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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Find all the roots of the given equations, using synthetic division and the given roots.x4 − 10x³ + 35x² − 50x + 24 = 0 (r1 = 1, r2 = 2)
Perform the indicated divisions by synthetic division.(p6 − 6p3 − 2p2 − 6) ÷ (p − 2)
Where does the graph of the function f(x) = 4x3 + 3x2 − 20x − 15 cross the x-axis?
Why cannot a third-degree polynomial function with real coefficients have zeros of 1, 2, and j?
Find all the roots of the given equations, using synthetic division and the given roots.3B³ − 10B² + B + 14 = 0 (r1 = 2)
Perform the indicated divisions by synthetic division.(2x3 − 4x2 + x − 1) ÷ (x + 2)
Find the remaining roots of the given equations using synthetic division, given the roots indicated.x6 − x5 − 2x3 − 3x2 − x − 2 = 0 (j is a double root)
Find rational values of a such that (x − a) will divide into x3 + x2 − 4x − 4 with a remainder of zero.
Find all the roots of the given equations, using synthetic division and the given roots.x³ − 4x² − 7x + 10 = 0 (r1 = 5)
Perform the indicated divisions by synthetic division.(x3 + 2x2 − 3x + 4) ÷ (x + 4
Find the remaining roots of the given equations using synthetic division, given the roots indicated.x6 + 2x5 − 4x4 − 10x3 − 41x2 − 72x − 36 = 0 (−1 is a double root; 2j is a root)
Solve the following system algebraically: y = x4 − 11x2; y = 12x − 4
Use synthetic division to determine whether or not the given numbers are zeros of the given functions.6W4 + 9W3 − 2W² +6W − 4; −3̅/2, −1/2
Find the remaining roots of the given equations using synthetic division, given the roots indicated.4x5 + x³ − 4x² − 1 = 0 (r1 = 1, r2 = 1/2j)
Perform the indicated divisions by synthetic division.(x3 − 3x2 − x + 2) ÷ (x − 3)
Solve the given equation. √√y-7=2
Solve the given systems of equations graphically by using a calculator. Find all values to at least the nearest 0.1.y = x² − 3x² + y² = 25
Solve the given equation. x 3√2x + 1 = -5 -
Solve the given systems of equations algebraically.wh = 9w + h = 6W
Solve the given equations algebraically.x2/3 − 2x1/3 − 15 = 0
Solve the given equation. 2√3x - x = 5
Solve the given systems of equations by use of a calculator.x²y = 63y = 25 − 2x²
Solve the given systems of equations graphically by using a calculator. Find all values to at least the nearest 0.1.y = − 2x²y = x² − 6
Solve the given systems of equations algebraically.6y − x = 6x² + 3y² = 36
Solve the given equations algebraically.√x + 34√x = 28
Solve the given systems of equations by use of a calculator.y = 11− x²y = 2x² − 1
Solve the given equation. √5x1+ 3 = x
Solve the given systems of equations by use of a calculator. X 22. 4 x² - y² = 1 + y² = 1
Solve the given systems of equations graphically by using a calculator. Find all values to at least the nearest 0.1.8y = 15x²xy = 20
Solve the given systems of equations algebraically.2x − y = 22x² + 3y² = 4
Solve the given equation. 2√3x + 2 = 6x
Solve the given equations algebraically.33√x − 56√x + 2 = 0
Solve the given systems of equations graphically by using a calculator. Find all values to at least the nearest 0.1.4x² + 25y2 = 2110y = 31 − 9x
Solve the given systems of equations algebraically.3x + 3y = 62х² − y2 = 1
Solve the given equations algebraically, explain your method.4x + 3√x = 1
Solve the given systems of equations by use of a calculator. = 1 x² + 4y² = 4
Solve the given systems of equations by use of a calculator.y = x² +14x² + 16y² = 35
Solve the given systems of equations graphically by using a calculator. Find all values to at least the nearest 0.1.y = x² −24y = 12x − 17
Solve the given systems of equations algebraically.x + y = 1x² − y² = 1
Solve the given equation. 2√2P + 5 = P
Solve the given equations algebraically.2x − 5√x + 3 = 0
Solve the given equation. √15 - 2x = x
Solve the given systems of equations by use of a calculator.x2 − 2y = 0y = 3x - 5
Solve the given systems of equations graphically by using a calculator. Find all values to at least the nearest 0.1.y = 3x − 6ху = 6
A rectangular desktop has a perimeter of 14.0 ft and an area of 10.0 ft2. Find the length and the width of the desktop.
Solve the given systems of equations algebraically.p² + 4h² = 4h = p + 1
The velocity v of an object falling under the influence of gravity in terms of its initial velocity v0, the acceleration due to gravity g, and the height h fallen is given bySolve for h. v = √√v
Solve the given equation. √x + 4 = 3
Solve the given equations algebraically.x−1 − x−1/ 2 = 2
Solve the given systems of equations graphically by using a calculator. Find all values to at least the nearest 0.1.x² + 2y² = 8x − 2y = 4
Solve for x and y graphically:x2 − y2 = 4xy = 2
Solve the given systems of equations algebraically.x + 2y = 3x² + y² = 26
Solve the given systems of equations graphically by using a calculator. Find all values to at least the nearest 0.1. y = 4 x² + y² = 16
Solve forx: 3/2x + 5 = 5.
Solve the given equations algebraically.x−4 + 2x−2 = 24
Solve the given systems of equations by use of a calculator.x + y = 3x² + y² = 25
Solve the given systems of equations graphically by using a calculator. Find all values to at least the nearest 0.1.5x − y = 5y = x² − 13
Solve the given systems of equations algebraically.y = 2x − 1 y = 2x² + 2x − 3
Solve the given equations algebraically.10x−2 + 3x−1 − 1 = 0
Determine each of the following as being either true or false. If it is false, explain why.A solution of the equationis x = 2. √3x + 1 = 0
Solve the given systems of equations by use of a calculator.x + 2y = 9y = 3x2
In Example 7, change the coefficient of y in the first equation to 3.Data from Example 7In a computer game, two rockets follow paths described by the equations x2 = 2y and 3x − y = 5. Determine if
Solve the given equation. √x - 8 = 2
In Example 4, change the left side of the first equation from 5x2 + 2y2 to 2x2 + 5y2 and then solve the system.Data from Example 4By addition or subtraction, solve the system of equationsMultiplying
Solve the given systems of equations algebraically.y = 2x + 9y = x² + 1
In Example 3, change the coefficient of x2 in the first equation from 2 to 1 and then solve the system.Data from Example 3By addition or subtraction, solve the system of equationsWe note that if we
Solve the given equations algebraically.3x−2 − 7x−1 − 6 = 0
In Example 5, change the 4 under the second radical to 14.Data from Example 5Solve the equationThis is most easily solved by first isolating one of the radicals by placing the other radical on the
Solve for x and y algebraically:x2 − 2y= 52x + 6y = 1
In Example 6, change the coefficient of x2 to 25.Data from Example 6Graphically solve the system of equations:Solving the first equation for y, we haveBecause this is an ellipse, as shown in Example
Solve the given equations algebraically.4R4 + 15R2 = 4
Determine each of the following as being either true or false. If it is false, explain why.A solution of the equation 8x−4 − 2x−2 − 1 = 0 is (√2, 1).
Solve for x: x4 − 17x2 + 16 = 0.
In Example 2, change the + sign before y2 to −.Data from Example 2Plot the graph of the equation x2 + y2 = 25. We first solve this equation for y, and we obtainwhich we write asWe now assume values
Solve the given equations algebraically.x4 − 10x2 + 9 = 0
In Example 2, change the right side of the second equation from 2 to 3 and then solve the system.Data from Example 2By substitution, solve the system of equationsFrom the first equation, we have y =
In Example 4, change the 3 on the left to 7.Data from Example 4Solve the equationWe first isolate the radical by subtracting 3 from each side. This gives usWe now square both sides and proceed with
In Example 3, change the 8 under the radical to 19.Data from Example 3Solve the equationCubing both sides of the equation, we haveChecking this solution in the original equation, we getTherefore, the
In Example 1, change the − sign before 6x to +.Data from Example 1Graph the equation y = 3x2 − 6x.We graphed equations of this form in Section 7.4. Because the general quadratic function is y =
Make the given changes in the indicated examples of this section and then solve the resulting equations.In Example 3, change the 2 to 6 and then solve the equation.Data from Example 3Solve the
Determine each of the following as being either true or false. If it is false, explain why.To get the calculator display of the equation 2x 2 + y 2 = 4, let Y₁ = √4 - 2x².
Determine each of the following as being either true or false. If it is false, explain why.A solution of the system x2 + 2y2 = 9, 2x2 − y = 3, is (−1, 2).
In Example 2, change the 3x on the right to 3.Data from Example 2Solve the equationSquaring both sides of the equation gives usChecking this solution in the original equation, we haveTherefore, the
In Example 1, change the sign before y in the first equation from − to + and then solve the system.Data from Example 1By substitution, solve the system of equationsWe solve the first equation for
In Example 2, change the + before the 7x2 to − and then solve the equation.Data from Example 2Solve the equation 2x4 + 7x2 = 4.We first let y = x2 to write the equation in quadratic form. We will
Solve for x: x1/2 − 2x1/4 = 3.
While checking logarithmic curves on a calculator, a machine design student noted that a certain robotic arm was shaped like part of the graph of y = ln(2x2/3). As a check, the student re-wrote the
The formula ln(I /I0) = −βh is used in estimating the thickness of the ozone layer. Here, I0 is the intensity of a wavelength of sunlight before reaching Earth’s atmosphere, I is the intensity
For the circuit in Fig. 13.30, the current i (in mA) is given by i = 1.6e−100t . Plot the graph of i as a function of t for the first 0.05 s on semilog paper. Fig. 13.30 6 mA 4 ΚΩ w 2 ΚΩ ww 3
The current I (in μA) and resistance R (inΩ) were measured as follows in a certain microcomputer circuit: 100 200 500 1000 2000 5000 16 8.2 4.0 1.6 R (Ω) 1(μΑ) 81 41 10,000 0.8
Under certain conditions, the temperature T and pressure p are related by the following equation, where T0 is the temperature at pressureSolve for k. (品)宗. To 0 T Po:
For a particular solar-energy system, the collector area A required to supply a fraction F of the total energy is given by A = 480F2.2. Plot A (in m2) as a function of F, from F = 0.1 to F = 0.9, on
To find the number n of years that an initial value A of equipment takes to have salvage value S, the equationis used. Here, d is the annual rate of depreciation. Solve for d. n = log Slog A log(1 d)
Pure water is running into a brine solution, and the same amount of solution is running out. The number n of kilograms of salt in the solution after t min is found by solving the equation ln n =
According to one projection, the number of users (in millions) of the Internet in North America is given by y = 200 log(3.47 + 1.80t), where t is the number of years after 2000. On a calculator,
The temperature T of an object with an initial temperature T1 in water at temperature T0 as a function of the time t is given by T = T1 + (T0 − T1)e−kt . Solve for t.
An equation that may be used for the angular velocity ω of the slider mechanism in Fig. 13.29 is 2 lnω = ln 3g + ln sinθ − ln l, where g is the acceleration due to gravity. Solve for sin θ.
The intensity I of light decreases from its value I0 as it passes a distance x through a medium. Given that x = k(ln I0 − ln I), where k is a constant depending on the medium, find x for I =
The efficiency e of a gasoline engine as a function of its compression ratio r is given by e = 1 − r1−ϒ, where ϒ is a constant. Find ϒ for e = 0.55 and r = 7.5.
The time t (in s) to chemically change 5 kg of a certain substance into another is given bywhere x is the number of kilograms that have been changed at any time. Sketch the graph. 1 = −5 log (5

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