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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Solve algebraically: 2x2 − x = 6 − 2x(3 − x)
Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify a, b, and c, with a > 0. Otherwise, explain why the resulting form is not quadratic.(3x −
Sketch the graph of each parabola by using only the vertex and the y-intercept. Check the graph using a calculator.y = −x2 − 4x − 3
Solve the given quadratic equations by using the square root property.x2 = 100
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.x2 + 2x − 15 = 0
Solve graphically using a calculator: 4x2 − 5x − 3 = 0
Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify a, b, and c, with a > 0. Otherwise, explain why the resulting form is not quadratic.x(x −
Make the given changes in the indicated examples of this section and then solve the resulting equations by the quadratic formula.In Example 2, change the coefficient of x2 from 2 to 3.Data from
Sketch the graph of each parabola by using only the vertex and the y-intercept. Check the graph using a calculator.y = x2 − 6x + 5
Solve the given quadratic equations by using the square root property.x2 = 25
Determine each of the following as being either true or false. If it is false, explain why.The first steps in solving the equation 2x2 + 4x − 7 = 0 by completing the square is to divide 4 by 2,
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 7, change 38 to 42 and then answer the questions.Data from Example 7 A projectile is
Make the given changes in the indicated examples of this section and then solve the resulting quadratic equations by completing the square.In Example 2, change the − sign before 6x to +.Data from
Make the given changes in the indicated examples of this section and then solve the resulting quadratic equations.In Example 8, change the numerator of the first term to 2 and the numerator of the
Make the given changes in the indicated examples of this section and then solve the resulting equations by the quadratic formula.In Example 1, change the − sign before 5x to +.Data from Example
Solve by using the quadratic formula: x2 = 3x + 5
Make the given changes in the indicated examples of this section and then solve the resulting quadratic equations.In Example 3(a), change the − sign before 7x to + and then solve.Data from
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 3, change the − sign before 8x to + and then sketch the graph.Data from Example
Simplify the given expressions involving the indicated multiplications and divisions. 4R² 36 R³25R 7R - 35 3R² + 9R
Determine each of the following as being either true or false. If it is false, explain why.The solution of the equation x2 − 2x = 0 is x = 2.
In Exercise solve the given equations and check the results. За a - 3 5
Solve by factoring: 2x2 + 5x = 12
Replace the A with the proper expression such that the fractions are equivalent. 3.x 20 A бу2
In Exercises perform the indicated operations and simplify. x+1_y-3 2x 4y
Divide the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 6x² + 13x - 5 6x³ - 2x² (by 1 - 3x)
Simplify the given expressions involving the indicated multiplications and divisions. Зах² - 9ах 9ax 10x² + 5x X 2x² + x a²x - 3a²
In Exercise solve the given equations and check the results. -18 2R || 2 1 + 3R 3
Simplify the given expressions involving the indicated multiplications and divisions. - 9B² 16 B + 1 ÷ (4 - 3B)
In Exercise solve the given equations and check the results. 3- x - 2 5x 115
Factor the given expressions completely.W2bx+2 − 144bx
In Exercises perform the indicated operations and simplify. -| 1 6 2A В 9 4C
Divide the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. $23s 10 2s² + 3s-2 - (by s + 2)
Simplify the given expressions involving the indicated multiplications and divisions. x4 - 9 x3 x² + 3 X
In Exercise solve the given equations and check the results. 2/3 + y 5 2y
Factor the given expressions completely.3ax − 6ax4 − 9a
In Exercises perform the indicated operations and simplify. 2 5a a a 10
Simplify the given expressions involving the indicated multiplications and divisions. 2a + 8 15 16 + 8a + a² 125
In Exercises perform the indicated operations and simplify. 6 5x3 + a 25x
In Exercise solve the given equations and check the results. 12 2y 2 4
Factor the given expressions completely.a2x2 + a2
In Exercise solve the given equations and check the results. 1 3 a a 5
Divide the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 4(R2) (R2)(R+ 2) (by R - 2)
Simplify the given expressions involving the indicated multiplications and divisions. a² - a 3a + 9 a² - 2a + 1 2 18 2²
Factor the given expressions completely.5s + 20t
In Exercises perform the indicated operations and simplify. 4 3x 3 X
Evaluate the given trigonometric functions by first changing the radian measure to degree measure. Round off results to four significant digits. ㅠ 6 cos-
An interstate route exit is a circular arc 330 m long with a central angle of 79.4°. What is the radius of curvature of the exit?
Evaluate the given trigonometric functions by first changing the radian measure to degree measure. Round off results to four significant digits. tan 5T 12
Evaluate the given trigonometric functions by first changing the radian measure to degree measure. Round off results to four significant digits. 71T 36 sin-
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.tanθ > 0, cosθ < 0
The given angles are approximate find θ for 0° ≤ θ < 360°.secθ = 2.047, cotθ < 0
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.cos 237.4°
The paddles of a riverboat have a radius of 8.50 ft and revolve at 20.0 r/min. What is the speed of a tip of one of the paddles?
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.sinθ > 0, tanθ > 0
The given angles are approximate find θ for 0° ≤ θ < 360°.cotθ = −0.3256, cscθ > 0
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.sin 141.3°
Evaluate the given trigonometric functions by first changing the radian measure to degree measure. Round off results to four significant digits. cos 5п 6
Evaluate the given trigonometric functions by first changing the radian measure to degree measure. Round off results to four significant digits. 마품) ㅠ 3 tan
The sweep second hand of a watch is 15.0 mm long. What is the linear velocity of the tip?
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.secθ > 0, csc θ < 0
The given angles are approximate find the exact value of each expression without the use of a calculator.cos 60° + cos 70° + cos 110°
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.cot 295°
A circular pottery wheel has a diameter of 25.00 cm and is spinning at a rate of 125.0 r/min. What is the linear velocity of a point on the outer edge?
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.sinθ > 0, cot θ < 0
The given angles are approximate find the exact value of each expression without the use of a calculator.sin 200° − sin 150° + sin 160°
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.tan 184°
A circular pottery wheel has a diameter of 25.00 cm and is spinning at a rate of 125.0 r/min. What is the linear velocity of a point on the outer edge?
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.tanθ > 0, csc θ < 0
The given angles are approximate find the exact value of each expression without the use of a calculator.tan 40° + tan 135° − tan 220°
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.csc 247.82°
Evaluate the given trigonometric functions by first changing the radian measure to degree measure. Round off results to four significant digits.sec 4.5920
GPS satellites orbit the Earth twice per day with an orbital radius of 26,600 km. What is the linear velocity (in km/s) of these satellites?
With (x, y) in the given quadrant, determine whether the given ratio is positive or negative.III, x/r
The given angles are approximate find the exact value of each expression without the use of a calculator.sec 130° − sec 230° + sec 300°
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.sec 96.17°
Evaluate the given trigonometric functions by first changing the radian measure to degree measure. Round off results to four significant digits.cot 3.2732
The sprocket assembly for a 28.0-in. bike is shown in Fig. 8.47. How fast (in r/min) does the rider have to pedal in order to go 15.0 mi/h on level ground? Fig. 8.47 14.0 in. 2.00 in. 5.00 in.
Assume that the Earth rotates around the sun in a circular orbit of radius 93,000,000 mi. (which is approximately correct). What is the Earth’s linear velocity (in mi/h)?
With (x, y) in the given quadrant, determine whether the given ratio is positive or negative.II, y/r
Determine the function that satisfies the given conditions.Find tanθ when sinθ = −0.5736 and cosθ > 0.
Evaluate the given trigonometric functions directly, without first changing to degree measure. Round answers to three significant digits.tan 0.7359
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.sin 542.8°
With (x, y) in the given quadrant, determine whether the given ratio is positive or negative.IV, y/x
Determine the function that satisfies the given conditions.Find sinθ when cosθ = 0.422 and tanθ < 0.
Evaluate the given trigonometric functions directly, without first changing to degree measure. Round answers to three significant digits.cos 1.4308
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.cos 326.72°
Two streets meet at an angle of 82.0°. What is the length of the piece of curved curbing at the intersection if it is constructed along the arc of a circle 15.0 ft in radius? See Fig. 8.48. Fig.
The flywheel of a car engine is 0.36 m in diameter. If it is revolving at 750 r/min, through what distance does a point on the rim move in 2.00 s?
With (x, y) in the given quadrant, determine whether the given ratio is positive or negative.III, x/y
Determine the function that satisfies the given conditions.Find cosθ when tanθ = −0.809 and cscθ > 0.
Evaluate the given trigonometric functions directly, without first changing to degree measure. Round answers to three significant digits.sin 4.24
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.tan 301.4°
Determine the function that satisfies the given conditions.Find cotθ when secθ = 6.122 and sinθ < 0.
Evaluate the given trigonometric functions directly, without first changing to degree measure. Round answers to three significant digits.tan 3.47
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.sin 703.9°
An ammeter needle is deflected 52.00° by a current of 0.2500 A. The needle is 3.750 in. long, and a circular scale is used. How long is the scale for a maximum current of 1.500 A?
Insert the proper sign, > or < or =, between the given expressions. Explain your answers.sin 90° 2sin 45°
Evaluate the given trigonometric functions directly, without first changing to degree measure. Round answers to three significant digits.sec 2.07
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate. Express answers to four significant digits. sin 9T 5
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.tan 436.42°

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