Answer:
C
Step-by-step explanation:
To determine which point lies on the graph, substitute the x-coordinate into f(x) and if the value is equal to the y-coordinate then the point is on the graph
A (15, 1)
f(15) = 3 × ≠ 1 ← not on graph
B (0, 15)
f(0) = 3 × = 3 × 1 = 3 ≠ 15 ← not on graph
C (1, 15)
f(1) = 3 × = 3 × 5 = 15 ← lies on graph
D (0, 0)
f(0) = 3 × = 3 × 1 = 3 ≠ 0 ← not on graph
Answer:
168 trumpets for $1702
Step-by-step explanation:
Profit is the measure to be maximized. We are given revenue and cost relationships as a function of units, x (trumpets). Profit is the difference:
Profit = Revenue[R(x)] - Cost[C(x)]
Profit = (76x – 0.25x^2) - (-7.75x + 5,312.5)
Profit = 76x - 0.25x^2 + 7.75x - 5,312.5
Profit = 76x - 0.25x^2 + 7.75x - 5,312.5
Profit = - 0.25x^2 + 83.75x - 5312.5
At this point we can find the trumpets needed for maximum profit by either of two approaches: algebraic and graphing. I'll do both.
<u>Mathematically</u>
The first derivative will give us the slope of this function for any value of x. The maximum will have a slope of zero (the curve changes direction at that point). Take the first derivative and set that equal to 0 and solve for x.
First derivative:
d(Profit)/dx = - 2(0.25x) + 83.75
d(Profit)/dx = - 0.50x + 83.75
0 = - 0.50x + 83.75
0.50x = 83.75
x = 167.5 trumpets
<u>Graphically</u>
Plot the profit function and look for the maximum. The graph is attached. The maximum is 167.5 trumpets.
Round up or down to get a whole trumpet. I'll go up: 168 trumpets.
<u>Maximum Profit</u>
Solve the profit equation for 168 trumpets:
Profit = - 0.25x^2 + 83.75x - 5312.5
Profit = - 0.25(168)^2 + 83.75(168) - 5312.5
<u>Profit = $1702</u>
Answer:
For ease of writing, θ
Step-by-step explanation:
Our angle is
To find our answers for and
, we will need to use a unit circle. (I have attached the image of one).
Recall that the of an angle is equal to the y-value of the corresponding ordered pair.
And the of an angle is equal to the x-value of the corresponding ordered pair.
For the angle , the ordered pair is
This means that
