Answer:
Given : Expression -
To find : How would the sum of cubes formula be used to factor given expression? Explain the process. Do not write the factorization.
Solution :
The formula of sum of cubes is,
First we convert the given expression in
Apply exponent rule :
Rewrite
Therefore, could be written as
On comparison with the formula,
a=xy , b=7
The revenue function is a quadratic equation and the graph of the function
has the shape of a parabola that is concave downwards.
The correct responses are;
Reasons:
The given function that gives the weekly revenue is; R = x·(82 - x)
Where;
R = The revenue in dollars
x = The number of lunches
(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;
R = x·(82 - x) = 82·x - x²
Which gives;
<em>Where, the constant term, c = 0</em>
(b) When 35 launches are sold, we have;
x = 35
Which by plugging in the value of x = 35, gives;
R = 35 × (82 - 35) = 1,645
(c) The given function for <em>R</em> is R = x·(82 - x) = -x² + 82·x
Given that the leading coefficient is negative, the shape of graph of the
function <em>R</em> is concave downward, and therefore, the graph has only a
maximum point.
(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;
(h, k) = The vertex of the equation
a = The leading coefficient
The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;
R = x·(82 - x) = -x² + 82·x
At the vertex, of the equation; f(x) = a·x² + b·x + c, we have;
Therefore, for the revenue function, the x-value of the vertex, is;
The revenue at the vertex is; = 41×(82 - 41) = 1,681
Which gives;
(h, k) = (41, 1,681)
a = -1 (The coefficient of x² in -x² + 82·x)
(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41
Therefore;
(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681
Learn more about the quadratic function here: