If A=38x-x^2 then
dA/dx=38-2x
d2A/dx2=-2
Since the acceleration, d2A/dx2 is a constant negative, when velocity, dA/dx=0, it will be an absolute maximum for A(x)
dA/dx=0 only when 38=2x, x=19
A(19)=38(19)-19^2
A(19)=722-361
A(19)=361 ft^2
So the maximum possible area is 361 ft^2
(This will always be true as the maximum possible area enclosed by a given amount of material will always be a perfect square...)
For 3x + 12 + x, do like terms:
4x + 12
For 4(3 + x), multiply
12 + 4x
They are both the same, just written in different ways. One is adding like terms and the other is multiplying with parentheses. Even though it may be switched around, it is still the same.
Hope this helps :)
The answer is 12.8 cm³
<span>The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p):
v = k/p
p * v = k (k - constant)
p1v1 = k
p2v2 = k
So, p1v1 = p2v2
v1 = 24 cm</span>³
p1 = 16 lb
v2 = ?
p2 = 30 lb
24 * 16 = x * 30
384 = x * 30
x = 384 / 30
x = 12.8 cm³
