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- Question : 1Q - x y x y ?3 9 1 1 ?2 4 2 4 ?1 1 3 9 0 0
- Question : 2Q - x y x y ?3 ?2 1 1 ?2 ?8 2 8 ?1 ?1 3 ?2 0 0
- Question : 3Q - x y x y 1 ?3 1 1 2 ?2 2 2 3 ?1 3 3 0 0
- Question : 4Q - x y x y 1 1 5 1 2 1 6 1 3 1 7 1 4 1
- Question : 5Q - x y x y 3 3 15 1 5 2 21 2 8 1 33 3 10 0
- Question : 6Q - x y x y ?7 11 1 ?2 ?2 5 3 4 ?2 1 6 11 0 ?1
- Question : 7Q - For the following exercises, find the values for each function, if they exist, then simplify. a. f (0) b. f (1) c. f (3) d. f (?x) e. f (a) f. f (a + h)
- Question : 8Q - f (x) = 5x ? 2
- Question : 9Q - f (x) = 4x2 ? 3x + 1
- Question : 10Q - f (x) =2x
- Question : 11Q - f (x) = |x ? 7| + 8
- Question : 12Q - f (x) = 6x + 5
- Question : 13Q - f (x) = 6x + 5
- Question : 14Q - f (x) = 9
- Question : 15Q - f (x) = x x2 ? 16
- Question : 16Q - g(x) = 8x ? 1
- Question : 17Q - h(x) = 3 x2 + 4
- Question : 18Q - f (x) = ?1 + x + 2
- Question : 19Q - f (x) = 1 x ? 9
- Question : 20Q - g(x) = 3 x ? 4
- Question : 21Q - f (x) = 4|x + 5|
- Question : 22Q - g(x) = 7 x ? 5
- Question : 23Q - f (x) = x2 + 1
- Question : 24Q - f (x) = 3x ? 6
- Question : 25Q - f (x) =12 x + 1
- Question : 26Q - f (x) = 2|x|
- Question : 27Q - f (x) = ?x2
- Question : 28Q - f (x) = x3
- Question : 29Q - f (x) = 3x + 4, g(x) = x ? 2
- Question : 30Q - f (x) = x ? 8, g(x) = 5x2
- Question : 31Q - f (x) = 3x2 + 4x + 1, g(x) = x + 1
- Question : 32Q - f (x) = 9 ? x2, g(x) = x2 ? 2x ? 3
- Question : 33Q - f (x) = x, g(x) = x ? 2
- Question : 34Q - f (x) = 6 +1x , g(x) =1x
- Question : 35Q - f (x) = 3x, g(x) = x + 5
- Question : 36Q - f (x) = x + 4, g(x) = 4x ? 1
- Question : 37Q - f (x) = 2x + 4, g(x) = x2 ? 2
- Question : 38Q - f (x) = x2 + 7, g(x) = x2 ? 3
- Question : 39Q - f (x) = x, g(x) = x + 9
- Question : 40Q - f (x) = 3 2x + 1, g(x) =2x
- Question : 41Q - f (x) = |x + 1|, g(x) = x2 + x ? 4
- Question : 42Q - The table below lists the NBA championship winners for the years 2001 to 2012. Year Winner 2001 LA Lakers 2002 LA Lakers 2003 San Antonio Spurs 2004 Detroit Pistons 2005 San Antonio Spurs 2006 Miami Heat 2007 San Antonio Spurs 2008 Boston Celtics 2009 LA Lakers 2010 LA Lakers 2011 Dallas Mavericks 2012 Miami Heat a. Consider the relation in which the domain values are the years 2001 to 2012 and the range is the corresponding winner. Is this relation a function? Explain why or why not. b. Consider the relation where the domain values are the winners and the range is the corresponding years. Is this relation a function? Explain why or why not.
- Question : 43Q - [T] The area A of a square depends on the length of the side s. a. Write a function A(s) for the area of a square. b. Find and interpret A(6.5). c. Find the exact and the two-significant-digit approximation to the length of the sides of a square with area 56 square units.
- Question : 44Q - [T] The volume of a cube depends on the length of the sides s. a. Write a function V(s) for the area of a square. b. Find and interpret V(11.8).
- Question : 45Q - [T] A rental car company rents cars for a flat fee of $20 and an hourly charge of $10.25. Therefore, the total cost C to rent a car is a function of the hours t the car is rented plus the flat fee. a. Write the formula for the function that models this situation. b. Find the total cost to rent a car for 2 days and 7 hours. c. Determine how long the car was rented if the bill is $432.73.
- Question : 46Q - [T] A vehicle has a 20-gal tank and gets 15 mpg. The number of miles N that can be driven depends on the amount of gas x in the tank. a.Write a formula that models this situation. b.Determine the number of miles the vehicle can travel on (i) a full tank of gas and (ii) 3/4 of a tank of gas. c.Determine the domain and range of the function. d.Determine how many times the driver had to stop for gas if she has driven a total of 578 mi.
- Question : 47Q - [T] The volume V of a sphere depends on the length of its radius as V = (4/3)?r 3. Because Earth is not a perfect sphere, we can use the mean radius when measuring from the center to its surface. The mean radius is the average distance from the physical center to the surface, based on a large number of samples. Find the volume of Earth with mean radius 6.371
- Question : 48Q - [T] A certain bacterium grows in culture in a circular region. The radius of the circle, measured in centimeters, is , where t is time measured in hours since a circle of a 1-cm radius of the bacterium was put into the culture. a. Express the area of the bacteria as a function of time. b. Find the exact and approximate area of the bacterial culture in 3 hours. c. Express the circumference of the bacteria as a function of time. d. Find the exact and approximate circumference of the bacteria in 3 hours.
- Question : 49Q - [T] An American tourist visits Paris and must convert U.S. dollars to Euros, which can be done using the function E(x) = 0.79x, where x is the number of U.S. dollars and E(x) is the equivalent number of Euros. Since conversion rates fluctuate, when the tourist returns to the United States 2 weeks later, the conversion from Euros to U.S. dollars is D(x) = 1.245x, where x is the number of Euros and D(x) is the equivalent number of U.S. dollars. a. Find the composite function that converts directly from U.S. dollars to U.S. dollars via Euros. Did this tourist lose value in the conversion process? b. Use (a) to determine how many U.S. dollars then tourist would get back at the end of her trip if she converted an extra $200 when she arrived in Paris.
- Question : 50Q - [T] The manager at a skateboard shop pays his workers a monthly salary S of $750 plus a commission of $8.50 for each skateboard they sell. a. Write a function y = S(x) that models a worker
- Question : 51Q - [T] Use a graphing calculator to graph the half-circle y = 25 ? (x ? 4)2. Then, use the INTERCEPT feature to find the value of both the x - and y -intercepts.
- Question : 52Q - (?2, 4) and (1, 1)
- Question : 53Q - (?1, 4) and (3, ?1)
- Question : 54Q - (3, 5) and (?1, 2)
- Question : 55Q - (6, 4) and (4, ?3)
- Question : 56Q - (2, 3) and (5, 7)
- Question : 57Q - (1, 9) and (?8, 5)
- Question : 58Q - (2, 4) and (1, 4)
- Question : 59Q - (1, 4) and (1, 0)
- Question : 60Q - Slope = ?6, passes through (1, 3)
- Question : 61Q - Slope = 3, passes through (?3, 2)
- Question : 62Q - Slope =13 , passes through (0, 4)
- Question : 63Q - Slope =25 , x -intercept = 8
- Question : 64Q - Passing through (2, 1) and (?2, ?1)
- Question : 65Q - Passing through (?3, 7) and (1, 2)
- Question : 66Q - x -intercept = 5 and y -intercept = ?3
- Question : 67Q - x -Intercept = ?6 and y -intercept = 9
- Question : 68Q - y = 2x ? 3
- Question : 69Q - y = ?17 x + 1
- Question : 70Q - f (x) = ?6x
- Question : 71Q - f (x) = ?5x + 4
- Question : 72Q - 4y + 24 = 0
- Question : 73Q - 8x ? 4 = 0
- Question : 74Q - 2x + 3y = 6
- Question : 75Q - f (x) = 2x2 ? 3x ? 5
- Question : 76Q - 6x ? 5y + 15 = 0
- Question : 77Q - f (x) = ?3x2 + 6x
- Question : 78Q - f (x) =12 x2 ? 1
- Question : 79Q - f (x) = x3 + 3x2 ? x ? 3
- Question : 80Q - f (x) = 3x ? x3
- Question : 81Q - g(x) = x2 ? 1
- Question : 82Q - g(x) = (x + 3)2 + 1
- Question : 83Q - g(x) = x + 2
- Question : 84Q - g(x) = ? x ? 1
- Question : 85Q - g(x) = f (x) + 1
- Question : 86Q - g(x) = f (x ? 1) + 2
- Question : 87Q - (x) = 4x + 3, x ? 0 ?x + 1, x > 0; f (?3); f (0); f (2)
- Question : 88Q - f (x) = x2 ? 3, x < 0 4x ? 3, x ? 0 ; f (?4); f (0); f (2)
- Question : 89Q - h(x) = x + 1, x ? 5 4, x > 5 ; h(0); h(?); h(5)
- Question : 90Q - g(x) = 3 x ? 2, x ? 2 4, x = 2 ; g(0); g(?4); g(2)
- Question : 91Q - g(x) = (4x + 1)/(7x ? 2) is a transcendental function.
- Question : 92Q - g(x) = 3 x is an odd root function
- Question : 93Q - A logarithmic function is an algebraic function
- Question : 94Q - A function of the form f (x) = xb, where b is a real valued constant, is an exponential function.
- Question : 95Q - The domain of an even root function is all real numbers.
- Question : 96Q - [T] A company purchases some computer equipment for $20,500. At the end of a 3-year period, the value of the equipment has decreased linearly to $12,300. a. Find a function y = V(t) that determines the value V of the equipment at the end of t years. b. Find and interpret the meaning of the x - and y - intercepts for this situation. c. What is the value of the equipment at the end of 5 years? d. When will the value of the equipment be $3000?
- Question : 97Q - [T] Total online shopping during the Christmas holidays has increased dramatically during the past 5 years. In 2012 (t = 0), total online holiday sales were $42.3 billion, whereas in 2013 they were $48.1 billion. a. Find a linear function S that estimates the total online holiday sales in the year t. b. Interpret the slope of the graph of S. c. Use part a. to predict the year when online shopping during Christmas will reach $60 billion.
- Question : 98Q - [T] A family bakery makes cupcakes and sells them at local outdoor festivals. For a music festival, there is a fixed cost of $125 to set up a cupcake stand. The owner estimates that it costs $0.75 to make each cupcake. The owner is interested in determining the total cost C as a function of number of cupcakes made. a. Find a linear function that relates cost C to x, the number of cupcakes made. b. Find the cost to bake 160 cupcakes. c. If the owner sells the cupcakes for $1.50 apiece, how many cupcakes does she need to sell to start making profit? (Hint: Use the INTERSECTION function on a calculator to find this number.)
- Question : 99Q - [T] A house purchased for $250,000 is expected to be worth twice its purchase price in 18 years. a. Find a linear function that models the price P of the house versus the number of years t since the original purchase. b. Interpret the slope of the graph of P. c. Find the price of the house 15 years from when it was originally purchased.
- Question : 100Q - [T] A car was purchased for $26,000. The value of the car depreciates by $1500 per year. a. Find a linear function that models the value V of the car after t years. b. Find and interpret V(4).
- Question : 101Q - [T] A condominium in an upscale part of the city was purchased for $432,000. In 35 years it is worth $60,500. Find the rate of depreciation.
- Question : 102Q - [T] The total cost C (in thousands of dollars) to produce a certain item is modeled by the function C(x) = 10.50x + 28,500, where x is the number of items produced. Determine the cost to produce 175 items.
- Question : 103Q - [T] A professor asks her class to report the amount of time t they spent writing two assignments. Most students report that it takes them about 45 minutes to type a fourpage assignment and about 1.5 hours to type a nine-page assignment. a. Find the linear function y = N(t) that models this situation, where N is the number of pages typed and t is the time in minutes. b. Use part a. to determine how many pages can be typed in 2 hours. c. Use part a. to determine how long it takes to type a 20-page assignment.
- Question : 104Q - [T] The output (as a percent of total capacity) of nuclear power plants in the United States can be modeled by the function P(t) = 1.8576t + 68.052, where t is time in years and t = 0 corresponds to the beginning of 2000. Use the model to predict the percentage output in 2015.
- Question : 105Q - [T] The admissions office at a public university estimates that 65% of the students offered admission to the class of 2019 will actually enroll. a. Find the linear function y = N(x), where N is the number of students that actually enroll and x is the number of all students offered admission to the class of 2019. b. If the university wants the 2019 freshman class size to be 1350, determine how many students should be admitted.
- Question : 106Q - 240
- Question : 107Q - 15
- Question : 108Q - ?60
- Question : 109Q - ?225
- Question : 110Q - 330
- Question : 111Q - ? 2 rad
- Question : 112Q - 7? 6 rad
- Question : 113Q - 11? 2 rad
- Question : 114Q - ?3? rad
- Question : 115Q - 5? 12 rad
- Question : 116Q - cos 4? 3
- Question : 117Q - tan 19? 4
- Question : 118Q - sin ?3? 4
- Question : 119Q - sec ? 6
- Question : 120Q - sin ? 12
- Question : 121Q - cos 5? 12
- Question : 122Q - a = 4, c = 7
- Question : 123Q - a = 21, c = 29
- Question : 124Q - a = 85.3, b = 125.5
- Question : 125Q - b = 40, c = 41
- Question : 126Q - a = 84, b = 13
- Question : 127Q - b = 28, c = 35
- Question : 128Q - P 7 25, y y > 0
- Question : 129Q - P ?15 17 , y y < 0
- Question : 130Q - P x, 7 3 x < 0
- Question : 131Q - P x, ? 15 4 x > 0
- Question : 132Q - tan2 x + sin xcsc x
- Question : 133Q - sec xsin xcot x
- Question : 134Q - tan2 x sec2 x
- Question : 135Q - sec x ? cos x
- Question : 136Q - (1 + tan?)2 ? 2tan?
- Question : 137Q - sin x(csc x ? sin x)
- Question : 138Q - cost sint + sint 1 + cost
- Question : 139Q - 1 + tan2 ? 1 + cot2 ?
- Question : 140Q - an? cot? csc? = sin?
- Question : 141Q - sec2 ? tan? = sec? csc?
- Question : 142Q - sint csct + cost sect = 1
- Question : 143Q - sin x cos x + 1 + cos x ? 1 sin x = 0
- Question : 144Q - cot? + tan? = sec? csc?
- Question : 145Q - sin2 ? + tan2 ? + cos2 ? = sec2 ?
- Question : 146Q - 1 ? sin? + 1 1 + sin? = 2sec2 ? cos x +
- Question : 147Q - tan? ? cot? sin? cos? = sec2 ? ? csc2 ?
- Question : 148Q - 2sin? ? 1 = 0
- Question : 149Q - 1 + cos? =12
- Question : 150Q - 2tan2 ? = 2
- Question : 151Q - 4sin2 ? ? 2 = 0
- Question : 152Q - 3cot? + 1 = 0
- Question : 153Q - 3sec? ? 2 3 = 0
- Question : 154Q - 2cos? sin? = sin?
- Question : 155Q - csc2 ? + 2csc? + 1 = 0
- Question : 156Q - y = sin x ? ? 4
- Question : 157Q - y = 3cos(2x + 3)
- Question : 158Q - y = ?1 2 sin 14 x
- Question : 159Q - y = 2cos x ? ? 3
- Question : 160Q - y = ?3sin(?x + 2)
- Question : 161Q - y = 4cos 2x ? ? 2
- Question : 162Q - [T] The diameter of a wheel rolling on the ground is 40 in. If the wheel rotates through an angle of 120
- Question : 163Q - [T] Find the length of the arc intercepted by central angle ? in a circle of radius r. Round to the nearest hundredth.
- Question : 164Q - [T] As a point P moves around a circle, the measure of the angle changes. The measure of how fast the angle is changing is called angular speed,
- Question : 165Q - [T] A total of 250,000 m2 of land is needed to build a nuclear power plant. Suppose it is decided that the area on which the power plant is to be built should be circular. a. Find the radius of the circular land area. b. If the land area is to form a 45
- Question : 166Q - [T] The area of an isosceles triangle with equal sides of length x is
- Question : 167Q - [T] A particle travels in a circular path at a constant angular speed ?. The angular speed is modeled by the function
- Question : 168Q - [T] An alternating current for outlets in a home has voltage given by the function
- Question : 169Q - [T] The number of hours of daylight in a northeast city is modeled by the function where t is the number of days after January 1. a. Find the amplitude and period. b. Determine the number of hours of daylight on the longest day of the year. c. Determine the number of hours daylight on the shortest day of the year. d. Determine the number of hours of daylight 90 days after January 1. e. Sketch the graph of the function for one period starting on January 1.
- Question : 170Q - [T] Suppose that T = 50 + 10sin ? 12(t ? 8) is a mathematical model of the temperature (in degrees Fahrenheit) at t hours after midnight on a certain day of the week. a. Determine the amplitude and period. b. Find the temperature 7 hours after midnight. c. At what time does T = 60
- Question : 171Q - [T] The function H(t) = 8sin ? 6t models the height H (in feet) of the tide t hours after midnight. Assume that t = 0 is midnight. a. Find the amplitude and period. b. Graph the function over one period. c. What is the height of the tide at 4:30 a.m.?
- Question : 172Q - f (x) = x2 ? 4, x ? 0
- Question : 173Q - f (x) = 3 x ? 4
- Question : 174Q - f (x) = x3 + 1
- Question : 175Q - f (x) = (x ? 1)2, x ? 1
- Question : 176Q - f (x) = x ? 1
- Question : 177Q - f (x) = 1 x + 2
- Question : 178Q - f (x) = 8x, g(x) = x8
- Question : 179Q - f (x) = 8x + 3, g(x) = x ? 3
- Question : 180Q - f (x) = 5x ? 7, g(x) = x + 5
- Question : 181Q - f (x) =23 x + 2, g(x) =32 x + 3
- Question : 182Q - f (x) = 1 x ? 1, x ? 1, g(x) =1x + 1, x ? 0
- Question : 183Q - f (x) = x3 + 1, g(x) = (x ? 1)1/3
- Question : 184Q - f (x) = x2 + 2x + 1, x ? ?1, g(x) = ?1 + x, x ? 0
- Question : 185Q - f (x) = 4 ? x2, 0 ? x ? 2, g(x) = 4 ? x2, 0 ? x ? 2
- Question : 186Q - tan?13 3
- Question : 187Q - cos?1 ? 2 2
- Question : 188Q - cot?1 (1)
- Question : 189Q - sin?1 (?1)
- Question : 190Q - cos?1 3 2
- Question : 191Q - vcos tan?1 3
- Question : 192Q - sin cos?1 2 2
- Question : 193Q - sin?1 sin ? 3
- Question : 194Q - tan?1 tan ?? 6
- Question : 195Q - The function C = T(F) = (5/9)(F ? 32) converts degrees Fahrenheit to degrees Celsius. a. Find the inverse function F = T ?1(C) b. What is the inverse function used for?
- Question : 196Q - [T] The velocity V (in centimeters per second) of blood in an artery at a distance x cm from the center of the artery can be modeled by the function V = f (x) = 500(0.04 ? x2) for 0 ? x ? 0.2. a. Find x = f ?1(V). b. Interpret what the inverse function is used for. c. Find the distance from the center of an artery with a velocity of 15 cm/sec, 10 cm/sec, and 5 cm/sec.
- Question : 197Q - A function that converts dress sizes in the United States to those in Europe is given by D(x) = 2x + 24. a. Find the European dress sizes that correspond to sizes 6, 8, 10, and 12 in the United States. b. Find the function that converts European dress sizes to U.S. dress sizes. c. Use part b. to find the dress sizes in the United States that correspond to 46, 52, 62, and 70.
- Question : 198Q - [T] The cost to remove a toxin from a lake is modeled by the function C(p) = 75p/(85 ? p), where C is the cost (in thousands of dollars) and p is the amount of toxin in a small lake (measured in parts per billion [ppb]). This model is valid only when the amount of toxin is less than 85 ppb. a. Find the cost to remove 25 ppb, 40 ppb, and 50 ppb of the toxin from the lake. b. Find the inverse function. c. Use part b. to determine how much of the toxin is removed for $50,000.
- Question : 199Q - [T] A race car is accelerating at a velocity given by v(t) = 25 4 t + 54, where v is the velocity (in feet per second) at time t. a. Find the velocity of the car at 10 sec. b. Find the inverse function. c. Use part b. to determine how long it takes for the car to reach a speed of 150 ft/sec.
- Question : 200Q - [T] An airplane
- Question : 201Q - [T] Using ? = 2sin?1 1M , find the Mach number M for the following angles. a. ? = ? 6 b. ? = 2? 7 c. ? = 3?
- Question : 202Q - [T] The temperature (in degrees Celsius) of a city in the northern United States can be modeled by the function T(x) = 5 + 18sin?? ? 6(x ? 4.6)? ?, where x is time in months and x = 1.00 corresponds to January 1. Determine the month and day when the temperature is 21
- Question : 203Q - [T] The depth (in feet) of water at a dock changes with the rise and fall of tides. It is modeled by the function D(t) = 5sin?? ? 6t ? 7? 6 ?? + 8, where t is the number of hours after midnight. Determine the first time after midnight when the depth is 11.75 ft.
- Question : 204Q - [T] An object moving in simple harmonic motion is modeled by the function s(t) = ?6cos?? ?t 2 ?? , where s is measured in inches and t is measured in seconds. Determine the first time when the distance moved is 4.5 ft.
- Question : 205Q - [T] A local art gallery has a portrait 3 ft in height that is hung 2.5 ft above the eye level of an average person. The viewing angle ? can be modeled by the function ? = tan?1 5x.5 ? tan?1 2x.5, where x is the distance (in feet) from the portrait. Find the viewing angle when a person is 4 ft from the portrait.
- Question : 206Q - [T] Use a calculator to evaluate tan?1 (tan(2.1)) and cos?1 (cos(2.1)). Explain the results of each.
- Question : 207Q - [T] Use a calculator to evaluate sin(sin?1(?2)) and tan(tan?1(?2)). Explain the results of each.
- Question : 208Q - f (x) = 5x a. x = 3 b. x =12 c. x = 2
- Question : 209Q - f (x) = (0.3)x a. x = ?1 b. x = 4 c. x = ?1.5
- Question : 210Q - f (x) = 10x a. x = ?2 b. x = 4 c. x =53
- Question : 211Q - f (x) = ex a. x = 2 b. x = ?3.2 c. x = ?
- Question : 212Q - f (x) = ex + 2
- Question : 213Q - f (x) = ?2x
- Question : 214Q - f (x) = 3x + 1
- Question : 215Q - f (x) = 1 ? 2?x
- Question : 216Q - f (x) = 4x ? 1
- Question : 217Q - f (x) = 5x + 1 + 2
- Question : 218Q - f (x) = e?x ? 1
- Question : 219Q - log3 81 = 4
- Question : 220Q - log8 2 =13
- Question : 221Q - log5 1 = 0
- Question : 222Q - log5 25 = 2
- Question : 223Q - log0.1 = ?1
- Question : 224Q - ln 1 e3= ?3
- Question : 225Q - log9 3 = 0.5
- Question : 226Q - ln1 = 0
- Question : 227Q - 23 = 8
- Question : 228Q - 4?2 = 1 16
- Question : 229Q - 102 = 100
- Question : 230Q - 90 = 1
- Question : 231Q - 13 3 = 1 27
- Question : 232Q - 64 3 = 4
- Question : 233Q - ex = y
- Question : 234Q - 9y = 150
- Question : 235Q - b3 = 45
- Question : 236Q - 4?3/2 = 0.125
- Question : 237Q - f (x) = 3 + ln x
- Question : 238Q - f (x) = ln(x ? 1)
- Question : 239Q - f (x) = ln(?x)
- Question : 240Q - f (x) = 1 ? ln x
- Question : 241Q - f (x) = log x ? 1
- Question : 242Q - f (x) = ln(x + 1)
- Question : 243Q - logx4 y
- Question : 244Q - log3 9a3
- Question : 245Q - lna3b
- Question : 246Q - log5 125xy3
- Question : 247Q - log4 3 xy 64
- Question : 248Q - ln 6e 3
- Question : 249Q - 5x = 125
- Question : 250Q - e3x ? 15 = 0
- Question : 251Q - 8x = 4
- Question : 252Q - 4x + 1 ? 32 = 0
- Question : 253Q - 3x/14 = 1 10
- Question : 254Q - 10x = 7.21
- Question : 255Q - 4
- Question : 256Q - 73x ? 2 = 11
- Question : 257Q - log3 x = 0
- Question : 258Q - vcos tan?1 3
- Question : 259Q - log4 (x + 5) = 0
- Question : 260Q - log(2x ? 7) = 0
- Question : 261Q - ln x + 3 = 2
- Question : 262Q - log6 (x + 9) + log6 x = 2
- Question : 263Q - log4 (x + 2) ? log4 (x ? 1) = 0
- Question : 264Q - ln x + ln(x ? 2) = ln4
- Question : 265Q - log5 47
- Question : 266Q - log7 82
- Question : 267Q - log6 103
- Question : 268Q - log0.5 211
- Question : 269Q - log2 ?
- Question : 270Q - log0.2 0.452
- Question : 271Q - Rewrite the following expressions in terms of exponentials and simplify. a. 2cosh(ln x) b. cosh4x + sinh4x c. cosh2x ? sinh2x d. ln(cosh x + sinh x) + ln(cosh x ? sinh x)
- Question : 272Q - [T] The number of bacteria N in a culture after t days can be modeled by the function N(t) = 1300
- Question : 273Q - [T] The demand D (in millions of barrels) for oil in an oil-rich country is given by the function D(p) = 150
- Question : 274Q - [T] The amount A of a $100,000 investment paying continuously and compounded for t years is given by A(t) = 100,000
- Question : 275Q - [T] An investment is compounded monthly, quarterly, or yearly and is given by the function A = P nt , where A is the value of the investment at time t, P is the initial principle that was invested, j is the annual interest rate, and n is the number of time the interest is compounded per year. Given a yearly interest rate of 3.5% and an initial principle of $100,000, find the amount A accumulated in 5 years for interest that is compounded a. daily, b., monthly, c. quarterly, and d. yearly.
- Question : 276Q - [T] The concentration of hydrogen ions in a substance is denoted by ? ?H+? ?, measured in moles per liter. The pH of a substance is defined by the logarithmic function pH = ?log? ?H+? ?. This function is used to measure the acidity of a substance. The pH of water is 7. A substance with a pH less than 7 is an acid, whereas one that has a pH of more than 7 is a base. a. Find the pH of the following substances. Round answers to one digit. b. Determine whether the substance is an acid or a base.
- Question : 277Q - [T] Iodine-131 is a radioactive substance that decays according to the function Q(t) = Q0
- Question : 278Q - [T] According to theWorld Bank, at the end of 2013 (t = 0 ) the U.S. population was 316 million and was increasing according to the following model: P(t) = 316e0.0074t, where P is measured in millions of people and t is measured in years after 2013. a. Based on this model, what will be the population of the United States in 2020? b. Determine when the U.S. population will be twice what it is in 2013.
- Question : 279Q - [T] The amount A accumulated after 1000 dollars is invested for t years at an interest rate of 4% is modeled by the function A(t) = 1000(1.04)t. a. Find the amount accumulated after 5 years and 10 years. b. Determine how long it takes for the original investment to triple.
- Question : 280Q - [T] A bacterial colony grown in a lab is known to double in number in 12 hours. Suppose, initially, there are 1000 bacteria present. a. Use the exponential function Q = Q0 ekt to determine the value k, which is the growth rate of the bacteria. Round to four decimal places. b. Determine approximately how long it takes for 200,000 bacteria to grow.
- Question : 281Q - [T] The rabbit population on a game reserve doubles every 6 months. Suppose there were 120 rabbits initially. a. Use the exponential function P = P0 at to determine the growth rate constant a. Round to four decimal places. b. Use the function in part a. to determine approximately how long it takes for the rabbit population to reach 3500.
- Question : 282Q - [T] The 1906 earthquake in San Francisco had a magnitude of 8.3 on the Richter scale. At the same time, in Japan, an earthquake with magnitude 4.9 caused only minor damage. Approximately how much more energy was released by the San Francisco earthquake than by the Japanese earthquake?

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