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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Perform indicated operations and simplify. 2 8 - x³ + 1 x² - x - 2
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(electric resistance in Fig. 6.5) - V = 1.2(5.0 + 8.0R 8.0 + R. for R
Perform the indicated operations and express results in simplest form. 4 9x 5 12x²
Factor the given expressions completely.8a6 + 64a3
In Exercise solve the given equations and check the results. X 6 -1/2 = X
Simplify the given expressions involving the indicated multiplications and divisions. 5 25 ÷ -13 16
Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 2 x + 3 (by x - 2)
Determine each of the following as being either true or false. If it is false, explain it. x y x + 1 y + 1 x + y 2 y² + y
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 7, change the numerator to x2 − 4x − 12 and then simplify.Data from Example
Perform indicated operations and simplify. 2 3 + a SIN
In Example 2, change the second denominator from b2 to b and then solve for x.Data from Example 2Solve forFirst, determine that the LCD of the terms of the equation is 2b2. Then multiply each term by
The following equation is used in electricity.Solve for R₁: 1/12 R 1 R₁ + r + -| R₂
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 3, change the first denominator to 4x − 10 and do the multiplication.Data from
In Example 5, add the fractionto those being added and then find the result.Data from Example 5When we multiply each fraction by the quantity required to obtain the proper denominator, we do not
In Example 3, solve for p.Data from Example 3An equation relating the focal length f of a lens with the object distance p and the image distance q is given below. See Fig. 6.4. Solve for q.Because
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 7, change the numerator x + 2 of the divisor to x + 3 and then simplify.Data from
Find the product: 2x(2x − 3)2.
In Example 7, change the denominator of the third fraction to s2 + 4s and then find the result.Data from Example 7The following expression is found in the analysis of the dynamics of missile firing.
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 10, change the numerator to 2x4 − 32x2 and then simplify.Data from Example 10Again,
Determine each of the following as being either true or false. If it is false, explain why.(2a − 3)2 = 4a2 − 9
Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 2/3 (by 7)
In Example 4, solve for G.Data from Example 4In astronomy, when developing the equations that describe the motion of the planets, the equationis found. Solve for M. First, determine that the LCD of
Reduce to simplest form: 2x² + 5x - 3 – 2x² + 12x + 18
Determine each of the following as being either true or false. If it is false, explain it.2x2 − 8 = 2(x − 2)(x + 2)
Simplify the given expressions involving the indicated multiplications and divisions. 3 10 X VIN
In Example 8, change the fraction in the numerator to 2/x2 and then simplify.Data from Example 8 2 X 1. 4 X || 2 X x - 4 X 2 X =xxA=x 4 xx = 4) || X 21 2 1 - 4
In Example 5, change the numerator on the right to 1 and then solve for x.Data from Example 5Solve forThe solution is as follows:Checking this solution in the original equation, notice the zero in
Simplify the given expressions involving the indicated multiplications and divisions. 11 x 13 33
Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 7 (by 9)
Determine each of the following as being either true or false. If it is false, explain it.6x2 − 7x + 1 = (3x − 1)(2x − 1)
Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. ax y (by 3a)
Factor: 4x2 − 16y2
Perform indicated operations and simplify. 13 + 13
In Exercise solve the given equations and check the results. + 6 = 2x
Simplify the given expressions involving the indicated multiplications and divisions. 4x Зу X 9у2 2
Determine each of the following as being either true or false. If it is false, explain it.(x + 2)3 = x3 + 8
Multiply the numerator and the denominator of each fraction by the given factor and obtain an equivalent fraction. 2х²у 3п (by 2xn2)
Simplify the given expressions involving the indicated multiplications and divisions. 18sy3 (ax)2 3.s ax
Factor: pb3 + 8a3 p (business application)
Simplify the given expressions involving the indicated multiplications and divisions. 219
Determine each of the following as being either true or false. If it is false, explain it. x² - y² 2x + 1 = (x + y) = x-y 2x + 1
In Exercise solve the given equations and check the results. +2 15 + x 10
Perform indicated operations and simplify. X 7 +
Factor: 2a − 4T − ba + 2bT
Factor: 36x2 + 14x − 16
Perform the indicated operations. Each expression occurs in the indicated area of application.(force of a weld) 3Px P (2)+(壹) 2L
After finding the simplest form of each fraction, explain why it cannot be simplified more.a.b. x²-x-2 x² - x
Find constants A and B such that the equation is true. x - 12 x2 + x - 6 A x +3 + B x - 2
After finding the simplest form of each fraction, explain why it cannot be simplified more.a. b. 1- x X - EX
Perform the indicated operations and express results in simplest form. X 4x² + 4x3 + 3 9 - 4x²
Find constants A and B such that the equation is true. 23 - x 2x² + 7x - 4 А 2x - 1 B x + 4
Perform the indicated operations. Each expression occurs in the indicated area of application.(electronics) = + R SL + R + 1 SC
Perform the indicated operations. Each expression occurs in the indicated area of application.(strength of materials) bh + C bh² 1 6bh
Perform the indicated operations and express results in simplest form. 3x 2x² - 2 2 4x² - 5x + 1
In Exercises, answer the given questions.If 3 − x < 0, is x² - 9 3-x 0?
In Exercises, answer the given questions.If x − 4 < 0, is x²16 x³ + 64 3
Perform the indicated operations and express results in simplest form. 2n-1 n+2 4-n 205n +
Perform the indicated operations. Each expression occurs in the indicated area of application.(airfoil design) 1 EI m с P c² 2
Perform the indicated operations and express results in simplest form. 3x x² + 2x - 3 2 x2 + 3x X 1
Perform the indicated operations. Each expression occurs in the indicated area of application.(electricity) * + (oc - ) R2 wL
Reduce each fraction to simplest form. Each is from the indicated area of application.(rectilinear motion) v² - v² V vt vot
Reduce each fraction to simplest form. Each is from the indicated area of application.(beam design) a³ - 6³ a³ - ab²
Perform the indicated operations and express results in simplest form. 3 y-1 + y4 2y³ - 8y² y² + 2y 2 _y - 3 y² - 4y 2
Perform the indicated operations. Each expression occurs in the indicated area of application.(optics) X h₁ 1+ + x - L h₂ (x-7)x h₁h₂
Reduce each fraction to simplest form. Each is from the indicated area of application.(nuclear energy) mu² mv² mu - my
Graphically check the results for the indicated exercises of this set on a calculator.Exercise 49Data from Exercises 49 6x²7x 2x²5x - 3 + 3
Reduce each fraction to simplest form. Each is from the indicated area of application.(rocket motion) 16(t² 2tto +t)(t-to - 3) 3t - 3to
Graphically check the results for the indicated exercises of this set on a calculator.Exercise 57Data from Exercises 57 x + x² 2 X +1 X
Graphically check the results for the indicated exercises of this set on a calculator.Exercise 52Data from Exercises 52 3 (6x = ³) ( ³) (4x² - 12x) 6
Reduce each fraction to simplest form. Each is from the indicated area of application.(electric power) E²R² - E²² (R² + 2Rr + ²)²
Graphically check the results for the indicated exercises of this set on a calculator.Exercise 66Data from Exercises 66 4x² + 4x - 3 + 3 9 - 4x²
Find the required expressions.A boat that travels at v km/h in still water travels 5 km upstream and then 5 km downstream in a stream that flows at w km/h. Write an expression for the total time the
Reduce each fraction to simplest form. Each is from the indicated area of application.(machine design) 3 一 r 听一听
Solve the given equations. X 2 - 3 x - 10 4
Find the required expressions.A person travels a distance d at an average speed v1, and then returns over the same route at an average speed v2. Write an expression in simplest form for the average
Solve the given equations. 2_1 at t = 2+ t for t
Solve the given equations. 4x C 2 2c || с x, for x
Solve the given equations. 3 1 a²y ay || 2 for y a
Solve the given equations. 2x 2x²5x 3 X 1 4x 10
Solve the given equations.Givensolve for x if f(x) = x x + 1'
Solve the given equations. 3 2 x² + 3x _1_ X 1 3 + x
Solve the given equations.Givensolve for x if f(x + 2) = 2 f (x) . f(x) = 1 x + 2'
Solve the given problems. Where indicated, the expression is found in the stated technical area.Show that xy [(x + y)² - (x - y)²].
Solve the given problems. Where indicated, the expression is found in the stated technical area.Show that x² + y² = 1⁄2 [(x + y)² + (x − y)²]. -
Solve the given problems. Where indicated, the expression is found in the stated technical area.In an algebraic fraction, what effect on the result is made if the sign is changed of:(a) An odd number
Solve the given problems. Where indicated, the expression is found in the stated technical area.Algebraically show that the reciprocal of the reciprocal of the number x is x.
Solve the given problems. Where indicated, the expression is found in the stated technical area.Multiply: Pb(L + b)(L − b) (architecture)
Solve the given problems. Where indicated, the expression is found in the stated technical area.Factor: πr12l + πr22l (jet plane fuel supply)
Solve the given problems. Where indicated, the expression is found in the stated technical area.Expand: [2b + (n − 1)λ]2 (optics)
Solve the given problems. Where indicated, the expression is found in the stated technical area.Multiply: kr(R − r) (blood flow)
Solve the given problems. Where indicated, the expression is found in the stated technical area.Factor: cT2 − cT1 + RT2 − RT1 (pipeline flow)
Solve the given problems. Where indicated, the expression is found in the stated technical area.Factor: 9600t + 8400t2 − 1200t3 (solar energy)
Solve the given problems. Where indicated, the expression is found in the stated technical area.Simplify and express in factored form: (2R − r)2 − (r2 + R2) (aircraft radar)
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(machine design) 2wtv2(bn²D2 ²-) (12) Dg n²
Solve the given problems. Where indicated, the expression is found in the stated technical area.Express in factored form: 2R(R + r) − (R + r)2 (electricity: power)
Solve the given problems. Where indicated, the expression is found in the stated technical area.Expand and simplify: (n + 1)3 (2n + 1)3 (fluid flow in pipes)
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(flywheel rotation) πλα ka (R4 (R4 - 2 πka(R² - 4) ²)
Solve the given problems. Where indicated, the expression is found in the stated technical area.Expand and simplify: 2(e1 − e2)2 + 2(e2 − e3)2 (mechanical design)
Solve the given problems. Where indicated, the expression is found in the stated technical area.Expand and simplify: 10a(T − t) + a(T − t)2 (instrumentation)
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(airfoil design) m C - [₁-(2)²] P

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