ࡱ> 463q` -bjbjqPqP .T::%,,,@    dl 4@O @####$$$]O_O_O_O_O_O_O$PhRO,4'$$4'4'O##O@+@+@+4'@8#,#]O@+4']O@+@+nK,N# p^ t'L ]OO0OLS(8S@NNS,N$h3%J@+}%<%{$$$OO0+$$$O4'4'4'4'@@@ @@@@@@  1.) A boardwalk is parallel to and 210 ft. inland from a straight shoreline. A sandy beach lies between the boardwalk and the shoreline. A man is standing on the boardwalk, exactly 750 ft. across the sand from his umbrella, which is right at the shoreline. The man walks 4 ft./s on the boardwalk and 2 ft./s on the sand. How far should he walk on the boardwalk before veering off onto the sand if he wishes to reach his umbrella in exactly 4 min. 45 s? Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. 2.)  EMBED Equation.DSMT4  +  EMBED Equation.DSMT4   EMBED Equation.DSMT4  0 In the vicinity of a bonfire, the temperature T in C at a distance of x meters from the center of the fire was given by T = EMBED Equation.DSMT4 . At what range of distances from the fires center was the temperature less than 500 C? Solve the inequality. Express the answer using interval notation. 3.) 2 EMBED Equation.DSMT4  +  EMBED Equation.DSMT4  + 3  EMBED Equation.DSMT4  51 4.)  EMBED Equation.DSMT4  EMBED Equation.DSMT4  5 5.) Plot the points P(-2,1) and Q(12,-1). Which (if either) of the points A(5,-7) and B(6,7) lies on the perpendicular bisector of the segment PQ? Make a table of values and sketch the graph of the equation. Find the x and y intercepts and test for symmetry. 6.) y = 9 - x EMBED Equation.DSMT4  7.) y = - EMBED Equation.DSMT4  Sketch the region given by the set. 8.) {(x,y) | 2x < x EMBED Equation.DSMT4 + y EMBED Equation.DSMT4  EMBED Equation.DSMT4  4 } Find an equation of the line that satisfies the given conditions. 9.) Through (-2,-11); perpendicular to the line passing through (1,1) and (5,-1). 10.) Find an equation for the line tangent to the circle x EMBED Equation.DSMT4 + y EMBED Equation.DSMT4 = 25 at the point (3,-4). At what other point on the circle will a tangent line be parallel to the tangent line in first question? 11.) A small business buys a computer for $4,000. After 4 years the value of the computer is expected to be $200. For accounting purposes, the business uses linear deprecation to assess the value of the computer at a given time. This means that if V is the value of the computer at time t, then a linear equation is used to relate V and t. a) Find a linear equation that relates V and t. b) Sketch the graph of this linear equation. c) What do the slope and V intercept of the graph represent? d) Find the depreciated value of the computer 3 years from the date of purchase. 12.) A car is traveling on a curve that forms a circular arc. The force F needed to keep the car from skidding is jointly proportional to the weight w of the car and the square of its speed s, and is inversely proportional to the radius r of the curve. a) Write an equation that expresses this variation. b) A car weighing 1600 lb. travels around a curve at 60 mi/h. The next car to round this curve weighs 2500 lb. and requires the same force as the first car to keep from skidding. How fast is the second car traveling? 13.) The value of a building lot on Galiano Island is jointly proportional to its area and the quantity of water produced by a well on the property. A 200 ft. by 300 ft. lot has a well producing 10 gallons of water per minute, and is valued at $48,000. What is the value of a 400 ft. by 400 ft. lot if the well on the lot produces 4 gallons of water per minute? 14.) The rate r at which a disease spreads in a population of size P is jointly proportional to the number x of infected people and the number P x who are not infected. An infection erupts in a small town with population P = 5,000. Write an equation that expresses r as a function of x. Compare the rate of spread of this infection when 10 people are infected to the rate of spread when 1,000 people are infected. Which rate is larger? By what factor? Calculate the rate of spread when the entire population is infected. Why does this answer make intuitive sense? 15.) Due to the curvature of the earth, the maximum distance D that you can see from the top of a tall building or from an airplane at height h is given by the function: D(h) =  EMBED Equation.DSMT4  Where r = 3960 mi. is the radius of the earth and D and h are measured in miles. Find D(0.1) and D(0.2). How far can you see from the observation deck of Torontos CN Tower, 1135 ft. above the ground? Commercial aircraft fly at an altitude of about 7 mi. How far can the pilot see? 16.) According to the theory of Relativity, the length L of an object is a function of its velocity v with respect to an observer. For an object whose length at rest is 10 m, the function is given by L(v) = 10  EMBED Equation.DSMT4  where c is the speed of light. a) Find L(0.5c), L(0.75c), and L(0.9c). b) How does the length of an object change as its velocity increases? 17.) Westside Energy charges its electric customers a base rate of $6.00 per month, plus 10 cents per kilowatt-hour (kWh) for the first 300 kWh used and 6 cents per kWh for all usage over 300 kWh. Suppose a customer uses x (kWh) of electricity in one month. a) Express the monthly cost E as a function of x. b) Graph the function E for 0 EMBED Equation.DSMT4  x  EMBED Equation.DSMT4  600. A function is given. Determine the average rate of change of the function between the given values of the variable. g(x) =  EMBED Equation.DSMT4 ; x = 0, x = h 19.) The temperature on a certain afternoon is modeled by the function C(t) =  EMBED Equation.DSMT4 t EMBED Equation.DSMT4 +2 where t represents hours after 12 noon (0  EMBED Equation.DSMT4  t  EMBED Equation.DSMT4  6), and C is measured in C. a) What shifting and shrinking operations must be performed on the function y = t EMBED Equation.DSMT4  to obtain the function y = C(t)? b) Suppose you want to measure the temperature in F instead. What transformation would you have to apply to the function y = C(t) to accomplish this? (Use the fact that the relationship between Celsius and Fahrenheit degrees is given by F =  EMBED Equation.DSMT4 C = 32.) Write the new function y = F(t) that results from this transformation. 20.) A ball is thrown across a playing field. Its path is given by the equation y = -0.005x EMBED Equation.DSMT4 + x + 5, where x is the distance the ball has traveled horizontally, and y is its height above ground level, both measured in feet. a) What is the maximum height attained by the ball? b) How far has it traveled horizontally when it hits the ground? 21.) A soft drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x EMBED Equation.DSMT4  + 3x 1800. What is his maximum profit per day, and how many cans must he sell for maximum profit? 22.) A print shop makes bumper stickers for election campaigns. 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