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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Some comets follow a parabolic path that can be described by the equation r = (k/2) csc2 (θ/2), where r is the distance to the sun and k is a constant. Show that this equation can be written as r =
The power p in a certain electric circuit is given by p = 2.5[cos α sin(ωt + ∅) − sin α cos(ωt + ∅)]. Solve for t.
In surveying, when determining an azimuth (a measure used for reference purposes), it might be necessary to simplify the expression (2cos αcos β)−1 − tan α tan β. Perform this operation by
In analyzing the motion of an automobile universal joint, the equation sec2 A − sin2 Btan2 A = sec2 C is used. Show that this equation is true if tan A cos B = tan C.
The instantaneous power p used by a certain motor is given by p = VI cos∅ cos2 ωt − VI sin∅ cosωt sinωt. Simplify this expression.
The angle of elevation of the top of the Washington Monument from a point on level ground 250 ft from the center of its base is twice the angle of elevation of the top from a point 610 ft farther
In studying waveforms, a sawtooth wave may often be approximated by y = sin πx + 1/2 sin 2πx + 1/3sinπx. For what values of x, 0 ≤ x < 2, is the sum of the first two terms equal to zero?
A person in the stands of a football field is “sitting” on the 50-yd line (which is 53.3 yd long), y yd above it and x yd horizontally from it.(a) Find the expression for θ, the angle subtended
A person is 100 m above the ground and x m on a direct line from an object on the ground. Find an expression for 2θ, where θ is the angle of depression from the person to the object.
A roof truss is in the shape of an isosceles triangle of height 6.4 ft. If the total length of the three members is 51.2 ft, what is the length of a rafter? Solve by setting up and solving an
If a plane surface inclined at angle θ moves horizontally, the angle for which the lifting force of the air is a maximum is found by solving the equation 2sin θ cos2 θ − sin3 θ = 0, where 0
To determine the angle between two sections of a certain robot arm, the equation 1.20 cosθ + 0.135cos2θ = 0 is to be solved. Find the required angle θ if 0° < θ < 180°.
In checking the angles of a section of a bridge support, an engineer finds the expression cos(2sin−1 0.40). Write a paragraph explaining how the value of this expression can be found without the
Solve the given inequalities. Graph each solution.2.50(1.50 − 3.40x) < 3.84 − 8.45x
A political candidate plans to spend no more than $9000 on newspaper and radio advertising, with no more than twice being spent on newspaper ads at $50 each than radio ads at $150 each. It is assumed
Solve the given inequalities. Graph each solution.8 + 3|3 − 2x| < 11
Solve each of the given inequalities algebraically. Graph each solution.8/x < 2
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check. x + 15 x - 9 > 0
Draw a sketch of the graph of the given inequality.y > |x| − 3
Solve the given inequalities. Graph each solution.(2x − 7)(x + 1) ≤ 4 − x(1 − 2x)
Solve each of the given inequalities algebraically. Graph each solution. 1 x-2 A 4
Give the inequalities equivalent to the following statements about the number x.Greater than or equal to −200 and less than 650.
Solve the given inequalities. Graph each solution. 들+그들-두 +1
An oil refinery refines types A and B of crude oil and can refine as much as 4000 barrels each week. Type A crude has 2 kg of impurities per barrel, type B has 3 kg of impurities per barrel, and the
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check. x² - 6x - 7 x + 5 > 0
Solve the given inequalities. Graph each solution.5 − 4|1 − 7x| > 13
Draw a sketch of the graph of the given inequality.−20 < 5y ≤ −10
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check. (x - 2)²(5-x) (4 - x)³ ≤0
Give the inequalities equivalent to the following statements about the number x.Less than −5, or greater than or equal to 3.
A manufacturer produces a business calculator and a graphing calculator. Each calculator is assembled in two sets of operations, where each operation is in production 8 h during each day. The average
Solve the given inequalities. Graph each solution.4|2 − 5x| ≥ 6
Solve each of the given inequalities algebraically. Graph each solution.|3x + 2| ≤ 4
Draw a sketch of the graph of the given inequality.y > |x + 3|
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check. X x + 3 > 1
Solve the given inequalities. Graph each solution. - 2>를.. | + 3)
Brands A and B of breakfast cereal are both enriched with vitamins P and Q. The necessary information about these cereals is as follows:(RDA is the Recommended Daily Allowance.) Find the amount of
Solve the given inequalities. Graph each solution. 3R -|³R²+1 < 8 5
Give the inequalities equivalent to the following statements about the number x.Less than or equal to 8, or greater than or equal to 12.
Solve the given inequalities. Graph each solution. It is suggested that you also graph the function on a calculator as a check. 2p P-1 > 3
Using the information given in Example 3, with the one change that the profit on each good-quality speaker system is $60 (instead of $30), how many of each system should be made? Explain why this one
Solve the given inequalities. Graph each solution.2.5|7.1 − 2.0x| ≤ 6.5
Draw a sketch of the graph of the given inequality.|x| < |y|
Solve the given inequalities. Graph each solution.−1 ≤ 2x + 1 ≤ 3
Give the inequalities equivalent to the following statements about the number x.Less than 1, or greater than 3 and less than or equal to 5.
Solve each of the given inequalities algebraically. Graph each solution. 312-리드
Solve each of the given inequalities algebraically. Graph each solution.|3 − 5x| > 7
Solve the given inequalities. Graph each solution. 4x 3 IV 7
Draw a sketch of the graph of the given inequality.2|x − 3y| > 4
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10 in Section 17.2. 3x2 + 5x ≥ 2 Data from Example 9 Data from Example 10. NORMAL FLOAT AUTO REAL
Solve the given inequalities. Graph each solution.4 < 6R + 2 ≤ 16
Give the inequalities equivalent to the following statements about the number x.Greater than or equal to 0 and less than or equal to 2, or greater than 5.
Solve the inequalities by displaying the solutions on a calculator. See Examples 9 and 10 in Section 17.2.12x2 + x < 1Data from Example 10 of Section 17.2Display the solution of the inequality
A computer company makes parts A and B in each of two different plants. It costs $4000 per day to operate the first plant and $5000 per day to operate the second plant. Each day the first plant
Solve the given inequalities. Graph each solution. |6.5-2 > 2.3
Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities.y > xy > 1− x
Solve the given inequalities. Graph each solution.−4 ≤ 1 − x < −1
Give the inequalities equivalent to the following statements about the number x.Greater than −2 and less than 2, or greater than or equal to 3 and less than 4.
Solve the given inequalities on a calculator such that the display is the graph of the solution.5 − 3x > 0
Solve the given inequalities. Graph each solution. 2w + 51 퀴 w+1 21
Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities.y ≤ 2x y ≥ x − 1
Solve the given inequalities. Graph each solution.0 ≤ 3 − 2x ≤ 6
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
Give the inequalities equivalent to the following statements about the number x.Less than −4, or greater than or equal to 0 and less than or equal to 1, or greater than or equal to 5.
Solve the given inequalities on a calculator such that the display is the graph of the solution.6 ≤ 2 − 4x < 9
Solve the given inequalities on a calculator such that the display is the graph of the solution. 2 < 4n - 2 3
Draw a sketch of the graph of the region in which the points satisfy the given system of inequalities.y ≤ 2x2y > x − 2
Solve the given inequalities by displaying the solutions on a calculator. See Example 6.|2x − 5| < 3Data from Example 6Display the solution to the inequalityon a calculator.On the calculator,
Solve the given inequalities. Graph each solution.2x < x − 1 ≤ 3x + 5
Give verbal statements equivalent to the given inequalities involving the number x.0 < x ≤ 9
What is the value after 20 years of an investment of $2500 if it draws 5% annual interest compounded annually?
Find the nth term of the geometric sequence with the given values.1/2,1, 2,. . . ; n = 9
Expand and simplify the given expressions by use of the binomial formula.(xy2 − z)5
Find the indicated term of each sequence.0.025, 0.01, 0.004, . . . (7th)
Find the nth term of the arithmetic sequence with the given values.−6,−4,−2,. . . ; n = 10
Find the sums of the given infinite geometric series.9 + 8.1 + 7.29 + . . .
Find the sum of the first 100 even integers.
Find the nth term of the geometric sequence with the given values.10,1, 0.1, . . . ; n = 8
Expand and simplify the given expressions by use of the binomial formula.(n + 2π3)5
Find the indicated term of each sequence.−1, 3.5, 8, . . . (16th)
Find the sums of the given infinite geometric series.4 + 7/2 + 40/16 + . . .
Find the nth term of the geometric sequence with the given values.125,−25, 5, . . . ; n = 7
Find the nth term of the arithmetic sequence with the given values.8/3, 5/3, 2/3, ...; n = 9
A ball is dropped from a height of 8.00 ft, and on each rebound, it rises to 1/2 of the height it last fell. If it bounces indefinitely, through what total distance will it move?
Expand and simplify the given expressions by use of the binomial formula.(1 − j)6 ( j = √−1)
Find the indicated term of each sequence.−1, −5/3, −7/3, . . . (25th)
Find the sums of the given infinite geometric series.6 − 4 +8/3 − . . .
Find the nth term of the geometric sequence with the given values.0.1, 0.3, 0.9, . . . ; n = 5
Find the nth term of the arithmetic sequence with the given values. 109 = u = p = 'v ¹²
Find the nth term of the arithmetic sequence with the given values.2, 0.5, −1, . . . ; n = 25
Expand and simplify the given expressions by use of the binomial formula. 6 a (1 + x) ° x
Expand and simplify the given expressions by use of the binomial formula.(2a − b2)6
Find the sums of the given infinite geometric series.1 + 10−4 + 10−8 + . . .
Find the nth term of the geometric sequence with the given values.a1 = −2700, r = −1/3, n = 10
Find the nth term of the arithmetic sequence with the given values.a1 = −0.7, d = 0.4, n = 80
Find the indicated term of each sequence.3/4, 1/2, 1/3,... (7th)
Find the sums of the given infinite geometric series.1000 − 300 + 90 − . . .
Find the nth term of the geometric sequence with the given values.a2 = 24, r = 1/2, n = 12
Find the indicated term of each sequence.5−2 , 50 , 52 , . . . (18th)
Expand and simplify the given expressions by use of Pascal’s triangle.(5x − 3)4
Find the sums of the given infinite geometric series.(2 + √3) + 1 + (2 − √3) + . . .

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