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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Solve the given problems. Where indicated, the expression is found in the stated technical area.Expand the third term and then factor by grouping: pa2 + (1 − p)b2 − [pa + (1 − p)b]2
Solve the given problems. Where indicated, the expression is found in the stated technical area.A metal cube of edge x is heated and each edge increases by 4 mm. Express the increase in volume in
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(bridge design) wx² 2To + kx 4 12To
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(electric motors) V -| kp RT 2 2 k²p²
Solve the given problems. Where indicated, the expression is found in the stated technical area.Express the difference in volumes of two ball bearings of radii r mm and 3 mm in factored form. (r >
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(aircraft emergency locator transmitter) 1 2 + d4 24 do 120
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(hydrodynamics) 1- За 4r a 3 4r 3
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(spring stress) 4k 1 + 4k - 4 2k
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(mechanism design) u² 2g 1 u² 2gc² 2g +x
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(rocket fuel) Am k 002 8 (7) ² + AML k
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(optics) +4 -I f d fF
Perform the indicated operations and simplify the given expressions. Each expression is from the indicated technical area of application.(electricity) V 1 + 2R 2R+ 2
Solve for the indicated letter. Each equation is from the indicated technical area of application.(rotational torque) T || الد t ول - لا for
Solve for the indicated letter. Each equation is from the indicated technical area of application.(architecture) R = WL H(w + L)' for L
Solve for the indicated letter. Each equation is from the indicated technical area of application.(mechanical vibrations) s² + CS m + kL² mb² 0, for c
Solve for the indicated letter. Each equation is from the indicated technical area of application.(nuclear physics) E = V₁ + (m + M)V² 2 + P² for I 21
Solve for the indicated letter. Each equation is from the indicated technical area of application.W = mgh2 − mgh1, for m (work done on object)
Solve for the indicated letter. Each equation is from the indicated technical area of application.(photography) 92 - 91 d f+91 for 91 D
Solve for the indicated letter. Each equation is from the indicated technical area of application.h(T1 + T2) = T2, for T1 (engine efficiency)
Solve for the indicated letter. Each equation is from the indicated technical area of application.(optics) I = A x 2 B (10x)2' for A
Solve for the indicated letter. Each equation is from the indicated technical area of application.(mechanics) F = m SC + Fo S for C
Solve for the indicated letter. Each equation is from the indicated technical area of application.(reinforced concrete design) C = n(1 k k) for k
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.If a certain car’s lights are left on, the battery will be dead in 4.0
Simplify the given expressions and then check your answers with a calculator as in Example 8.Data from Example 8To graphically check the result of Example 7, we first let y1 equal the original
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.Two pumps are being used to fight a fire. One pumps 5000 gal in 20 min,
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A number m is the harmonic mean of number x and y if 1/m equals the
In analyzing a certain electric circuit, the expressionis used. Simplify this expression, and write a paragraph describing your procedure. When you “cancel,” explain what basic operation is being
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.An auto mechanic can do a certain motor job in 3.0 h, and with an
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.The relative density of an object may be defined as its weight in air wa,
Simplify the given expressions and then check your answers with a calculator as in Example 8.Data from Example 8To graphically check the result of Example 7, we first let y1 equal the original
Perform indicated operations and simplify. Check the solution with a graphing calculator. X 3 X - 1
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A car travels halfway to its destination at 80.0 km/h and the remainder
Reduce each fraction to simplest form. x2 x² - 10x + 25 x² - 25
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.For electric resistors in parallel, the reciprocal of the combined
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A fire engine averaged 48 mi/h going to a fire, and 36 mi/h on its return
Reduce each fraction to simplest form. 4a²+12ab + 9b² 4a² + 6ab
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(environmental pollution) с 7 P 100 - P for p
Perform indicated operations and simplify. Check the solution with a graphing calculator. a 1 a n
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(FM transmission) Z = 1jX 8mR 8m for R
Perform indicated operations and simplify. x y 1+ y x V X
Factor the given expressions completely.8x3 + 27
Simplify the given expressions. The technical application of each is indicated. 2T / a + bi 2ab abx .2a + 26. (optics)
Simplify the given expressions. The technical application of each is indicated.(electromagnetism) 8лn²eu my² 72 ) ( 2m² mv² mvu²/2mv² - 2ne²,
Factor the given expressions completely.2a6 + 4a3 + 2
Reduce each fraction to simplest form. 2w4+5w23 w4 + 11w2 + 24
Perform indicated operations and simplify. V²-9 V 1 > 3
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(architecture) A-wp-w²w², for p = 8
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(thermodynamics) P = RT V-b a V2 for T
Simplify the given expressions. The technical application of each is indicated.(cosmology) CA² - CA chổ X2 1² + 12 X²
Reduce each fraction to simplest form. 3y³ + 7y² + 4y 4 + 5y + y² 2
Factor the given expressions completely.ab2 − 3b2 + a − 3
Perform indicated operations and simplify. X x + 1 1 x + zx x - 1
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(photography) X + nx 7, for f f
Reduce each fraction to simplest form. 5x²6x8. x³ + x² - 6x
Factor the given expressions completely.axy − ay + ax − a
Simplify the given expressions. The technical application of each is indicated.(hydrodynamics) (P1 - P2) + πατρι – πατρι 81u
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(electricity: capacitors) 1/2 = 1 / 2 + -, for C₁ C₁ + C3'
Perform indicated operations and simplify. 1+ 1 + 1 1 + T X
Reduce each fraction to simplest form. 5s²+8rs 4s² - + 5s² 6r²17rs
The expression f(x + h) − f(x) is frequently used in the study of calculus. Determine and then simplify this expression for the given functions. f(x)= X x + 1
Factor the given expressions completely.nx + 5n − x2 + 25
Perform the indicated operations and express results in simplest form. 48ax³y6 9a³xy6
The speed v of a satellite can be found from the equation Simplify the right side of the equation and then solve for v. v2 GmM r² m r
Reduce each fraction to simplest form. N4 - 16 8N 16
Factor the given expressions completely.ty − 4t + y2 − 16
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(beam design) D= wx4 wLx3 24EI 6EI wL²x² 4EI for w
Simplify the following expression involving units (the number 2 is exact): 2 (28 m²) ² S 2(0.90) (9.8)
The expression f(x + h) − f(x) is frequently used in the study of calculus. Determine and then simplify this expression for the given functions. f(x) = 3 1 - 2x
Reduce each fraction to simplest form. 3 + x(4+ x) 3+x
Perform the indicated operations and express results in simplest form. -39r²5418 52rs St
Perform the indicated operations and express results in simplest form. 6x²7x 2x²5x - 3 + 3
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(optics) f(n-1)= R₁ 1 -, for R₁ R₂
The expression f(x + h) − f(x) is frequently used in the study of calculus. Determine and then simplify this expression for the given functions. f(x) = 1 x² 2
Reduce each fraction to simplest form. 1+ 4 (2t + 9)t + 4
Perform the indicated operations and express results in simplest form. p4-4p²-4 12 + p² - p4
Solve for the indicated letter. Each of the given formulas arises in the technical or scientific area of study listed.(business) P = 1 1+i 1+i for i
The expression f(x + h) − f(x) is frequently used in the study of calculus. Determine and then simplify this expression for the given functions. f(x) = 2 x² + 4
Reduce each fraction to simplest form. 2A³ + 8A4 + 8A³ 4A + 2
Reduce each fraction to simplest form. (x - 1)(3 + x) (3 - x)(1-x)
Perform the indicated operations and express results in simplest form. 4x + 4y 28x 35x² x² - y² X 2
Perform the indicated operations and express results in simplest form. 4x² - 12x 6 - 12x 3 (6x = ³) (²
Perform the indicated operations and express results in simplest form. 18 - 6L L² - 6L +9 L² - 2L 15 L² - 9
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.One pump can empty an oil tanker in 5.0 h, and a second pump can
Reduce each fraction to simplest form. (2x - 1)(x + 6) (x - 3)(1-2x)
Simplify the given expressions.If f(x) = 2x − x2 , find ƒ(1). a
Simplify the given expressions.Using the definitions of the trigonometric functions given in Section 4.2, find an expression that is equivalent to (tanθ)(cotθ) + (sinθ)2 − cosθ, in terms of x,
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.One company determines that it will take its crew 450 h to clean up a
Simplify the given expressions.If f(x) = x2 + x, find ƒ(a + ¹).
Simplify the given expressions.Using the definitions of the trigonometric functions given in Section 4.2, find an expression that is equivalent to secθ − (cotθ)2 + cscθ, in terms of x, y, and r.
Reduce each fraction to simplest form. 2 2 y² - x² 2x - 2y
Perform the indicated operations and express results in simplest form. 6x² - xy-y² 2x² + xy - y² ÷ 16y² - 4x² 2x² + 6xy + 4y²
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.One automatic packaging machine can package 100 boxes of machine parts in
Reduce each fraction to simplest form. x² - y² - 4x + 4y x² - y² + 4x - 4y
Reduce each fraction to simplest form. n³ + n² − n − n³n² n + 1 -
Perform the indicated operations and express results in simplest form. 3x 7x2 + 13x – 2 6x2 x2 + 4x + 4 gul
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A painting crew can paint a structure in 12 h, or the crew can paint it
Perform the indicated operations and express results in simplest form. 3у - 3x 2х² + 3xу - 202 2y² 3x² - 3у2 x2 + 4xy + 4у2
Perform the indicated operations and express results in simplest form. x + x2 1+ X +1 1
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A beam of light travels from the source to a water tank and then through
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.An elevator traveled from the first floor to the top floor of a building

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