math calculus

fuzyna
timer Asked: Feb 3rd, 2016

Question Description

i have 50 problems 

cal._1_hw_1___spr._2016_copy.pdf

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Calculus I Dr. S. Farmer, I nstructor H omework #1 Spring 2016 Directions: (10 pts. each) Answer each of the following questions below. In order to receive ANY credit for a question, you must SHOW YOUR WORK using proper notation and clear and concise logic. You're graded on both the accuracy of your answers AND your explanations that sufficiently support your answers. Unless otherwise stated, you're to give the EXACT VALUES of answers instead of decimal approximations. In order to receive ANY credit for any applied/word problem (i.e. Problems #30 to the end), you M UST declare a variable (unless the variable(s) have already been declared in the problem) and set up and solve an appropriate mathematical expression that can be used to answer the question. Proper units must also be included in answers to applied problems. NO CREDI T WILL BE GI VEN FOR EI THER GUESSING OR CHECKING POSSIBLE ANSWERS WI THOUT SOLVING THE PROBLEM . Finally, write ONLY FINAL ANSWERS ON THESE PAGES; you must show your work both according to homework guidelines and on YOUR OWN PAPER. SH ORT AN SWER. Write the word or phrase that best completes each statement or answers the question. M ultiply or divide as indicated. Write your answer in factored form. x 2 - 9x + 14 x2 - 16x + 48 · 1) x 2 - 12x + 32 x2 - 18x + 77 1) Use the given conditions to find an equation in slope- intercept form of each of the nonvertical lines. Write vertical lines in the form x = h. 2) Parallel to 5x + 2y = - 37; passing through (- 5, - 15) 2) 3) Perpendicular to 9x + 5y = 52; passing through (8, - 4) 3) Find the center (h, k) and radius r of the circle with the given equation. 4) 4x 2 + 4y 2 - 12x + 16y - 5 = 0 4) Solve the problem. 5) Find all values of k so that the given points are (- 5, 5), (k, 0) 29 units apart. Simplify the complex rational expression. 4 1 x 2 - 4x - 32 x - 8 6) 1 +1 x +4 5) 6) Find the difference quotient for the function and simplify it. 7) g(x) = 6x2 + 14x - 1 7) Find the domain and range of the function. Write your answers using interval notation. 8) g(z) = 16 - z2 8) 1 Find a formula for the function f(x) graphed. 9) 9) State the domain of the composition. 10) (g h)(x) w ith g(x) = x + 5 and h(x) = 8x + 7 10) Solve the equation by multiplying both sides by the LCD. 2 3 =1 11) 3x x + 1 11) Solve the equation. 12) x + 6 + 2 - x = 4 12) 13) (4x - 2)2/3 + 6 = 15 13) 14) 3x + 4 = x - 1 14) Find the real solutions of the equation by factoring. 15) x3 + 8x 2 - x - 8 = 0 15) Solve the equation by making an appropriate substitution. 16) (x2 - 2x)2 - 11(x 2 - 2x) + 24 = 0 16) Solve the logarithmic equation. 17) log4 (x - 5) + log4 (x - 5) = 1 17) Solve the exponential equation. Express the solution set in terms of natural logarithms. 18) 4x + 4 = 52x + 5 18) Solve the inequality and express the solution in interval notation. 19) 7 x - 1 2 19) 2 Solve the inequality. Write your answer using interval notation. 20) x3 - 7x 2 - 18x > 0 20) Solve the rational inequality. Write your answer using interval notation. 1 1 2 + 21) x - 2 x +2 3 21) Write the equation as f(x) = a(x - h)2 + k. I dentify the vertex, range, and axis of symmetry of the function. 22) f(x) = x 2 + 5x + 2 22) Find a and k and then evaluate the function. Round your answer to three decimal places when necessary. 9 1 w ith f(0) = 3 and f(1) = . Find f(2). 23) f(x) = 23) kx 3 2 + ae Use the change- of- base formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. 142.6 24) log 24) 2 Use the given information to find the exact value of the expression. 4 2 25) Find cos ( - ). sin = , lies in quadrant II, and cos = , 5 5 lies in quadrant I. 25) Use the information given about the angle , to find the exact value of the indicated trigonometric function. 7 , in quadrant III Find sin 2 . 26) tan = 26) 24 Use the given information given to find the exact value of the trigonometric function. 5 lies in quadrant II Find sin . 27) sec = - , 3 2 Find all solutions of the equation in the interval [0, 2 ). 3 28) cot 3x = 3 27) 28) 29) 2 cos2 x + sin x - 2 = 0 29) Solve the equation on the interval [0, 2 ). 30) tan2 x sin x = tan2 x 30) 31) sin 2x + sin x = 0 31) Find all solutions to the equation. Express each result in radians. 32) 2 sin 2 x + sin x = 1 3 32) Solve the problem. 33) Find the exponential function of the form f(x) = aebx that passes through the points (0, 3) and (3, 9). 33) 34) A closed box with a square base has to have a volume of 7000 cubic inches. Find a function for the surface area of the box. 34) 35) The acceleration due to gravity g (in meters per second per second) at a height h meters 3.99 × 1014 above sea level is given by g(h) = w here 6.374 × 106 is the radius of (6.374 × 106 + h)2 35) Earth in meters. Death Valley in California is 86 m below sea level. a) Find the value of g(h) at Death Valley to four decimal places. b) Compare the value in (a) to the value of g(h) at sea level. 36) A n adjustable water sprinkler that sprays w ater in a circular pattern is placed at the center of a square field whose area is 1250 square feet. What is the shortest radius setting that can be used if the field is to completely enclosed w ithin the circle? WRITE A N EXA CT ANSWER ON LY A N D DO N OT USE DECIM AL APPROXIM A TION S. Solve the problem. 37) The medians of a triangle intersect at a point. The distance from the vertex to the point is exactly two- thirds of the distance from the vertex to the midpoint of the opposite side. Find the exact distance of that point from the vertex A (3, 4) of a triangle, given that the other tw o vertices are at (0, 0) and (8, 0). 38) A group of friends agree to equally share the cost of a $480,000 vacation condominium. Before the purchase is made, four more people join the group and enter the agreement. A s a result, each person's share is reduced by $32,000. How many people w ere in the original group? Solve the problem. 39) Tom Quig traveled 240 miles east of St. Louis. For most of the trip he averaged 70 mph, but for one period of time he was slow ed to 20 mph due to a major accident. If the total time of travel w as 7 hours, how many miles did he drive at the reduced speed? 36) 37) 38) 39) 40) A rectangular piece of cardboard measuring 12 inches by 42 inches is to be made into a box w ith an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square. What is the maximum volume of this box? If necessary, round to 2 decimal places. 40) 41) In one city, the local cable TV company charges $3.98 for each pay- per- view movie watched. In addition, each monthly bill contains a basic customer charge of $22.50. If last month's bills ranged from a low of $38.42 to a high of $66.28, over what range did customers w atch pay- per- view movies? 41) 4 42) A landscaping company sells 40- pound bags of top soil. The actual w eight x of a bag, how ever, may differ from the advertised weight by as much as 0.75 pound. Write an inequality involving absolute value that expresses the relationship betw een the actual w eight x of a bag and 40 pounds. Over w hat range may the weight of a 40- pound bag of to soil vary? 42) 43) Every Sunday, Jarod buys a loaf of fresh bread for his family from the corner bakery for $3.00. The local department store has a sale on breadmakers for $59. If the bread- making supplies cost $0.67 per w eek, for how many weeks w ould Jarod have to bake a loaf of bread at home before the breadmaker starts saving him money? 43) 44) A certain radioactive isotope has a half- life of approximately 1100 years. How many years to the nearest year w ould be required for a given amount of this isotope to decay to 30% of that amount? 44) 45) A ball is thrown vertically upw ard w ith an initial velocity of 128 feet per second. The distance in feet of the ball from the ground after t seconds is s = 128t - 16t 2. For what intervals of time is the ball less than 240 above the ground (after it is tossed until it returns to the ground)? 45) 46) The sum of 36 times a number and the reciprocal of the number is positive. Find the numbers which satisfy this condition. 46) 47) A surveyor is measuring the distance across a small lake. H e has set up his transit on one side of the lake 110 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 35°. What is the distance between the piling and the pier to the nearest foot? 47) 48) The total sales in dollars of some small businesses fluctuates according to the equation S= A + B sin x/6, w here x is the time in months, w ith x = 1 corresponding to January, A = 7800, and B = 3500. Determine the month with the greatest total sales and give the sales in that month. 48) 49) The angle of elevation from the top of a house to a plane flying 7200 meters above the house is x radians. If d represents the horizontal distance, in meters, of the plane from the house, express d in terms of a trigonometric function of x. 49) 50) A coil of w ire rotating in a magnetic field induces a voltage given by e = 20 sin t , 4 2 where t is time in seconds. Find the smallest positive time to produce a voltage of 10 2. 5 50)
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