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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Use a calculator to solve the given inequalities. Graph the appropriate function and from the graph determine the solution.x3 + x + 1 < 0
Use a calculator to solve the given inequalities. Graph the appropriate function and from the graph determine the solution. 4 R + 2 Л 6
Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities.|y + 2| < 5|x − 3| ≤ 2
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10.1/3x − 2 ≤ 1/2x + 1Data from Example 10Display the solution of the inequality −1 < 2x + 3 < 6
Graph the given inequalities on the number line.x ≤ −1 or x > 0.5
Determine the values for x for which the radicals represent real numbers. √-2x - x²
Solve the given quadratic inequalities. Check each by displaying the solution on a calculator.|x2 + 3x − 1| < 3 (See Exercise 31.)Data from Exercises 31|x2 + x − 4| < 2[Use Eq. (17.2), and
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10.0.1 < 0.5 − 0.2t < 0.9Data from Example 10Display the solution of the inequality −1 < 2x + 3
Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities.16x + 3y − 12 > 0 y > x² − 2x − 3|2x − 3| < 3
Graph the given inequalities on the number line.x < −300 or x ≥ 0
Determine the values for x for which the radicals represent real numbers. x³ + 6x² + 8x 3-x
Use a calculator to solve the given inequalities. Graph the appropriate function and from the graph determine the solution.e−t > 0.5
Solve for x if |x| < a and a ≤ 0. Explain.
Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities.y > 0, x < 0, y ≤ x
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10.−3 < 2 −s/3 ≤ −1Data from Example 10Display the solution of the inequality −1 < 2x + 3 < 6
Graph the given inequalities on the number line.0 ≤ x < 5
Use a calculator to solve the given inequalities. Graph the appropriate function and from the graph determine the solution.sin 2x < 0.8 (0 < x < 4)
Solve for x if |x − 1| < 4 and x ≥ 0.
Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.x3 − x > 2Data from Example 8Use a calculator to solve the inequality
Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities.y ≤ 0, x ≥ 0, y ≥ x
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10.x − 3 < 2x + 5 < 6x + 7Data from Example 10Display the solution of the inequality −1 < 2x + 3
Graph the given inequalities on the number line.−4 < y < −2
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.y > 12 − 3x
Solve for x: |x − 5| < 3 and |x − 7| < 2.
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10.n − 3 < 2n + 4 ≤ 1 − nData from Example 10Display the solution of the inequality −1 < 2x + 3
Use a calculator to display the solution of the given inequality or system of inequalities.2x + y < 5
Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.0.5x3 < 3 − 2x2Data from Example 8Use a calculator to solve the
Graph the given inequalities on the number line.x ≥ −3 and x < 5
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.y < 1/2x + 2
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10.−2(2.5x) + 5 ≥ 3Data from Example 10Display the solution of the inequality −1 < 2x + 3 < 6 (see
Solve for x: 1 < |x − 2| < 3.
Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.x4 < x2 − 2x − 1Data from Example 8Use a calculator to solve the
Use a calculator to display the solution of the given inequality or system of inequalities.4x − 2y > 1
Graph the given inequalities on the number line.x > 4 and x < 3
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10.ln(x − 3) ≥ 1Data from Example 10Display the solution of the inequality −1 < 2x + 3 < 6 (see
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.4y − 6x − 8 ≤ 0
If |x − 1| < 4, find a and b if a < x + 4 < b.
Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.3x4 + x + 1 > 5x2Data from Example 8Use a calculator to solve the
Use a calculator to display the solution of the given inequality or system of inequalities.y ≥ 1 − x2
Graph the given inequalities on the number line.x < −1 or 1 ≤ x < 4
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.3y − x + 6 ≥ 0
Solve for x if |x − 1| > 4 and |x − 3| < 5.
Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.2x > x + 2Data from Example 8Use a calculator to solve the inequality x3
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities. y≤ 6 x² - 49
Use a calculator to display the solution of the given inequality or system of inequalities.y < |4 − 2x|
Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.log x < 1 − 2x2Data from Example 8Use a calculator to solve the
Graph each solution. Determine the values of x that are in the domain of the function f(x)=√2x 10. -
Graph the given inequalities on the number line.−3 < x < 0 or x > 3
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.2x > 6 − y
Graph each solution. Determine the values of x that are in the domain of the function f(x)=1/√30.5.x.
The thickness t (in km) of Earth’s crust varies and can be described as |t − 27| ≤ 23. What are the minimum and maximum values of the thickness of Earth’s crust?
Use a calculator to display the solution of the given inequality or system of inequalities.y > 2x − 1y < x4 − 8
Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.sin x < 0.1x2 − 1Data from Example 8Use a calculator to solve the
Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.sin x < 0.1x2 − 1Data from Example 8Use a calculator to solve the
Graph the given inequalities on the number line.−3 < x < −1 or 0.5 < x ≤ 3
A motorist notes the gasoline gauge and estimates there are about 9 gal in the tank, but knows the estimate may be off by as much as 1 gal. This means we can write |n − 9| ≤ 1, where n is the
Use a calculator to display the solution of the given inequality or system of inequalities.y < 3 − xy > 3x − x3
Graph the given inequalities on the number line.x ≤ 4 or x > −4
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.y − |x + 1| < 0
The production p (in barrels) of oil at a refinery is estimated at 2,000,000 ± 200,000. Express p using an inequality with absolute values and describe the production in a verbal statement.
Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.4 cos2x > 2x − 3Data from Example 8Use a calculator to solve the
Use a calculator to display the solution of the given inequality or system of inequalities.y > x² + 2x − 8y < 1/x − 2
For what values of k are the roots of the equation x2 − kx + 9 = 0 imaginary?
Graph the given inequalities on the number line.t ≤ −5 and t ≥ −5
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.2y + 2x3 + 6x > 3
According to the Waze navigation app, the time required for a driver to reach his destination is 52 min. If this time is accurate to ±3 min, express the travel time t using an inequality with
Use a calculator to display the solution of the given inequality or system of inequalities.2y > −4x2y <1 −e−x
Graph the given inequalities on the number line.x < 1 or 1 < x ≤ 4
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.y > x + 1y < 4 − x2
The temperature T (in °C) at which a certain machine can operate properly is 70 ± 20. Express the temperature T for proper operation using an inequality with absolute values.
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities. y ≤ y < 4 x² + 1 x-3
Use inequalities to solve the given problems.Is x2 > x for all x? Explain.
Use a calculator to display the solution of the given inequality or system of inequalities.y ≤ |2x − 3|y >1 − 2x²
Solve the given problems by setting up and solving appropriate inequalities. Graph each solution.For −6 < x < 2, find a and b if a < 5 − x < b.
Graph the given inequalities on the number line.(x ≤ 5 or x ≥ 8) and (3 < x < 10)
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.y > 2x − x2y ≥ −2
The Mach number M of a moving object is the ratio of its velocity v to the velocity of sound vs, and vs varies with temperature. A jet traveling at 1650 km/h changes its altitude from 500 m to 5500
Use inequalities to solve the given problems.Is x > 1/x for all x? Explain.
Use a calculator to display the solution of the given inequality or system of inequalities.y ≥ |4 − x²|y < 2 In|x|
Solve the given problems by setting up and solving appropriate inequalities. Graph each solution.For 8 > −x > −4, find a and b such that a < x + 1 < b.
Graph the given inequalities on the number line.(x < 7 and x > 2) or (x ≥ 10 or x < 1)
The diameter d of a certain type of tubing is 3.675 cm with a tolerance of 0.002 cm. Express this as an inequality with absolute values.
Find an inequality of the form ax2 + bx + c < 0 with a > 0 for which the solution is −1 < x < 4.
By an inequality, define the region below the line 9x − 3y + 12 = 0.
Answer the given questions about the inequality 0 < a < b.Is a2 < b2 a conditional inequality or an absolute inequality?
The velocity v (in ft/s) of a projectile launched upward from the ground is given by v = −32t + 56, where t is given in seconds. Given that speed = |velocity|, find the times at which the speed is
Draw a sketch of the region in which the points satisfy the given inequality or system of inequalities.y < cos 1/2x y > 1/2ex –π < x < π
Find an inequality of the form ax3 + bx < 0 with a > 0 for which the solution is x < −1 or 0 < x < 1.
By an inequality, define the region that is bounded by or includes the parabola x2 − 2y = 0, and that contains the point (1, 0.4).
Answer the given questions about the inequality 0 < a < b.Is |a − b| < b − a?
The voltage v in a certain circuit is given by v = 6.0 − 200i, where i is the current (in A). For what values of the current is the absolute value of the voltage less than 2.0 V?
Algebraically find the values of x for which 2x+2 > 32x−3.
A rocket is fired from a plane flying horizontally at 9000 ft. The height h (in ft) of the rocket above the plane is given by h = 560t − 16t2, where t is the time (in s) of flight of the rocket.
Use a calculator to display the region in which the points satisfy the given inequality or system of inequalities.y < 3x + 5
For Ax + By < C, if B < 0, would you shade above or below the line?
What range of annual interest I will give between $120 and $150 annual income from an investment of $7500?
Answer the given questions about the inequality 0 < a < b.If each member of the inequality 2 > 1 is multiplied by a − b, is the result 2(a − b) > (a − b)?
Use a calculator to display the region in which the points satisfy the given inequality or system of inequalities.x > 8 − 4y
Graphically find the values of x for which 2 log2 x < log3 (x + 1).
Find a system of inequalities that would describe the region within the triangle with vertices (0, 0), (0, 4), and (2, 0).

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