Answer:
The domain of function is set of all real numbers.
Domain: (-∞,∞)
Step-by-step explanation:
Given:
the domain of both the above functions is all real number.
To find domain of :
Substituting functions and
to find
The product can be written as difference of squares.
∴
The degree of the function is 2 as the exponent of leading term
is 2. Thus its a quadratic equation.
For any quadratic equation the domain is set of all real numbers.
So Domain of is (-∞,∞)
Answer:
a. V = (20-x)
b . 1185.185
Step-by-step explanation:
Given that:
a. Write a polynomial function in factored form modeling the volume V of the box.
As we know that, this is a rectangular box has a square base so the Volume of it is:
V = h *
<=> V = (20-x)
b. What is the maximum possible volume of the box?
To maximum the volume of it, we need to use first derivative of the volume.
<=> dV / Dx = -3 + 40x
Let dV / Dx = 0, we have:
-3 + 40x = 0
<=> x = 40/3
=>the height h = 20/3
So the maximum possible volume of the box is:
V = 20/3 * 40/3 *40/3
= 1185.185