Saturday, April 01, 2006

Solutions to Episode Five

a) f(x)= 4x-x^2 and g(x)=5-2x
in this case 4x-x^2 lagrer than or equal to 5-2x. The graph interest where 4x-x^2=5-2x
solving this equation,
4x-x^2=5-2x
x^2-6x+5=0
(x-1)(x-5)=0
x=1 or x=5
we substitute in either formula and find that graphs intersect at (1,3) and (5,-5)
then,
Area(x) = S (from 1 to 5) ((4x-x^2) - (5-2x)) dx
=(3x^2- (1/3 )x^3- 5x) (from 1 to 5)
=75-125/3-25)-(3-1/3-5)
=32/3
b)1/14S (from 6 to 14) -(80-10 cos (pai t/12) dt
=-1/8(697.2957795)
=-87 F
c) -(80 -10 cos (pai t/12) >/ -78
80 - 10 cos (pai t/12) /<>
-5.230>/t>/-18.769
between this time it will have the storm