mass m of the weather balloon in Exercise 29 as a function of any height h.Data from Exercises 29Upon ascending, a weather balloon ices up at the rate of 0.5 kg/m after reaching an altitude of 1000 m. If the mass of the balloon below 1000 m is 110 kg,
The stopping distance d (in ft) of a car going v mi/h is given by d = v + 0.05v2. Because d = f (v), find f(30), f(2v), and f(60), using both f(v) and f(2v).
The rate H (in W) at which heat is developed in the filament of an electric light bulb as a function of the electric current I (in A) is H = 240I2. Plot H as a function of I.
A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator.y = −2x2, down 3, left 2
Using a piecewise-defined function, express the cost C of installing any length l of the underground cable in Exercise 31.Data from Exercises 31A company installs underground cable at a cost of $500 for the first 50 ft (or up to 50 ft) and $5 for each foot thereafter. Express the cost C as a
A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator. y = √2x + 1, up 1, left 1
Use a calculator to solve the given equations to the nearest 0.1.√x = 2x − 1
Use a calculator to find the range of the given function. y=x√4x²
The total annual fraction f of energy supplied by solar energy to a home as a function of the area A (in m2) of the solar collector is f = √0.065 A. Plot f as a function of A.
A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator.y = −4x, up 4, right 3
Use a calculator to find the range of the given function.y = x4 − 5x2
A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator. 2 y = √√x² + 4, down 2, right 2
The maximum speed v (in mi/h) at which a car can safely travel around a circular turn of radius r (in ft) is given by r = 0.42v2. Plot r as a function of v.
Use a calculator to find the range of the given function. A = w + 2 W
A spherical buoy 36 in. in diameter is floating in a lake and is more than half above the water. (a) Express the circumference c of the circle of intersection of the buoy and water as a function of the depth d to which the buoy sinks. (b) Find the domain and range of the function.
Use the function for which the graph is shown in Fig. 3.38 to sketch graphs of the indicated functions.f(x + 2)Fig. 3.38 х- 0 У
The sales tax in a city is 7.00%. The price tag on an item is D dollars. If the store has a 19% off price tag sale, express the total cost of the item as a function of D.
The height h (in m) of a rocket as a function of the time t (in s) is given by the function h = 1500t − 4.9t2. Plot h as a function of t, assuming level terrain.
For f (x + 2) = |x| , find f(0).
For f (x) = x2, find f(x +h)-f(x) h
A motorist travels at 55 km/h for t hours and then at 65 km/h for t + 1 hours. Express the distance d traveled as a function of t.
Use a calculator to find the range of the given function. y = 2x + 3
Use the function for which the graph is shown in Fig. 3.38 to sketch graphs of the indicated functions.f(x − 2)Fig. 3.38 х- 0 У
The power P (in W/h) that a certain windmill generates is given by P = 0.004v3, where v is the wind speed (in km/h). Plot the graph of P vs. v.
An astronaut weighs 750 N at sea level. The astronaut’s weight at an altitude of x km above sea level is given byPlot w as a function of x for x = 0 to x = 8000 km. w = 750 6400 6400 + x 2
A person considering the purchase of a car has two options: (1) Purchase it for $35,000, (2) Lease it for three years for payments of $450/month plus $2000 down, with the option of buying the car at the end of the lease for $18,000. (a) For the lease option, express the amount P paid
Forand g(x) = x2, find the domain of g[f(x)]. Explain. f(x)=√x - 1
Use the function for which the graph is shown in Fig. 3.38 to sketch graphs of the indicated functions.f(x − 2) + 2Fig. 3.38 х- 0 У
(a) Explain the meaning of f [f(x)]. (b) Find f [f(x)] for f (x) = 2x2 .
What is the range of the function f(x) = |x| + |x − 2|?
Explain how A(a, b) and B(b, a) may be in different quadrants.
Use the function for which the graph is shown in Fig. 3.38 to sketch graphs of the indicated functions.f(x + 2) + 2Fig. 3.38 х- 0 У
A formula used to determine the number N of board feet of lumber that can be cut from a 4-ft section of a log of diameter d (in in.) is N = 0.22d2 − 0.71d. Plot N as a function of d for values of d from 10 in. to 40 in.
If f (x) = x and g(x) = x2, find (a) f[g(x)], (b) g[f(x)].
A guideline of the maximum affordable monthly mortgage M on a home is M = 0.25(I − E), where I is the homeowner’s monthly income and E is the homeowner’s monthly expenses. If E = $600, graph M as a function of I for I = $2000 to I = $10,000.
Two vertices of an equilateral triangle are (0, 0) and (2, 0). What is the third vertex?
Solve the indicated equations graphically. Assume all data are accurate to two significant digits unless greater accuracy is given.In an electric circuit, the current i (in A) as a function of voltage v is given by i = 0.01v − 0.06. Find v for i = 0.
An airline requires that any carry-on bag has total dimensions (length + width + height) that do not exceed 45 in. For a carry-on that just meets this requirement and h as a length that is twice the width, express the volume V as a function of the width w. Draw the graph of V = f (w).
State the instructions of the function in words as in Example 8.∅(s) = 8 − 5s + s2Data from Example 8The function f(x) = x2 − 3x tells us to “square the input, multiply the input by 3, and subtract the second result from the first.” An analogy would be a computer that was programmed so
The points (1, 2) and (1,−3) are two adjacent vertices of a square. Find the other vertices
Solve the indicated equations graphically. Assume all data are accurate to two significant digits unless greater accuracy is given.For tax purposes, a corporation assumes that one of its computer systems depreciates according to the equation V = 90,000 − 12,000t, where V is the value (in dollars)
Graph given functions. y = √x² - 16
A copper electrode with a mass of 25.0 g is placed in a solution of copper sulfate. An electric current is passed through the solution, and 1.6 g of copper is deposited on the electrode each hour. Express the total mass m on the electrode as a function of the time t and plot the graph.
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. y = X x² - 4 2
If the point (a, b) is in the second quadrant, in which quadrant is (a,−b)?
To subscribe to satellite radio, a customer is charged $15 for the activation fee and then an additional $18 per month. Express the total cost C as a function of the number of months of service x. If C(x) = $375, find x.
Plot the graphs of the given functions. Check these graphs by using a calculator. I + x x
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. Y(y) = y + 1 √y - 2
State the instructions of the function in words as in Example 8.R(r) = 3(2r + 5)Data from Example 8The function f(x) = x2 − 3x tells us to “square the input, multiply the input by 3, and subtract the second result from the first.” An analogy would be a computer that was programmed so that
Use the graph to determine the domain and range of the given function.Fig. 3.24(a) y 4 0 3-2-1 0 1 2 3 -2 -3 (a) 3/4 $ X
Plot the graphs of the given functions. Check these graphs by using a calculator.y = x4 − 4x
State the instructions of the function in words as in Example 8.Data from Example 8The function f(x) = x2 − 3x tells us to “square the input, multiply the input by 3, and subtract the second result from the first.” An analogy would be a computer that was programmed so that when an input
The points (3,−1), (3, 0), and (x, y) are on the same straight line. Describe this line.
Use the graph to determine the domain and range of the given function.Fig. 3.24(b) 3 2 6 4 2 0 10 -4 6 (b) 3 X
For studying the electric current that is induced in wire rotating through a magnetic field, a piece of wire 60 cm long is cut into two pieces. One of these is bent into a circle and the other into a square. Express the total area A of the two figures as a function of the perimeter p of the square.
The cross section of an air-conditioning duct is in the shape of a square with semicircles on each side. See Fig. 3.6. Express the area A of this cross section as a function of the diameter d(in cm) of the circular part. H d Fig. 3.6
A helicopter 120 m from a person takes off vertically. Express the distance d from the person to the helicopter as a function of the height h of the helicopter. What are the domain and the range of d = f (h)? See Fig. 3.7. d 120 m Fig. 3.7 Helicopter h
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. f(n) = n² 6 - 2n
Plot the graphs of the given functions. Check these graphs by using a calculator. Z = √25 2R²
On a circular machine part, holes are to be drilled at the points (2, 2), (−2, 2), (−2,−2), and (2,−2), where (0, 0) represents the center. Plot these points and find the distance between the points in quadrants I and III.
Use the graph to determine the domain and range of the given function.Fig. 3.24(c) to 1 3 2 1 0 0 5 6 x
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. f(D) D² + 8D - 8 D(D2) + 4(D - 2)
Join the points (−1,−2), (4,−2), (7, 2), (2, 2), and (−1,−2) in order with straight-line segments. Find the distances between successive points and then identify the geometric figure formed.
Write the equation as given by the statement. Then write the indicated function using functional notation.The surface area A of a cubical open-top aquarium equals 5 times the square of an edge e of the aquarium.
Use the graph to determine the domain and range of the given function.Fig. 3.24(d) y $ 210 5 4 3 x+ 9 st & t 1017-ES9 -2 र्ट -4 -5 (P)
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. g(x) = √x-2 x - 3
Use a calculator to solve the given equations to the nearest 0.1.7x − 3 = 0
A computer program displays a circular image of radius 6 in. If the radius is decreased by x in., express the area of the image as a function of x. What are the domain and range of A = f(x)?
A helicopter is at an altitude of 1000 m and is x m horizontally from a fire. Its distance d from the fire is the square root of the sum of 1000 squared and x squared.
Use a calculator to solve the given equations to the nearest 0.1.3x + 11 = 0
A truck travels 300 km in t − 3h. Express the average speed s of the truck as a function of t. What are the domain and range of s = f (t)?
Write the equation as given by the statement. Then write the indicated function using functional notation.The area A of the Bering Glacier in Alaska, given that its present area is 5175 km2 and that it is melting at the rate of 1.200 km2 per year. Let t represent the number of years.
The resonant frequency f of a certain electric circuit as a function of the capacitance isDescribe the domain. f = 1 2T√C T
In blending gasoline, the number of gallons n of 85-octane gas to be blended with m gal of 92-octane gas is given by the equation n = 0.40m. Plot n as a function of m.
Use a calculator to solve the given equations to the nearest 0.1.x2 + 1 = 6x
A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator.y = 3x, up 1
A rectangular grazing range with an area of 8mi2 is to be fenced. Express the length l of the field as a function of its width w. What are the domain and range of l = f (w)?
Write the equation as given by the statement. Then write the indicated function using functional notation.The electrical resistance R of a certain ammeter, in which the resistance of the coil is Rc, is the product of 10 and Rc divided by the sum of 10 and Rc.
The consumption of fuel c (in L/h) of a certain engine is determined as a function of the number r of r/min of the engine, to be c = 0.011r + 40. This formula is valid for 500 r/min to 3000 r/min. Plot c as a function of r. (r is the symbol for revolution.)
Use a calculator to solve the given equations to the nearest 0.1.3t − 2 = t2
A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator.y = x3, down 2
A demolition ball is used to tear down a building. Its distance s (in m) above the ground as a function of time t (in s) after it is dropped is s = 17.5 − 4.9t2. Because s = f (t), find f(1.2).
Use a calculator to solve the given equations to the nearest 0.1.x3 − x2 = 2 − x
For a certain model of truck, its resale value V (in dollars) as a function of its mileage m is V = 50,000 − 0.2m. Plot V as a function of m for m ≤ 100,000 mi.
A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator.y = √x, right 3
Refer to the definitions of the trigonometric functions in Eqs. (4.1). Is the quotient of one of the functions divided by cosθ equal to tanθ? ExplainData from Eqs.(4.1)Six trigonometric functions are defined as follows: sine of 0 cosine of 0 sin = cos = tangent of tan0 = y r y X cosecant
Use a calculator to verify the given relationships or statements. [sin2θ = (sinθ)2]sin277.5° + cos277.5° = 1
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.cot θ = 0.7561
Use a calculator to verify the given relationships or statements. [sin2θ = (sinθ)2] tan 70° tan 30° + tan 40° 1- (tan 30°) (tan 40°)
What is the angle between the base of a cubical glass paperweight and a diagonal of the cube (from one corner to the opposite corner)?
The given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.31°, 310°
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.secθ = 34.2

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