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study help
mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
Find an algebraic expression for each of the given expressions.sin(2 sin−1 x)
The vertical displacement y (in m) of the end of a robot arm is given by y = 2.30 cos0.1t − 1.35sin 0.2t. Find the first four values of t (in s) for which y = 0.
For a first-quadrant angle, express the first function listed in terms of the second function listed.tan x, csc x
For voltages V1 = 20sin120πt and V2 = 20 cos120πt, show that V= V1 + V2 20√2 sin(120πt + π/4). Use a calculator to verify this result.
Find the exact value of cos 2x + sin 2x tan x.
Prove the given identities.cos(x − y) cos y − sin(x − y) sin y = cos x
Find an algebraic expression for each of the given expressions.cos(2 tan−1 x)
In finding the maximum illuminance from a point source of light, it is necessary to solve the equation cosθ sin2θ − sin3θ = 0. Find θ if 0 < θ < 90°.
For a first-quadrant angle, express the first function listed in terms of the second function listed.cot x, sec x
The displacements y1 and y2 of two waves traveling through the same medium are given by y1= A sin 2π(t/T − x/λ) and y2 = A sin 2π(t/T +x/λ). Find an expression for the displacement y1 + y2 of the combination of the waves.
Find the exact value of cos4 x − sin4 x − cos2x.
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x. sec x sin x secxsinx
To find the angle θ subtended by a certain object on a camera film, it is necessary to solve the equationwhere p is the distance from the camera to the object. Find θ if p = 4.8 m. p² tane ptan 0.0063 = 1.6,
Solve the given problems with the use of the inverse trigonometric functions.Is sin−1(sin x) = x for all x? Explain.
A weight w is held in equilibrium by forces F and T as shown in Fig. 20.13. Equations relating w, F, and T areShow thatFig. 20.13 F cos 0 w+ Fsin0 Tsina = T cosa
Use a calculator to verify the given identities by comparing the graphs of each side.sin x(csc x − sin x) = cos2 x
The displacement d of a water wave is given by the equation d = d0 sin(ωt + α). Show that this can be written as d = d1 sinωt + d2 cosωt, where d1 = d0 cos α and d2 = d0 sin α.
Simplify: log(cos x − sin x) + log(cos x + sin x).
Show that the area A of a segment of a circle of radius r, bounded by a chord at a distance d from the center, is given by A r² cos-¹(d/r) - d√r²d². =
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x.cos x cot x + sin x
Solve the given problems with the use of the inverse trigonometric functions. In the analysis of ocean tides, the equation y = Acos2(ωt + ∅) is used. Solve for t.
For the two bevel gears shown in Fig. 20.14, the equationis used. Here, R is the ratio of gear 1 to gear 2. Show that tana = sin 3 R+ cos 3
The velocity of a certain piston is maximum when the acute crank angle θ satisfies the equation 8cosθ + cos2θ = 0. Find this angle.
Use a calculator to verify the given identities by comparing the graphs of each side.cos y(sec y − cos y) = sin2 y
Use a calculator to verify the given identities by comparing the graphs of each side. secx + cscx 1+ tanx = csc x
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x.sin x tan x + cos x
For an acute angle θ, show that 2sinθ > sin2θ.
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x. tan xcscx sinx — cotx
In the analysis of the angles of incidence i and reflection r of a light ray subject to certain conditions, the following expression is found:Show that E2 tanr tani +1] = E₁ (-1) tanr tan i
Resolve a force of 500.0 N into two components, perpendicular to each other, for which the sum of their magnitudes is 700.0 N, by using the angle between a component and the resultant.
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x. sinxcotx+ cos.x 2cotx
Use a calculator to verify the given identities by comparing the graphs of each side. cotx +1 cotx 1+tanx
Without graphing, determine the amplitude and period of the function y = 4sin x cos x. Explain.
For an object of weight w on an inclined plane that is at an angle θ to the horizontal, the equation relating w and θ is μw cosθ = w sinθ, where μ is the coefficient of friction between the surfaces in contact. Solve for θ.
Looking for a lost ship in the North Atlantic Ocean, a plane flew from Reykjavik, Iceland, 160 km west. It then turned and flew due north and then made a final turn to fly directly back to Reykjavik. If the total distance flown was 480 km, how long were the final two legs of the flight? Solve by
Without graphing, determine the amplitude and period of the function y = cos2 x − sin2 x.
Solve the given problems with the use of the inverse trigonometric functions. The electric current in a certain circuit is given by i = Im [sin(ωt + α) cos∅ + cos(ωt +α) sin∅] Solve for t.
Find the indicated maximum and minimum values by the linear programming method of this section, the constraints are shown below the objective function.Minimum C: C = 6x + 4y x ≥ 0, y ≥ 0 2x + y 26 x + y 2 5
Draw a sketch of the graph of the given inequality.y ≤ 2x2 − 3
Solve the given inequalities. Graph each solution.1/3x + 2 ≥ 1
For the inequality 4 < 9, state the inequality that results when the given operations are performed on both members.Divide by 0.5.
Find the indicated maximum and minimum values by the linear programming method of this section, the constraints are shown below the objective function.Maximum and minimum F: F = x + 3y x ≥ 1, y ≥ 2 y-x ≤ 3 y + 2x < 8
Solve the given inequalities. Graph each solution. 5 5
Solve the given inequalities. Graph each solution.3 + |3x + 1| ≥ 5
Solve each of the given inequalities algebraically. Graph each solution.2x < x + 1 < 4x + 7
The length of a rectangular lot is 20 m more than its width. If the area is to be at least 4800 m2, what values may the width be?
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check.R2 + 4 > 0
Draw a sketch of the graph of the given inequality.2x2 − 4x − y > 0
Solve the given inequalities. Graph each solution.12 − 2y > 16
For the inequality 4 < 9, state the inequality that results when the given operations are performed on both members.Square both.
Solve the given inequalities. Graph each solution. | 2x - 91 4
Find the indicated maximum and minimum values by the linear programming method of this section, the constraints are shown below the objective function.Maximum and minimum F: F = 3x-y x ≥ 1, y ≥ 0 x + 4y ≤ 8 4x + y ≤ 8
Solve each of the given inequalities algebraically. Graph each solution.5x2 + 9x < 2
Type A wire costs $0.10 per foot, and type B wire costs $0.20 per foot. Use a graph to show the possible combinations of lengths of wire that can be purchased for less than $5.00.
Solve the given inequalities. Graph each solution. 4x - 5 2 < x
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check.2x4 + 4 < 2
Draw a sketch of the graph of the given inequality.y ≤ x 3 − 8
For the inequality 4 < 9, state the inequality that results when the given operations are performed on both members.Take square roots.
Find the indicated maximum and minimum values by the linear programming method of this section, the constraints are shown below the objective function.Maximum P: P = 8x + 6y x ≥ 0, y ≥ 0 2x + 5y < 10 4x + 2y < 12
Solve each of the given inequalities algebraically. Graph each solution.x2 + 2x > 63
The range of the visible spectrum in terms of the wavelength λ of light ranges from about λ = 400 nm (violet) to about λ = 700 nm (red). Express these values using an inequality with absolute values.
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check.x3 + x2 − 2x < 0
Draw a sketch of the graph of the given inequality.y < 32x − x4
Find the indicated maximum and minimum values by the linear programming method of this section, the constraints are shown below the objective function.Minimum C: C = 3x + 8y x ≥ 0, y ≥ 0 6x + y ≥ 6 x + 4y > 4
Draw a sketch of the graph of the given inequality. y ≤ √2x + 5
Give the inequalities equivalent to the following statements about the number x.Greater than −2.
Solve the given inequalities. Graph each solution.|20x + 85| ≤ 46
Solve each of the given inequalities algebraically. Graph each solution.6n2 − n > 35
Solve the inequality x2 > 12 − x on a graphing calculator such that the display is the graph of the solution.
Solve the given inequalities. Graph each solution.1.5 − 5.2x ≥ 3.7 + 2.3x
Give the inequalities equivalent to the following statements about the number x.Less than 0.7.
Solve the given inequalities. Graph each solution.
Solve each of the given inequalities algebraically. Graph each solution.2x3 + 4 ≤ x2 + 8x
By using linear programming, find the maximum value of the objective function P = 5x + 3y subject to the following constraints: x ≥ 0, y ≥ 0, 2x + 3y ≤ 12, 4x + y ≤ 8.
Draw a sketch of the graph of the given inequality. y > 10 x² + 1 2
Solve each of the given inequalities algebraically. Graph each solution. (2x - 1)(3x) > 0 x + 4
Find the indicated maximum and minimum values by the linear programming method of this section, the constraints are shown below the objective function.Minimum C: C = 6x + 4y y ≥ 2 x + y ≤ 12 x + 2y > 12 2x + y ≥ 12
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check.s3 + 2s2 − s ≥ 2
Find the indicated maximum and minimum values by the linear programming method of this section, the constraints are shown below the objective function.Maximum P: P = 3x + 4y 2x + y 2 2 x + 2y = 2 x + y ≤ 2
Solve the given inequalities. Graph each solution.180 − 6(T + 12) > 14T + 285
Solve the given inequalities. Graph each solution. -2[x - (32x)] > 1 – 5x 3 +2
Give the inequalities equivalent to the following statements about the number x.Less than or equal to 38.
Solve the given inequalities. Graph each solution.2|x − 24| > 84
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check. 2x 3 x + 6
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check.n4 − 2n3 + 8n + 12 ≤ 7n2
Draw a sketch of the graph of the given inequality.y < ln x
Give the inequalities equivalent to the following statements about the number x.Greater than or equal to −6.
Solve the given inequalities. Graph each solution.3|4 − 3x| ≤ 10
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10 in Section 17.2.Data from Example 10 of Section 17.2Display the solution of the inequality −1 < 2x + 3 < 6 (see Example 6) on a calculator. In order to display the solution, we must write the
Solve each of the given inequalities algebraically. Graph each solution.x4 + x2 ≤ 0
Solve the given inequalities by displaying the solutions on a calculator. See Example 6.2|6 − T| > 5Data from Example 6Display the solution to the inequalityon a calculator.On the calculator, set y1 = abs(x/2 − 3) < 1 and obtain the display shown in Fig. 17.35. From this display, we see
Draw a sketch of the graph of the given inequality.y > 1 + sin 2x
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10 in Section 17.2.Data from Example 10 of Section 17.2Display the solution of the inequality −1 < 2x + 3 < 6 (see Example 6) on a calculator. In order to display the solution, we must write the
Give the inequalities equivalent to the following statements about the number x.Greater than 1 and less than 7.
Solve each of the given inequalities algebraically. Graph each solution.|4 − 3x| ≥ 7
Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities.y > x2y < x + 4
Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities. 2 y > {x² A VI y ≤ 4x - x²
Solve the given inequalities on a calculator such that the display is the graph of the solution. 8- R 2R+1 ≤0
Solve the given inequalities. Graph each solution.x + 19 ≤ 25 − x < 2x
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10 in Section 17.2. Data from Example 9 Data from Example 10 In Figure 17.10 4- x 3+ 2xx > 0
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