Worksheet 5
3.6 #12 A wire 10 meters long is to be cut into two pieces. One piece will be shaped as an
equilateral triangle, and the other piece will be shaped as a circle.
a) Express the total area A enclosed by the pieces of wire as a function of the length x of a side of
the equilateral triangle.
The area of a triangle is
the Pythagorean Theorem we see
. Using
so
So the area of the triangle is
.
As for the circle, the circumference is 2 r = 10 – 3x, thus
. Hence the area of the circle =
The total area enclosed =
b) The domain of A is (0,
the largest x can be is
. Since the smallest x can be is zero (and the entire wire a circle) and
(and the entire wire an equilateral triangle).
3.5 #48
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c) g(x) = -f(x)
f) g(x) = f(-x)
a) g(x) = f(x) + 3
d) g(x) = f(x+1) – 2
g) g(x) = f(2x)
b) g(x) = f(x+2)
e) g(x) = 1/2*f(x)