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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

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
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
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
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
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,
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
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
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
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
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
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
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)
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 ,
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 +
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
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
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
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.
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
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
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) +
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
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
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 -
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) =
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)
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
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
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
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
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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