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mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
One ball bearing is 1.00 mm more in radius and has twice the volume of another ball bearing. What is the radius of each?
Graph given functions. V = √16 - h²
State the instructions of the function in words as in Example 8.g(y) = 6y − y3Data 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
Find the inner surface area A of a cylindrical 250.0-cm3 cup as a function of the radius r of the base. Then if A = 175.0 cm2, solve for r. Write one or two paragraphs explaining your method for setting up the function, and how you used a graphing calculator to solve for r with the given value of A.
Plot the graphs of the given functions. Check these graphs by using a calculator.A = 6 − s4
Graph given functions. y = √4 - x
A company finds that it earns a profit of $120 on each cell phone and a profit of $80 on each tablet that it sells. If x cell phones and y tablets are sold, the profit is $68,000. Express y as a function of x.
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. y 4 x2 x² - 4
State the instructions of the function in words as in Example 8.f(x) = 2x − 6Data 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
Plot the graphs of the given functions. Check these graphs by using a calculator.V = 3 − 0.5s3
State the instructions of the function in words as in Example 8.f(x) = x2 + 2Data 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
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. Ī + x^91 = {
A city does not tax the first $30,000 of a resident’s income but taxes any amount over $30,000 at 5%. (a) Find the tax T as a function of a resident’s income I (b) Find f(25,000) and f(45,000).
Graph given functions. P 1 n2 + 0.5
Plot the graphs of the given functions. Check these graphs by using a calculator.y = 3 − x − 2x2
The capacities (in L) of two oil-storage tanks are x and y. The tanks are initially full; 1200 L is removed from them by taking 10% of the contents of the first tank and 40% of the contents of the second tank. (a) Express y as a function of x. (b) Find f(400).
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. y 10x 1 + x²
Plot the graphs of the given functions. Check these graphs by using a calculator.y = x2 − 8x − 5
Determine the function y = f(x) that is represented by the given set of instructions.Square the input, divide the input by 4, and then add the second result to the first.
The mechanical advantage of an inclined plane is the ratio of the length of the plane to its height. Express the mechanical advantage M of a plane of length 8 m as a function of its height h.
Plot the graphs of the given functions. Check these graphs by using a calculator.s = 4t − t2
Graph the given functions.y = 4/x2
A method of finding values beyond those given is considered. By using a straight-line segment to extend a graph beyond the last known point, we can estimate values from the extension of the graph. The method is known as linear extrapolation. Use this method to estimate the required values from the
Determine the function y = f(x) that is represented by the given set of instructions.Cube the input, multiply the input by 7, and then subtract the second result from the first.
A 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 function of the length l of underground cable if l > 50 ft.
Plot the graphs of the given functions. Check these graphs by using a calculator.y = 5x − 10
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed.y = 3x2 + 12x − 4
Graph the given functions.y = 4/(x+2)
Determine the function y = f(x) that is represented by the given set of instructions.Cube the input, add 2 to this result, and then multiply this entire result by 5.
A chemist adds x L of a solution that is 50% alcohol to 100 L of a solution that is 70% alcohol. Express the number n of liters of alcohol in the final solution as a function of x.
A method of finding values beyond those given is considered. By using a straight-line segment to extend a graph beyond the last known point, we can estimate values from the extension of the graph. The method is known as linear extrapolation. Use this method to estimate the required values from the
Plot the graphs of the given functions. Check these graphs by using a calculator.y = 4x + 2
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed.y = −4x2 + 8x + 3
Graph the given functions.P = 8/V + 3
Determine the function y = f(x) that is represented by the given set of instructions.Square the input, multiply this result by 3, and then subtract 4 from this result.
Upon 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, express its mass m as a function of its altitude h if h > 1000 m.
Use a graphing calculator to solve the given equations to the nearest 0.001.3x2 − x4 = 2 + x
Graph the given functions.y = −2x3
Evaluate the given functions.f(x) = 2x2 + 1; find f (x + 2) − [f(x) + 2].
Use the following table that gives the rate R of discharge from a tank of water as a function of the height H of water. Find the indicated values by linear interpolation.Find H for R = 25 ft3/s. Height (ft) Rate (ft³/s) 0 1.0 2.0 4.0 6.0 8.0 12 0 10 15 22 27 31 35
Evaluate the given functions.f(x) = 8x + 3; find f (3x) − 3f(x).
Graph the given functions.V = e3
Use a graphing calculator to solve the given equations to the nearest 0.001.s3 − 4s2 = 6
Determine the domain and the range of the given functions.f(x) = x4 + 1
Evaluate the indicated functions.Find f(1) and f (−0.25). F(t) = f(x) = 3t 12 (fort 2) h(s) 1 x+1 √x + 3 (for x < 1) (for x ≥ 1) 1 = 2s s+1 g(x) = (for s< -1) (for s2 -1) 1 X 0 (for x = 0) (for x = 0)
Answer the given questions.Where are all points whose x-coordinates equal their y-coordinates?
Use the following table, which gives the fraction (as a decimal) of the total heating load of a certain system that will be supplied by a solar collector of area A (in m2). Find the indicated values by linear interpolation.For A = 36 m2, find f. f A(m²) 0.22 0.30 0.37 0.44 0.44 20 40 30 50 0.50
Use a graphing calculator to solve the given equations to the nearest 0.001. T-2: T
Evaluate the given functions. The values of the independent variable are approximate.Givenfind f(1.9654). f(x) = x4-2.0965 6x
A method of finding values beyond those given is considered. By using a straight-line segment to extend a graph beyond the last known point, we can estimate values from the extension of the graph. The method is known as linear extrapolation. Use this method to estimate the required values from the
Determine the domain and the range of the given functions.F(x) = 3 − |x|
Determine the domain and the range of the given functions. f(n) = 1 + 2 (n = 5)²
Graph the given functions.y = x3 − x4
Use a graphing calculator to solve the given equations to the nearest 0.001. 1 x² + 1 2 = 0
Evaluate the given functions. The values of the independent variable are approximate.Givenfind F(−84.466). F(H) = 2H² H+ 36.85*
Determine the appropriate functions.A computer part costs $3 to produce and distribute. Express the profit p made by selling 100 of these parts as a function of the price of c dollars each.
A method of finding values beyond those given is considered. By using a straight-line segment to extend a graph beyond the last known point, we can estimate values from the extension of the graph. The method is known as linear extrapolation. Use this method to estimate the required values from the
Answer the given questions.Where are all points for which x > 0?
Graph the given functions.D = v4 − 4v2
A rocket burns up at the rate of 2 tons/min after falling out of orbit into the atmosphere. If the rocket weighed 5500 tons before reentry, express its weight w as a function of the time t, in minutes, of reentry.
What is the y-coordinate of all points on the x-axis?
Evaluate the given functions. The values of the independent variable are approximate.Givenfind g(0.9261). g(t) = √t + 1.0604 613
Determine the domain and the range of the given functions. g(t) = 8 √t + 4
Use the following table, which gives the fraction (as a decimal) of the total heating load of a certain system that will be supplied by a solar collector of area A (in m2). Find the indicated values by linear interpolation.For f = 0.27, find A. f A(m²) 0.22 0.30 0.37 0.44 0.44 20 40 30 50 0.50
Determine the domain and the range of the given functions.F(y) = 1 − 2√y
Use a graphing calculator to solve the given equations to the nearest 0.001.√x + 3x = 7
Graph the given functions.L = 3e − e3
Use a graphing calculator to solve the given equations to the nearest 0.001. √5R+ 2 = 3
Determine the appropriate functions.Express the cost C of insulating a cylindrical water tank of height 2 m as a function of its radius r, if the cost of insulation is $3 per square meter.
Answer the given questions.What is the x-coordinate of all points on the y-axis?
Use the following table, which gives the fraction (as a decimal) of the total heating load of a certain system that will be supplied by a solar collector of area A (in m2). Find the indicated values by linear interpolation.For f = 0.59, find A. f A(m²) 0.22 0.30 0.37 0.44 0.44 20 40 30 50 0.50
Graph the given functions.y = x3 − x2
Evaluate the given functions. The values of the independent variable are approximate.Given f(x) = 5x2 − 3x, find f(3.86) and f(−6.92).
Determine the appropriate functions.A motorist travels at 40 mi/h for t h, and then continues at 55 mi/h for 2 h. Express the total distance d traveled as a function of t.
Evaluate the indicated functions.Find g(0.2) and g(0). F(t) = f(x) = 3t 12 (fort 2) h(s) 1 x+1 √x + 3 (for x < 1) (for x ≥ 1) 1 = 2s s+1 g(x) = (for s< -1) (for s2 -1) 1 X 0 (for x = 0) (for x = 0)
Where are all points whose x-coordinates equal the negative of their y-coordinates?
Determine the domain and the range of the given functions. G(z) Z 3
Evaluate the indicated functions.Find h(−8) and h(−0.5). F(t) = f(x) = 3t 12 (fort 2) h(s) 1 x+1 √x + 3 (for x < 1) (for x ≥ 1) 1 = 2s s+1 g(x) = (for s< -1) (for s2 -1) 1 X 0 (for x = 0) (for x = 0)
Evaluate the given functions. Values of the independent variable are approximate.find h(8.91) and h(−4.91). h(t) t² - 4t t³ + 564'
Answer the given questions.Where are all points such that |x| = 2?
Use the following table that gives the rate R of discharge from a tank of water as a function of the height H of water. Find the indicated values by linear interpolation.Find R for H = 1.7 ft. Height (ft) Rate (ft³/s) 0 1.0 2.0 4.0 6.0 8.0 12 0 10 15 22 27 31 35
Evaluate the given functions. Values of the independent variable are approximate.find G(0.17427) and G(0.053206). G(S) = S 0.087629 3.0125S
Evaluate the indicated functions.Find F(1), F(2), and F(3). F(t) = f(x) = 3t 12 (fort 2) h(s) 1 x+1 √x + 3 (for x < 1) (for x ≥ 1) 1 = 2s s+1 g(x) = (for s< -1) (for s2 -1) 1 X 0 (for x = 0) (for x = 0)
Use a graphing calculator to solve the given equations to the nearest 0.001.x4 − 2x = 0
Graph the given functions.y = 2 + 3x + x2
Evaluate the given functions.T(t) = 5t + 7; find T(2t + a − 1) and T(2t) + a − 1.
Use the following table that gives the rate R of discharge from a tank of water as a function of the height H of water. Plot the graph and find the values from the graph.(a) For R = 34 ft3/s, find H. (b) For H = 6.4 ft, find R. Height (ft) Rate (ft³/s) 0 1.0 2.0 4.0 6.0 8.0 12 0 10 15 22 27
Answer the given questions.Where are all points such that y = 3?
Use a graphing calculator to solve the given equations to the nearest 0.001.x3 − 3 = 3x
Find the domain of the given functions.Forwhat is the domain of f(x + 4)? f(x) = 쭈 X
Evaluate the given functions.find s(−2) and s(a2). s(y) = 6√y + 11 – 3;
Graph the given functions.y = x2 − 3x + 1
Evaluate the given functions.K(s) = 3s2 − s + 6; find K(−s + 2) and K(−s) + 2.
Find the domain of the given functions.Forfind y as a function of x, and the domain of f(x). X = 3 y-1'
Use the following table that gives the rate R of discharge from a tank of water as a function of the height H of water. Plot the graph and find the values from the graph.(a) for R = 20 ft3/s, find H. (b) For H = 2.5 ft, find R. Height (ft) Rate (ft³/s) 0 1.0 2.0 4.0 6.0 8.0 12 0 10 15 22 27
Answer the given questions.Where are all points whose y-coordinates are −3?
Use a graphing calculator to solve the given equations to the nearest 0.001.v2 − 2v − 4 = 0
Evaluate the given functions. Values of the independent variable are approximate.g(x) = 7x − x2; find g(45.81) and g(−21.85).
Graph the given functions.h = 20t − 5t2
Find the indicated values by means of linear interpolation.In Exercise 8, find the torque for f = 2300 r/min.Data from Exercises 8The 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
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