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mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
Solve the given problems.Is division associative? That is, is it true (if b ≠ 0, c ≠ 0) that (a ÷ b) ÷ c = a ÷ (b ÷ c)?
Solve the given problems.What is the ratio of 8 ×10−3 to 2 ×104?
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is given.The pressure gauge for an automobile tire shows a pressure of 32 lb/in.2. What is this pressure in N/m2?
Simplify the given expressions.When analyzing the motion of a communications satellite, the expression is used. Perform the indicated division. k²r2h²k + h²rv² k²r
Simplify the given expressions.One transmitter antenna is (x − 2a)ft long, and another is (x + 2a)yd long. What is the sum, in feet, of their lengths?
Simplify the given expressions.A computer analysis of the velocity of a link in an industrial robot leads to the expression 4(t + h) − 2(t + h)2. Simplify this expression.
Solve the given problems.In solving the equation x − (3 − x) = 2x − 3, what conclusion can be made?
Solve the given problems.Does the value of (3 ×18) ÷ 9 − 6 change if the parentheses are removed?
Solve the given problems.Show that (x − y)3 = −(y − x)3.
Solve the given problems.What is the ratio of to √4 ? √4 + 36
A certain automobile engine produces a maximum torque of 110 N · m. Convert this to foot pounds.
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is given.A certain engine produces 250 hp. What is this power in kilowatts (kW)?
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is given.The voltage across a resistor equals the current times the resistance. In a microprocessor circuit, one resistor is 1200 Ω greater than another. The sum of the voltages across them is 12.0
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is given.In testing the rate at which a polluted stream flows, a boat that travels at 5.5 mi/h in still water took 5.0 h to go downstream between two points, and it took 8.0 h to go upstream between
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is givenA ship enters Lake Superior from Sault Ste. Marie, moving toward Duluth at 17.4 km/h. Two hours later, a second ship leaves Duluth moving toward Sault Ste. Marie at 21.8 km/h. When will the
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is given.One road crew constructs 450m of road bed in 12h. If another crew works at the same rate, how long will it take them to construct another 250m of road bed?
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is givenA helicopter used in fighting a forest fire travels at 105 mi/h from the fire to a pond and 70 mi/h with water from the pond to the fire. If a round-trip takes 30 min, how long does it take
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is givenEach day a mining company crushes 18,000 Mg of shale-oil rock, some of it 72 L/Mg and the rest 150 L/Mg of oil. How much of each type of rock is needed to produce 120 L/Mg?
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is givenOne grade of oil has 0.50% of an additive, and a higher grade has 0.75% of the additive. How many liters of each must be used to have 1000L of a mixture with 0.65% of the additive?
In calculating the simple interest earned by an investment, the equation P = P0 + P0 rt is used, where P is the value after an initial principal P0 is invested for t years at interest rate r. Solve for r, and then evaluate r for P = $7625, P0 = $6250, and t = 4.000 years. Write a paragraph or
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is givenA karat equals 1/24 part of gold in an alloy (for example, 9-karat gold is 9/24 gold). How many grams of 9-karat gold must be mixed with 18-karat gold to get 200 g of 14-karat gold?
Solve the given problems. All data are accurate to two significant digits unless greater accuracy is givenAn architect plans to have 25% of the floor area of a house in ceramic tile. In all but the kitchen and entry, there are 2200ft2 of floor area, 15% of which is tile. What area can be planned
Make the given changes in the indicated examples of this section and then perform the indicated divisions.In Example 1(c), change the denominator to −2a2xy5.Data from Example 1(c) -ба2ху2 2axy4 -4-12/2 a2-1x1-1 у4-2 -За 2
Solve for the given letter from the indicated example of this section.For the formula in Example 2, solve for a.Data from Example 2A formula relating acceleration a, velocity v, initial velocity v , 0 and time is v = v + at. 0 Solve for t. V-Vo = at t = V - Vo a
Make the given changes in the indicated examples of this section and then perform the indicated divisions.In Example 2(b), change the denominator to 2xy2.Data from Example 2(b) 4x³y8x³y2 + 2x²y 2x²y 4x³y 8x³y2 2x²y 2x²y 2x - 4xy + 1 + 2x²y 2x²y
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 3, change 12 to −12 in each of the four illustrations and then solve.Data from Example 3In each of the following equations, we may isolate x, and thereby solve the equation, by
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 2(b), change the factor (−st4)2 to (−st 4)3.Data from Example 2(b)2s3(−st 4)2 (4s2t) = 2s3 ( s2t8)( 4s2t) = 8s7t9
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 4, change 2t − 7 to 7 − 2t and then solve.Data from Example 4Solve the equation 2t − 7 = 9.We are to perform basic operations to both sides of the equation to finally isolate t on
Solve for the given letter from the indicated example of this section.For the formula in Example 3, solve for w.Data from Example 3In the study of the forces on a certain beam, the equationis used. Solve for P. W L(WL + 2P) 8
Make the given changes in the indicated examples of this section and then perform the indicated divisions.In Example 4, change the dividend to 6x2 − 7x + 2.Data from Example 4Perform the division (6x2 + x − 2) ÷ (2x − 1).This division can also be indicated in the fractional formWe set up the
In the first line of Example 1, change the 5 to −7 and the −19 to 12. What other changes must then be made in the first paragraph?Data from Example 1
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 6(a), change 2x to 2y.Data from Example 6(a)3x + 2x − 5y = 5x − 5y
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 5, change (6x − 8) to (8 − 6x) and then solve.Data from Example 5Solve the equation x − 7 = 3x − (6x − 8).Checking in the original equation, we obtain (after simplifying)
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 4, change the factor (x + 3) to (x − 3).Data from Example 4 (x-2)(x + 3) = x(x) + x(3) + (-2)(x) + (-2)(3) = x² + 3x - 2xw - 6 = x² + x = 6
Make the given changes in the indicated examples of this section and then perform the indicated divisions.In Example 5, change the sign of the middle term of the numeratorfrom + to −.Data from Example 5Perform the divisionBecause there is no x-term in the dividend, we should leave space for any
Solve for the given letter from the indicated example of this section.For the formula in Example 4, solve for T0.Data from Example 4The effect of temperature on measurements is important when measurements must be made with great accuracy. The volume V of a special precision container at temperature
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 5(b), change the exponent 3 to 2.Data from Example 5(b) (2a - b)³ = (2a - b)(2a - b)(2a - b) the exponent 3 indicates three (2a - b) (4a² - 2ab - 2ab + b²) factors = (2a - b) (4a²
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 3(a), change the factor 2ax to −2ax.Data from Example 3(a)2ax( 3ax3 − 4yz) = 2ax( 3ax2) + (2ax)(−4yz) = 6a2x3 − 8axyz
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 10(a), change [ax − (5s − 2ax)] to [(ax − 5s) − 2ax].Data from Example 10(a) Зах -[ax - (5s - 2ax)] = 3ax - [ax - 5s +2ax] Зах ax + 5s - 2ax remove parentheses remove
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 8(a), change the sign before (2b − c) from + to −.Data from Example 8(a)3c + (2b − c) = 3c + 2b − c = 2b + 2c
Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example 8, change 8 5 to 7/4 and then solve.Data from Example 8The supports for a roof are triangular trusses for which the longest side is 8 5 as long as the shortest side for all of the
Solve for the given letter from the indicated example of this section.For the formula in Example 5, solve for β.Data from Example 5The volume V (in mm3) of a copper sphere changes with the temperature T (in °C) according to V = V0 + V0 βT, where V0 is the volume at 0°C. For a given
Make the given changes in the indicated examples of this section, and then solve the resulting problems.In Example 10(b), change {[a − (2a2b − a)] + 2b} to {a − [2a2b − (a + 2b)]}.Data from Example 10(b) 3a²b {[a (2a²b-a)] 3a²ba2a²b = 3a²ba+2a²b-a =5a²b 2a 2b = = - + 2b} + a + 2b} -
Perform the indicated divisions. 3 2 8x³y² -2xy
Perform the indicated divisions. -18b7c³ bc² 2
Perform the indicated divisions. - 16r³t5 -4r St
Perform the indicated multiplications.(a2)(ax)
Simplify the given algebraic expressions.5x + 7x − 4x
Solve the given equations.x − 2 = 7
Perform the indicated multiplications.(2xy)(x2y3)
Perform the indicated divisions. 51mn³ 17m²n²
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.PV = nRT, for T (chemistry)
Simplify the given algebraic expressions.6t − 3t − 4t
Solve the given equations.x − 4 = −1
Perform the indicated multiplications.−a2c2(a2cx3)
Perform the indicated divisions. (15x²y)(2xz) 10xy
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.rL = g2 − g1 , for g1 (surveying)
Simplify the given algebraic expressions.2y − y + 4x
Solve the given equations.x + 5 = 4
Perform the indicated multiplications.−2cs2 (−4cs)2
Perform the indicated divisions. (5sT)(88²T ³) 10s³7² 2
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for n (construction management) B = nTWL 12
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.W = SdT − Q, for Q (air conditioning)
Simplify the given algebraic expressions.−4C + L − 6C
Solve the given equations. t 2 5
Solve the given equations.s + 6 = −3
Solve the given equations. X -4 2
Perform the indicated multiplications.(2ax2)2 (−2ax)
Perform the indicated divisions. (4a³)(2x)² (4ax)²
Simplify the given algebraic expressions.3t − 4s − 3t − s
Perform the indicated multiplications.6pq3(3pq2)2
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.P = 2πTf , for T (mechanics)
Perform the indicated divisions. 12a2b (3ab2)2
Solve the given equations. y - 8 3 = 4
Simplify the given algebraic expressions.−8a − b + 12a + b
Solve the given equations. 7-r 6
Perform the indicated multiplications.i2(Ri + 2i)
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.p = pa + dgh, for g (hydrodynamics)
Simplify the given algebraic expressions.2F − 2T − 2 + 3F − T
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for r (centripetal force) Fe mv² 2 r
Insert the correct sign of inequality (> or <) between the given numbers.6 8
Perform the indicated divisions. За2х + 6ху 3x
Perform the indicated multiplications.2x(−p − q)
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for F (automotive trades) P = 4F TD²'
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.2Q = 2I + A + S, for I (nuclear physics)
Simplify the given algebraic expressions.x − 2y − 3x − y + z
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for A (welding) ST A 5T + 0.05d, for A
Perform the indicated multiplications.−3s(s2 − 5t)
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for L (spectroscopy) u = eL for L 2m
Solve the given equations.4E = −20
Simplify the given algebraic expressions.a2b − a2b2 − 2a2b
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for m2 (kinetic energy) K₁ K, Tele mi
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for d (traffic flow) T = c+d V
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for M (pulleys) a = 2mg M + 2m'
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for R (magnetic field) B = Hol 2TR
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for d (photography) f F d - F'
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.ct2 = 0.3t − ac, for a (medical technology)
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.2p + dv2 = 2d(C − W), for W (fluid flow)
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for M (ballistics) v = V(m + M) m
Each of the given formulas arises in the technical or scientific area of study shown. Solve for the indicated letter.for V (electronics) C² = C²(1 + 2V),
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