Given:
In the given triangle,
With respect to y, Perpendicular = 10 cm and Base = 8 cm
To find the value of y.
Formula
By Trigonometric Ratio we get,
Now,
Putting the values of perpendicular and base we get,
or,
or,
Rounding off to the nearest tenth, we have;
Hence,
The value of y is 51.3°.
~
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: