Determine the value of x or as requested. Round results to an appropriate number of significant digits. 1) Determine the value of.

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1 MAT C SPRING 2010 Name REVIEW FOR FINAL EXAM Determine the value of x or as requested. Round results to an appropriate number of significant digits. 1) Determine the value of. 1) 20.7 ft 70.1 ft Solve the problem. 2) From a boat on the lake, the angle of elevation to the top of a cliff is If the base of the 2) cliff is 446 ft from the boat, how high is the cliff (to the nearest foot)? For the given function value determine the quadrants in which the terminal side of the angle can lie. 3) sin = ) 4) tan = 1.3 4) Express the angle in radian measure in terms of. 5) 330 5) The given number expresses angle measure. Express the measure in terms of degrees. 6) ) Convert the radian measure to degrees. Round your answer to two decimal places. 7) ) Find the indicated trigonometric function, given that is an angle in standard position with the terminal side passing through the given point. 8) (1.5, -3.6); Find sin. 8) 1

2 Find the horizontal and vertical components of the vector shown in the given figure. Round to one decimal place. 9) The magnitude of the vector is ) Determine the indicated component or components of the vector. Round to one decimal place. 10) Magnitude = 25.5, = ) Find the horizontal and vertical components of V. Vectors A and B are at right angles. Find the magnitude and direction (from vector A) of the resultant. Round to one decimal place. 11) A = ) B = 158 With the given set of components, find R and. Give magnitude to one decimal place; angle to nearest degree. 12) Rx = -6.0, Ry = ) Add the given vectors by using the trigonometric functions and the Pythagorean theorem. 13) A = 13, = ) B = 30, = 181 Add the given vectors. 14) 14)

3 Find the missing parts of the triangle. Round angle measures to one decimal place and lengths to two decimal places. 15) B = ) C = b = ) B = ) b = 6.62 a = ) B = ) b = a = ) C = ) a = 8.00 b = ) a = ) b = 13.7 c = 15.1 Find the amplitude, period or phase shift. 20) Find the amplitude of y = -4 sin (3x + ). 20) 3 21) Find the period of y = -2 sin (8x + ). 21) 2 22) Find the phase shift of y = sin (4x + ). 22) 2 Graph at least one period of the function. Label the key values on the x axis. 23) y = 1 2 sin 2 3 x 23) 24) y = -2 cos (2x - 2 ) 24) Express the given expression in simplest form with only positive exponents. x5y3-4 25) wz4 25) Evaluate the given expression. 26) (-125)5/3 26) 3

4 27) (-64) 2/3-8 27) Simplify the given expression. Express answer with positive exponents. 28) 3-2/3 34 x- 6 31/3x-2 28) Write the expression in simplest form. If a radical appears in the denominator, rationalize the denominator. 29) 80 29) 30) 72k7q8 30) 31) 25a9b6 2a5 31) 32) 3 729x4y5 32) Simplify the expression. Give answer in radical form. 33) 5 10y 33) Rationalize the denominator. 2T 34) L 34) Express the radical in simplest form and perform the indicated operations. 35) ) 36) 7 27x2z + 4x 108z 36) Perform the indicated operations, expressing the answer in simplest form with rationalized denominators. 37) ) 38) 5x2y 10x5y4 38) 39) ( ) 2 39) 40) ) Solve the radical equations. Check for extraneous solutions. 41) 5q - 4 = 4 41) 4

5 42) x = x ) Solve the inequality. 43) -24r (3r - 5) 43) Solve the inequality. 44) -11-3c + 4 < -2 44) Solve the absolute value inequality. 45) b > 10 45) Solve the problem. 46) Determine the values of x that are in the domain of the function f(x) = 6-2x. 46) Express the ratio in simplest form. 47) 9 yd to 12 ft 47) 48) 3 and 1 3 days to 4 weeks 48) 49) 0.28 kg to 3500 mg 49) 50) 240 s to 6 min 50) Find the required ratio. 51) The ratio of the cylinder volume to the compressed volume in an automobile engine is 51) called the compression ratio. If the cylinder volume of 910 cm3 is compressed to 120 cm3, find the compression ratio, correct to the nearest hundredth. 52) Power (in watts) is defined as the ratio of the work done (in joules) to the time required to 52) do the work. If an engine performs 4150 joules of work in 23 seconds, find the power developed by the engine, correct to the nearest watt. 53) The percent grade of a road is the ratio of the vertical rise to the horizontal change in 53) distance, expressed as a percentage. If a highway rises 70 ft for each 1700 ft along the horizontal, what is the percent grade to the nearest hundredth? Solve the problem. 54) According to Boyle's law, the relation P 1 P2 = V 2 V1 holds for pressures P 1 and P2 and volumes 54) V1 and V2 of a gas at a constant temperature. Find V1 if P1 = 22.8 kpa, P2 = 46.9 kpa, and V2 = m3. If necessary, round to three decimal places. 5

6 Answer the given question by setting up and solving the appropriate proportion. If necessary, round the answer to two decimal places. 55) Given that 1.50 L = 1.59 qt, what capacity in quarts is 3.50 L? 55) 56) If a computer prints lines in 4.00 seconds, how many lines can it print per minute? 56) Set up the general equation from the given statement. 57) a varies directly as b. 57) 58) w is proportional to the square of x and inversely proportional to y. 58) 59) m is proportional to the square of n and inversely proportional to y and x. 59) 60) R is varies jointly as m and p. 60) 61) The centrifugal force C on a circular curve varies inversely as the radius r of the turn. 61) 62) The power P required to propel a ship varies as the cube of the speed s. 62) 63) The illumination I produced on a surface by a source of light varies directly as the 63) candlepower c of the source and inversely as the square of the distance d between the source and the surface. Give the specific equation relating the variables after evaluating the constant of proportionality for the given set of values. 64) A varies jointly as F and G and inversely as H, and A = 280 when F = 10, G = 4, and H = 9. 64) 9 65) m is inversely proportional to the square of d, and m = 1 48 when d = 4. 65) Find the required value by setting up the general equation and then evaluating. 66) Find s when t is 3.0 if s varies directly as the square of t, and s = 576 when t = ) 67) Find y for x = 5 and z = 4 if y varies directly as x and inversely as z, and y = 64 when x = 4 67) and z = ) Find f when p = 49 if f varies directly as the square root of p, and f = 3 when p = ) Solve the given applied problems involving variation. 69) The weight of a liquid varies directly as its volume V. If the weight of the liquid in a 69) cubical container 5 cm on a side is 250 g, find the weight of the liquid in a cubical container 3 cm on a side. 6

7 70) The period of vibration P for a pendulum varies directly as the square root of the length L. 70) If the period of vibration is 2 s when the length is 16 in., what is the period when L = in.? 71) The gravitational attraction A between two masses varies inversely as the square of the 71) distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction when the masses are 6 ft apart? 72) The volume V of a given mass of gas varies directly as the temperature T and inversely as 72) the pressure P. If V = 75.0 in.3 when T = 100 and P = 20 lb/in.2, what is the volume when T = 320 and P = 15 lb/in.2? Convert to logarithmic form. 73) 41/2 = 2 73) Express the equation in exponential form. 74) log 4 1 = -3 74) 64 Find the inverse of the given function. 75) y = e x 75) Provide an appropriate response. 76) What is the domain of the function y = log x? 76) 7 77) What is the range of the function y = log x? 77) 9 Solve. 78) log = x 78) 79) log 6 1 = x 79) Use the properties of logarithms to write each expression as a sum or difference of logarithms. Your results should not contain any exponents or radicals. 80) log 4 9x 80) 81) log 3 x 3y4 z 5 w4 81) Use the properties of logarithms to rewrite the expression as the logarithm of a single quantity. 82) 4 loga x - loga y 82) 7

8 83) 1 log s + 3 log m 83) 2 Find the value of the expression. 84) log ) 85) log ) Determine the value of the logarithm. Round to the nearest hundredth. 86) log ) Solve the exponential equation. Round answers to three decimal places, where appropriate. 87) 4(5-3x) = ) 88) 3x = 8 88) Solve the equation. Round answers to three decimal places. 89) ln 2x + ln 7x = ln 15 89) 90) 7ln x = 2 90) Solve. 91) There are currently 70 million cars in a certain country, decreasing by 4.1% annually. The 91) number of cars, in millions, at time t, in years, is given by the function A(t) = 70(0.959)t. How many years will it take for this country to have 40 million cars? Round to the nearest year. Express the number in terms of j. 92) ) Simplify the expression. 93) ) 94) j11 94) 95) ) Simplify the complex number to its rectangular form. 96) 9j ) 8

9 Perform the indicated operations. Write the result in the form a + bj. 97) (6-2j)(9 + 5j) 97) 98) 7j ) 99) 7 - j 3j 99) Graph the complex number. 100) 5 + 4j 100) Write the complex number in polar form. Round angle to tenth of a degree. 101) j 101) 102) ) Change the complex number to rectangular form. Round values to three decimal places. 103) 5(cos j sin 324 ) 103) 104) ) Express the number in exponential form. Round values to three sig digits. 105) 1.52(cos j sin 16.2 ) 105) 106) ) Express the given number in exponential form. Round values to three sig digits. 107) 5 + 8j 107) 108) -7 - j 108) Express the given complex number in polar form, with angle in degrees to nearest tenth. 109) 4.96e2.66j 109) 9

10 110) 6.00e2.00j 110) Express the given complex number in rectangular form. 111) 5.00e4.00j 111) 112) 4.38e-2.17j 112) 10