Answer:
7x?
Step-by-step explanation:
Answer: the widget would be sold for $84.3
Step-by-step explanation:
The amount of profit, y made by the company, is related to the selling price of each widget, x, by the given equation which is expressed as
y = - x² + 77x - 615
At the point of breaking even, profit = 0. This means that
- x² + 77x - 615 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = - 1
b = 77
c = - 615
Therefore,
x = [- 77 ± √(77² - 4 × - 1 × - 615)]/2 × + 1
x = [- 77 ± √(8389)]/- 2
x = (- 77 + 91.59)/2 or x = (- 77 - 91.59)/- 2
x = - 7.295 or x = 84.3
Since the price cannot be negative, then x = $84.3
Let's take a look at the <em>relationship</em> between x and y in this function. When we look at the first non-zero pair, (-1, 1), we can see that, in the transition from x to y, our x value was had to have been multiplied by -1. For now, we could tentatively say that y = -x. Unfortunately, the next pair, (-4, 2), debunks this hypothesis pretty quickly, as 2 ≠ -(-4). We'll need to reexamine the relationship between x and y here.
One patter that we can be fairly confident in is that multiplication by -1; the sign is flipped from negative to positive when we go from x to y in each case, so we can hold onto that component of the function. Something else is happening before that sign flip, though, and we'll need to look into that by seeing how else the numbers are connected.
Ignoring the negative signs for a moment, let's take a look at the pairs (1,1) and (4, 2). We can transform 1 to 1 pretty easily; we simply multiply or divide it by 1. From 4 to 2, we can either divide it by 2 or multiply it by 1/2. Let's thing in terms of division for now. We know that
1/1 = 1 (obviously)
4/2 = 2
We might have something here! It looks like the number we divide by and the number we obtain are the same, so let's explore this further. Multiplying both sides by those denominators, we find:
1 = 1²
4 = 2²
Almost there! To finally find the relationship, we just square root both sides to get:
√1 = 1
√4 = 2
So that was the function we'd been looking for - a square root! Putting that together with what we said about changing the sign at the beginning, we have:
y =√(-x)
To verify this, we just need to plug in a few pairs, and we find that indeed:
1 = √-(-1) = √1 = 1
2 = √-(-4) = √4 = 2
Based on the function for the bounded area of the curve, the shaded area bounded by the curve and the x-axis between the points where x = -2 and x = 1 is 12 units².
<h3>What is the area of the shaded area?</h3>
To find the shaded area, you need to integrate the function of the bounded area as shown below:
= ∫(x² + 3) dx
This gives:
= (x³/3 + 3)
= (1 / 3 + 3) - (8 /3 - 6)
= 1/3 + 3 + 8/3 + 6
= 9/3 + 9
= 12 units²
In conclusion, shaded area bounded by the curve and the x-axis between the points where x = -2 and x = 1 is 12 units².
Find out more on the area of a shaded region at brainly.com/question/1297097.
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Divide the stack into halves, if the stacks are equal, they are even. If they aren't, they are odd.
