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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- Fall '10