Work the following exercises.
First-Class Postage The accompanying table shows the cost
Weight not over (ounces) | Price ($) |
1 | 0.47 |
2 | 0.68 |
3 | 0.89 |
3.5 | 1.10 |
sketch a graph of
Find all values on the interval (0,3.5) where x is discontinuous.
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Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
- For the following exercises, use the graph of g shown in Figure 1. 23. Approximate the local minimum of the function. Express the answer as an ordered pair.arrow_forwardFor the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a companyin a given year, t, where t represents the number of years since 1980. 31. Find the linear function y, where y depends on t, the number of years since 1980.arrow_forwardFor the following exercises, use a calculator or graphing technology to complete the task 103. Graph the linear function f on a domain of [0.1,0.1] for the function whose slope is 75 and y-intercept is 22.5 .Label the points for the input values of 0.1 and 0.1.arrow_forward
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- Weight loss Jared Fogle, also known as the “Subway SandwichGuy,” weighed 425 lb in 1997 before losing more than 240 lb in12 months (http://en.wikipedia.org/wiki/Jared_Fogle). A chartshowing his possible dramatic weight loss is given in the accompanying figure a. Estimate Jared’s rate of weight loss wheni) t = 1 ii) t = 4 iii) t = 11b. When does Jared lose weight most rapidly and what is this rate of weight loss?c. Use the graphical technique of Example 3 to graph the derivative of weight W.arrow_forwardExercise 3. For the manufacture of gutters for rainwater, sheets of 30 cm wide are available. Calculate the measure x that the folds must have so that a gutter of maximum capacity is obtained. Determine the following characteristics. a) The function that relates the measure of the fold x to the area of the gutter f (x). b) Sketch the graph for values of x greater than 0 cm, but less than 15 cm. c) Calculate the measure x that the bends must have so that a maximum capacity gutter is obtained.arrow_forwardThe demand for a certain type of cosmetic is given byp = 500 - x,where p is the price in dollars when x units are demanded.(a) Find the revenue R(x) that would be obtained at a price p. (b) Graph the revenue function R(x).(c) Find the price that will produce maximum revenue.(d) What is the maximum revenue?arrow_forward
- You are designing an RPG (role-playing game) for a gaming console and have decided to use an open world design, where players can explore the terrain freely, encountering enemies by chance. Your design team has coded this in-game world to exist on the circle x^2 + y^2 ≤ 900 on the xy-plane. At any point (x,y) in this world you've also associated a danger function d(x,y) that measures how likely it is to encounter an enemy at that point. Thus high values of d(x,y) correspond to dangerous points, while low values of d(x,y) correspond to safe points. If d(x,y) = e^(-x^2)(y), find the safest point(s) and most dangerous point(s) in-game.arrow_forwardPip is building model car racing tracks using a large supply of the two types of square plate shown. Ignoring the tabs and slots where plates are snapped together, both types measure 20cm x 20cm. In the first type, the track is a straight line joining the middles of opposite sides. In the seconds, the track is a quarter circle joining the middle of adjacent sides. Plates can be snapped together in any orientation, as long as the track is continuous. Pip wants to complete the track shown below but, because there is limited space, additional plates can only be put in the 4 x 4 grid indicated by dotted lines. 1. Explain why, no matter how the circuit is completed, Pip must place an even number of additional curved plates. 2. Explain why, no matter how the circuit is completed, Pip must place an odd number of additional straight plates.arrow_forwardFind the point P on the graph of the function y=√x closest to the point (5,0) The x coordinate of P is?arrow_forward
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