Adalyn used 2.5 yards of fabric to make 3 decorative pillows. If she makes 12 pillows, how many yards of fabric will she need?
1 answer:
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Answer: The average rate of change is 6.
First, plug in each value of <em>t</em> into the function, v(t) to find there coordinate pairs.
v(2) = (2)^2 - (2) + 10
v(2) = 4 + 8
v(2) = 12
v(5) = (5)^2 - (5) + 10
v(5) = 25 + 5
v(5) = 30
You can write these values as coordinate pairs, like so: (2, 12) and (5, 30).
The formula for the average rate of change is
. When you plug in the values from this particular case, the average rate of change formula becomes 
, or 
.
Looking at the equation, you can solve for the average rate of change between t = 2 and t = 5, which equals 6.
First, plug in each value of <em>t</em> into the function, v(t) to find there coordinate pairs.
v(2) = (2)^2 - (2) + 10
v(2) = 4 + 8
v(2) = 12
v(5) = (5)^2 - (5) + 10
v(5) = 25 + 5
v(5) = 30
You can write these values as coordinate pairs, like so: (2, 12) and (5, 30).
The formula for the average rate of change is
Looking at the equation, you can solve for the average rate of change between t = 2 and t = 5, which equals 6.
Answer:
Widgets should be sold by $38.88 to maximize the profit.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
It's vertex is the point
In which
Where
If a<0, the vertex is a maximum point, that is, the maximum value happens at , and it's value is
.
In this question:
The profit is given by:
Which is a quadratic function with
The maximum profit happens at the x of the vertex. Thus
Widgets should be sold by $38.88 to maximize the profit.