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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

With the given sets of components, find R and θ.Rx = −31.2, Ry = −41.2
Add the given vectors by drawing the appropriate resultant.
Solve the triangles with the given parts.a = 0.130, A = 55.2°, B = 117.5°
Solve the triangles with the given parts.a = 2140, c = 428, B = 86.3°
A storm front is moving east at 18.0 km/h and south at 12.5 km/h. Find the resultant velocity of the front.
Find the x-and y-components of the given vectors by use of the trigonometric functions. The magnitude is shown first, followed by the direction as an angle in standard position.76.8 m/s, θ = 145.0°
Vectors A and B are at right angles. Find the magnitude and direction (from A) of the resultant.A = 5296B = 3298
With the given sets of components, find R and θ.Rx = 6941, Ry = −1246
Solve the triangles with the given parts.b = 4384, B = 47.43°, C = 64.56°
Solve the triangles with the given parts.a = 1.13, b = 0.510, C = 77.6°
To move forward, a helicopter pilot tilts the helicopter forward. If the rotor generates a force of 3200 lb, with a horizontal component (thrust) of 420 lb, what is the vertical component (lift)?
In the study of the velocities of deep-water waves, the equationoccurs. Solve for L. (3 + 7 ) z 1 = z4
By adding the same amount to its length and its width, a developer increased the area of a rectangular lot by 3000 m2 to make it 80 m by 100 m. What were the original dimensions of the lot? See Fig.
In testing the effects of a drug, the percent of the drug in the blood was given by p = 0.090t − 0.015t2, where t is the time (in h) after the drug was administered. Sketch the graph of p = f(t).
A machinery pedestal is made of two concrete cubes, one on top of the other. The pedestal is 8.00 ft high and contains 152 ft3 of concrete. Find the edge of each cube.
Concrete contracts as it dries. If the volume of a cubical concrete block is 29 cm3 less and each edge is 0.10 cm less after drying, what was the original length of an edge of the block?
The change p (in lb/in.2) in pressure in a certain fire hose, as a function of time (in min), is found to be p = 2.3t2 − 9.2t. Sketch the graph of p = f (t) for t < 5 min.
A jet flew 1200 mi with a tailwind of 50 mi/h. The tailwind then changed to 20 mi/h for the remaining 570 mi of the flight. If the total time of the flight was 3.0 h, find the speed of the jet
A food company increased the profit on a package of frozen vegetables by decreasing the volume, and keeping the price the same. The thickness of the rectangular package remained at 4.00 cm, but the
Use a calculator to graph all three parabolas on the same coordinate system. Describe (a) the shifts and (b) the stretching and shrinking.(a) y = x2 (b) y = −3(x − 2)2 (c) y = 1/3(x +
Solve the given quadratic equations by completing the square.2x2 = 3x − 2a
Solve the given quadratic equations by factoring.t(43 + t) = 9 − 9t2
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.13.2x = 15.5 − 12.5x2
Solve the given quadratic equations by any appropriate algebraic method. If there are no real roots, state this as the answer.12y2 = 20y
Use a calculator to find the vertex of s = −9.8t2 + 25t + 4. Round the coordinates to the nearest hundredth.
Solve the given quadratic equations by completing the square.x2 + 2bx + c = 0
Solve the given quadratic equations by factoring.6y2 + by = 2b2
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.x2 + 2cx − 1 = 0
Solve the given quadratic equations by any appropriate algebraic method. If there are no real roots, state this as the answer.x2 + 4x − 4 = 0
Find the range of the function s = −16t2 + 64t + 6.
Solve the given quadratic equations by completing the square.px2 + qx + r = 0
Solve the given quadratic equations by factoring.2x2 − 7ax + 4a2 = a2
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.x2 − 7x + (6 + a) = 0
Solve the given quadratic equations by any appropriate algebraic method. If there are no real roots, state this as the answer.x2 + 3x + 1 = 0
Find the equation of the quadratic function that has vertex (0, 0) and passes through the point (25, 125).
The voltage V across a certain electronic device is related to the temperature T (in °C) by V = 4.0T − 0.2T2. For what temperature(s) is V = 15V?
Solve the given quadratic equations by factoring.8s2 + 16s = 90
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.b2x2 + 1 − a = (b + 1)x
Solve the given quadratic equations by any appropriate algebraic method. If there are no real roots, state this as the answer.3x2 + 8x + 2 = 0
A parabolic satellite dish is 8.40 in. deep and 36.0 in. across its opening. If the dish is positioned so it opens directly upward with its vertex at the origin, find the equation of its parabolic
A flare is shot vertically into the air such that its distance s (in ft) above the ground is given by s = 64t − 16t2, where t is the time (in s) after it was fired. Find t for s = 48 ft.
Solve the given quadratic equations by factoring.18t2 = 48t − 32
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.c2x2 − x − 1 = x2
Solve the given quadratic equations by any appropriate algebraic method. If there are no real roots, state this as the answer.3p2 = 28 − 5p
Find the smallest integer value of c such that y = 2x2 − 4x − c has at least one real root.
A woman is holding a selfie stick so her cell phone camera is exactly 30 in. from her face. The horizontal distance between the woman’s face and the cell phone is exactly 6 in. more than the
Solve the given quadratic equations by factoring.(x + 2)3 = x3 + 8
Without solving the given equations, determine the character of the roots.2x2 − 7x = −8
Solve the given quadratic equations by any appropriate algebraic method. If there are no real roots, state this as the answer.4v2 + v = 3
Find the smallest integer value of c such that y = 3x2 − 12x + c has no real roots.
A rectangular storage area is 8.0 m longer than it is wide. If the area is 28 m2, what are its dimensions?
Solve the given quadratic equations by factoring.V(V2 − 4) = V2(V − 1)
Without solving the given equations, determine the character of the roots.3x2 = 14 − 19x
Solve the given quadratic equations by any appropriate algebraic method. If there are no real roots, state this as the answer.3n − 6 = 18n2
A computer analysis shows that the number n of electronic components a company should produce for supply to equal demand is found by solving. n² 500,000 144 n 500 Find n.
Find the equation of the parabola that contains the points (−2, −3), (0, −3), and (2, 5).
To determine the resistances of two resistors that are to be in parallel in an electric circuit, it is necessary to solve the equationFind R (to nearest 1Ω). 20 + R 20 R + 10 5
A computer design of a certain rectangular container uses the equation 12x2 − 80x + 96 = 0. Solve for x, if x < 4.
In fighting a fire, it is necessary to spray over nearby trees such that the height h (in m) of the spray is h = 1.5 + 7.2x − 1.2x2 , where x (in m) is the horizontal distance from the nozzle. What
A computer analysis shows that the cost C (in dollars) for a company to make x units of a certain product is given by C = 0.1x2 + 0.8x + 7. How many units can be made for $50?
For laminar flow of fluids, the coefficient K used to calculate energy loss due to sudden enlargements is given by K = 1.00 − 2.67R + R2 , where R is the ratio of cross-sectional areas. If K =
At an altitude h (in ft) above sea level, the boiling point of water is lower by T°F than the boiling point at sea level, which is 212°F. The difference can be approximated by solving the equation
In a natural gas pipeline, the velocity v (in m/s) of the gas as a function of the distance x (in cm) from the wall of the pipe is given by v = 5.2x − x2. Determine x for v = 4.8m/s.
The height h of an object ejected at an angle θ from a vehicle moving with velocity v is given by h = vtsinθ − 16t2 , where t is the time of flight. Find t (to 0.1 s) if v = 44 ft /s,θ = 65°,
In studying the emission of light, in order to determine the angle at which the intensity is a given value, the equation sin2 A − 4sin A + 1 = 0 must be solved. Find angle A (to 0.1°). [sin2 A =
Solve the given quadratic equations by any appropriate method. All numbers are accurate to at least two significant digits.In designing a cylindrical container, the formula A = 2πr2 + 2πrh is used.
Solve the given quadratic equations by any appropriate method. All numbers are accurate to at least two significant digits.In determining the number of bytes b that can be stored on a hard disk, the
Solve the given quadratic equations by any appropriate method. All numbers are accurate to at least two significant digits.In the study of population growth, the equation p2 = p1 + rp1(1 − p1)
In Example 2, change the denominator of the third fraction to 4a2b2 and then find the LCD.Data from Example 2Find the LCD of the fractionsWe first express each denominator in terms of powers of its
Where are all points for which y > 4?
In Exercise solve the given equations and check the results. 3.x 7 5 21 2-x 14
Where are all points for which xy > 0?
Perform indicated operations and simplify. a +3 a a 2
Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 7 a-1 (by a + 2)
Where are all points for which y/x < 0?
Where are all points for which xy = 0?
Where are all points for which x < y?
Simplify the given expressions involving the indicated multiplications and divisions. 2y² + 6y 6z X WN. y²-9
Determine the distance from the origin to the point (a, b).
Where are all points for which |y/x| > 0?
Solve for (business application) x: 3 2x² – 3x + x 3 2x - 3
Divide the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 25 65 (by 5)
Divide the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 4x²y 8.xy² (by 2x)
Find the products by inspection. No intermediate steps should be necessary.(3a + 4b)(3a − 4b)
In Exercise solve the given equations and check the results. F-3 12 2 3 || 1 - 3F 2
In Exercise solve the given equations and check the results. T 2= = +2 5 3
Simplify the given expressions involving the indicated multiplications and divisions. u² - v2 и + 2v -(3и + бv)
Simplify the given expressions involving the indicated multiplications and divisions. x + 2y x² - y² 2 (x - y)-
Perform indicated operations and simplify. a X b 2 x²
Divide the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 6a3b2 9a5b4 (by 3a2b2)
Find the products by inspection. No intermediate steps should be necessary.(x − 4z)(x + 4z)
Perform indicated operations and simplify. a 2b бу 3y4
Divide the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. (x + 5)(x-3) 3(x + 5) (by x + 5)
Perform indicated operations and simplify. 3 2s² + 5 4s
Solve the given quadratic equations by using the square root property. (x - 2)² 100
Find the products by inspection. No intermediate steps should be necessary.(b − 2)(b + 8)
Find the products by inspection. No intermediate steps should be necessary.(5 − y)(7 − y)
Factor the given expressions completely.7x − 28y
Sketch the graph of each parabola by using the vertex, the y-intercept, and the x-intercepts. Check the graph using a calculator.u = −3v2 + 12v − 9
Solve the given quadratic equations by factoring.6x2 = 13x − 6

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