1. The Parcel Service will only accept packages with a length of no more than 15
ID: 3342305 • Letter: 1
Question
1. The Parcel Service will only accept packages with a length of no more than 150 inches and length plus girth of no more than 159 inches. (See the figure.) Assuming that the front face of the package (as shown in the figure) is square, what is the largest volume package that the Parcel Service will accept?
They want the answer in inches cubed
2. The oxygen consumption of a turkey embryo increases from the time the egg is laid through the time the chick hatches. In a brush turkey, the oxygen consumption can be approximated by c(t), where t is the time (in days) since the egg was laid. (An egg will typically hatch at around t = 50.) When, to the nearest day, is c'(t) a maximum? (Round all answers to the nearest tenth.)
c(t)= -0.0283t^3 + 2.87t^2 - 44t + 95 mililiters per day (20 less than or equal to t but greater than or equal to 50)
a) t= how many days??
b) This means that the embryo's oxygen consumption is increasing most rapidly how many days after the egg is laid?
3. The position s of a point (in feet) is given as a function of time t (in seconds). s=-15 + t - 18t^2
a) Find the point's acceleration as a function of t. how many feet per second squared?
b) Find the point's acceleration at the specified time t = 5. how many feet per second squared?
Explanation / Answer
1.let length be l , breadth be b, height be h
given, b=h
l <150 --(i)
l+ 2(b+h) <159
=>l+4b <159 --(ii)
sutracting (i) from (ii),
l+4b-l < 159-150
=>4b<9
=>b<9/4
Largest volume package = l*b*h = l*b^2 = 150 * (9/4)^2 = 759.375 cu.in
2. (a) c(t)= -0.0283t^3 + 2.87t^2 - 44t + 95
c'(t) = -0.0849t^2 +5.74t -44
c'(t) will be maximum if c"(t) =0
=>-0.1698t + 5.74 = 0
=>t = 5.74/0.1698 = 33.3 ~ 34 days
(b)the embryo's oxygen consumption is increasing most rapidly 34 days after the egg is laid.
3. (a) s(t) =-15 + t - 18t^2
s'(t) = 1 - 36t
s"(t) = -36
acceleration = s"(t) = -36 feet/sq.sec
(b) since s"(t) is a constant ,so, the acceleration doesn't change with time.
So, acceleration at t=5 is -36 feet/sq.sec
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