Part A.
Y intercept is the coordinate (0,y), when the function has an x value of 0, it is the y intercept.
In this case:
(0,5) =
y intercept = 5
IT tells about the turtle that it starts at a nest displacement of 5 miles.
Part B
The average rate of change represents the speed .
x1=1 ,y1=27
x2=4 ,y2=93
We have to calculate the slope if the function:
Replace:
Part C.
speed = distance /time
time= distance / speed
time= 225 / 22 = 10.22 hours
The domain will be
0< x ≤ 10.22
The maximum revenue generated is $160000.
Given that, the revenue function for a sporting goods company is given by R(x) = x⋅p(x) dollars where x is the number of units sold and p(x) = 400−0.25x is the unit price. And we have to find the maximum revenue. Let's proceed to solve this question.
R(x) = x⋅p(x)
And, p(x) = 400−0.25x
Put the value of p(x) in R(x), we get
R(x) = x(400−0.25x)
R(x) = 400x - 0.25x²
This is the equation for a parabola. The maximum can be found at the vertex of the parabola using the formula:
x = -b/2a from the parabolic equation ax²+bx+c where a = -0.25, b = 400 for this case.
Now, calculating the value of x, we get
x = -(400)/2×-0.25
x = 400/0.5
x = 4000/5
x = 800
The value of x comes out to be 800. Now, we will be calculating the revenue at x = 800 and it will be the maximum one.
R(800) = 400x - 0.25x²
= 400×800 - 0.25(800)²
= 320000 - 160000
= 160000
Therefore, the maximum revenue generated is $160000.
Hence, $160000 is the required answer.
Learn more in depth about revenue function problems at brainly.com/question/25623677
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Answer:
Step-by-step explanation:
<u>Given the sequence</u>
<u>To find </u>
- Sum of terms from i=5 to i=15
<h3>Solution</h3>
We see the sequence is AP
<u>The required sum is</u>
<u>Using sum of AP formula</u>
<u>Finding the required terms</u>
- i₁ = - 4- 6 = -10
- i₄ = -4 -6*4 = - 28
- i₁₅ = -4 -6*15 = -94
<u>Getting the sum</u>
- S₄ = 1/2*4*(-10 - 28) = -76
- S₁₅ = 1/2*15*(-10 - 94) = -780
- S₅₋₁₅ = S₁₅ - S₄ = -780 - (-76) = - 704
Answer:
-3 1/3
Step-by-step explanation:
The quadratic
... y = ax² +bx +c
has its extreme value at
... x = -b/(2a)
Since a = 3 is positive, we know the parabola opens upward and the extreme value is a minimum. (We also know that from the problem statement asking us to find the minimum value.) The value of x at the minimum is -(-4)/(2·3) = 2/3.
To find the minimum value, we need to evaluate the function for x=2/3.
The most straightforward way to do this is to substitue 2/3 for x.
... y = 3(2/3)² -4(2/3) -2 = 3(4/9) -8/3 -2
... y = (4 -8 -6)/3 = -10/3
... y = -3 1/3
_____
<em>Confirmation</em>
You can also use a graphing calculator to show you the minimum.
