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Calc 1 Lab 2, pg2 - 4 Using the fact that the area must be...

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Unformatted text preview: 4. Using the fact that the area must be 300 ( and, hence, l and w are related in a special way) find a formula for the perimeter that depends only on w. 5. Now if we graph this function (for positive values of w only — why?) the lowest point on the graph will give us the info we need. The first coordinate will give the optimal value of w and the second coordinate will give the optimal perimeter. So graph this function in Maple and use the graph to find the approximate values of w and the perimeter. From this info you should be able to find an approximate value for 1. Q2. An isosceles triangle has a perimeter of 500 in. Obviously, there are all sorts of possible shapes for this triangle. 1. Express A, the area of the triangle, as a function of the base b, A = g(b). (The Pythagorean Theorem may be via/useful: 2. What is the natural domain of this function? HE: is t 6 practical domain? X [I fosi‘llVe 3. Have Maple plot a graph of the function over the practical domain. What is the range of this function? Is b a function of A in this situation? Explain why or why not? If it is, try to find a formula for this function. Q3 Suppose that you drop a dense object (feathers and tissue paper don't count) from the top of a tall building. Let t be the number of seconds since you released the object and d be the total distance the object has fallen in feet since you released the object. Experimental data (from a long time ago) has shown that d = l6t2 is a very simple but accurate relationship between d and t. 1. How far does the object fall in the first second? The first two seconds? The first three seconds? Given this info (and your experience with falling objects) the longer the object falls does its speed (velocity) - stay the same, decrease or increase? 2. We can get some info about the objects speed (at least its average speed) easily from the d = 16t2 function. Recall that you can calculate the average speed of any moving object during any time interval by using the following simple formula average speed (during the time interval) = distance traveled elapsed time For instance, if you drive on an expressway between 1 PM and 3 PM and cover 125 miles during those two hours, you average speed is 125/2 = 62.5 mph. Back to the falling object. Between t=l and t=4, how far does the object travel? What is its average speed during these 3 seconds? ...
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