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Questions and Answers of College Algebra

The time for one complete swing of a simple pendulum is given bywhere t is time in seconds, L is the length of the pendulum in feet, and g, the force due to gravity, is about 32 ft per sec2. Find the
Find each power of i. i83
Find each power of i. i89
Use a calculator to approximate each radical to three decimal places. √23.8
Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. V8 3-√2
Simplify. Assume that all variables represent positive real numbers. -V500r¹1
Simplify each expression. Assume that all variables represent positive real numbers. k114 K-312 - KIR
Find each power of i. i48
Use a calculator to approximate each radical to three decimal places. √98.4
Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. V27 3-√√3
Simplify. Assume that all variables represent positive real numbers. je - V/200p¹3
Simplify each expression. Assume that all variables represent positive real numbers. (Died + Th S/E₁
Find each power of i. i38
Use the electronics formulato calculate the resonant frequency ƒ of a circuit, in cycles per second, to the nearest thousand for the following values of L and C.(a) L = 7.237 × 10-5 and C = 2.5 ×
Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. 2 3√5 +2V/3
Simplify each expression. Assume that all variables represent positive real numbers. 6a7/4 (a-7/4 + 3a-3/4) ба
The threshold weight T for a person is the weight above which the risk of death increases greatly. The threshold weight in pounds for men aged 40–49 is related to height h in inches by the
Find each power of i. i102
Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. √2-√3 SA-9A
Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. -1 3√2-2√7
Simplify. Assume that all variables represent positive real numbers. V23kºp¹4 14
Simplify each expression. Assume that all variables represent positive real numbers. -2/3 - 4m-5/3) 4m5/3 (m-2/3-
Find each power of i. i43
According to an article in The World Scanner Report, the distance D, in miles, to the horizon from an observer’s point of view over water or “flat” earth is given bywhere H is the height of the
Simplify. Assume that all variables represent positive real numbers. 8269
Simplify each expression. Assume that all variables represent positive real numbers. -5x7/6(x5/6-x-1/6)
Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. √x5 √x8
Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. √x - √y √x + Vy
Heron’s formula gives a method of finding the area of a triangle if the lengths of its sides are known. Suppose that a, b, and c are the lengths of the sides. Let s denote one-half of the perimeter
A student simplified i-18 as shown. Provide justification for this correct work. i-18i-18. i20 = i-18+20= 2 = −1
Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. √ks 3 Vk²
Simplify. Assume that all variables represent positive real numbers. -W162r-15,9
Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. Vxz. Vz
Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. 51 k 2√k + √q 9
Simplify. Assume that all variables represent positive real numbers. 11 yll 36
Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. Vy. Vyz
Find E if I = 1 - i, R = 2, XL = 3, and Xc = 1.
Heron’s formula gives a method of finding the area of a triangle if the lengths of its sides are known. Suppose that a, b, and c are the lengths of the sides. Let s denote one-half of the perimeter
Simplify. Assume that all variables represent positive real numbers. -√32k5m¹1
Find I if E = 2 + 3i, R = 5, XL = 4, and Xc = 3.
Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. Va+Vb Va - Vb
Suppose someone claims thatmust equal a + b, because when a = 1 and b = 0, a true statement results:Explain why this is faulty reasoning. Wan + bn
Write each quotient in lowest terms. Assume that all variables represent positive real numbers. 12 - 9V/72 18
Simplify. Assume that x ≥ 0. +25
Write each quotient in lowest terms. Assume that all variables represent positive real numbers. 16-4√8 12
Simplify. Assume that x ≥ 0. V50²
Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. YAA
Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. 心
Simplify. Assume that all variables represent positive real numbers. 3 y17 125
Simplify. Assume that x ≥ 0. 48²
Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. √√√k
Write each quotient in lowest terms. Assume that all variables represent positive real numbers. 3-3√5 3
Simplify. Assume that all variables represent positive real numbers. x16 27
Write each quotient in lowest terms. Assume that all variables represent positive real numbers. 24 + 12V/5 12
Write each quotient in lowest terms. Assume that all variables represent positive real numbers. 30+20 V/6 10
Some equations have nonreal complex solutions. Work Exercises in order, to see how these nonreal complex solutions are related.Show that 3 + 2i is a solution of the equation x2 - 6x + 13 = 0.
Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. MAA 'm
Simplify. Assume that all variables represent positive real numbers. 13 49
Simplify. Assume that x ≥ 0. 8A
Write each quotient in lowest terms. Assume that all variables represent positive real numbers. бр 6р + V24p3 3р
Meteorologists can determine the duration of a storm using the functionwhere d is the diameter of the storm in miles and T is the time in hours. Find the duration of a storm with a diameter of 16 mi.
Simplify. Assume that x ≥ 0. 10, x25
Write each quotient in lowest terms. Assume that all variables represent positive real numbers. lly- 11y - V242y5 22y
The threshold weight t, in pounds, for a person is the weight above which the risk of death increases greatly. The threshold weight in pounds for men aged 40–49 is related to height H in inches by
Simplify. Assume that x ≥ 0. 12, x44
Rationalize each denominator. Assume that all radicals represent real numbers and that no denominators are 0. 3 Vx+y
The windchill factor is a measure of the cooling effect that the wind has on a person’s skin. It calculates the equivalent cooling temperature if there were no wind. The National Weather Service
Simplify. Assume that all variables represent positive real numbers. √4. √3
Rationalize each denominator. Assume that all radicals represent real numbers and that no denominators are 0. 9 V5+q
Rationalize each denominator. Assume that all radicals represent real numbers and that no denominators are 0. P Vp +2
Simplify. Assume that x ≥ 0. 12, x38
The windchill factor is a measure of the cooling effect that the wind has on a person’s skin. It calculates the equivalent cooling temperature if there were no wind. The National Weather Service
Rationalize each denominator. Assume that all radicals represent real numbers and that no denominators are 0. 5 √m-n
Simplify. Assume that x ≥ 0. 10 x16
The windchill factor is a measure of the cooling effect that the wind has on a person’s skin. It calculates the equivalent cooling temperature if there were no wind. The National Weather Service
The windchill factor is a measure of the cooling effect that the wind has on a person’s skin. It calculates the equivalent cooling temperature if there were no wind. The National Weather Service
Simplify. Assume that all variables represent positive real numbers. √√5. √6
Explain why the following two expressions must be equal. Ohm’s law for the current I in a circuit with voltage E, resistance R, capacitive reactance Xc, and inductive reactance XL is (46 +25i) (3
Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. 3Vx √x-2√y
Write each quotient in lowest terms. Assume that all variables represent positive real numbers. −5+5√₂ 5
In calculus, it is sometimes desirable to rationalize the numerator. To rationalize a numerator, we multiply the numerator and the denominator by the conjugate of the numerator. For
In calculus, it is sometimes desirable to rationalize the numerator. To rationalize a numerator, we multiply the numerator and the denominator by the conjugate of the numerator. For
In calculus, it is sometimes desirable to rationalize the numerator. To rationalize a numerator, we multiply the numerator and the denominator by the conjugate of the numerator. For
Simplify. Assume that all variables represent positive real numbers. Vy. Vy
Find the length of the unknown side in each right triangle. Simplify answers if possible. 9 b 6
Find the length of the unknown side in each right triangle. Simplify answers if possible. 3 C 4
Find the length of the unknown side in each right triangle. Simplify answers if possible. a 5
Find the length of the unknown side in each right triangle. Simplify answers if possible. 5 C 12
Find the length of the unknown side in each right triangle. Simplify answers if possible. 12 b 4
Find the distance between each pair of points. (6, 13) and (1, 1)
Find the distance between each pair of points. (-6, 5) and (3, -4)
Find the length of the unknown side in each right triangle. Simplify answers if possible. 11 나 a 7
Find the distance between each pair of points. (-8, 2) and (-4,1)
Find the distance between each pair of points. (8, 13) and (2, 5)
Find the distance between each pair of points. (4.7, 2.3) and (1.7, -1.7)
Find the distance between each pair of points. (-1, 5) and (-7, 7)
Find the distance between each pair of points. (V2, V6) and (-2√2, 4√6)
Find the distance between each pair of points. (-1, 2) and (5,3)
Find the distance between each pair of points. (c, c - d) and (d, c + d)
Find the distance between each pair of points. (√7,9√3) and (-√7, 4√3)

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