A company that produces ribbon has found that the marginal cost of producing x yards of fancy ribbon is given by Upper C prime (
x )equalsnegative 0.00001 x squared minus 0.02 x plus 58 for x less than or equals 1600, where Upper C prime (x )is in cents. Approximate the total cost of manufacturing 1600 yards of ribbon, using 5 subintervals over [0 comma 1600 ]and the left endpoint of each subinterval.
1 answer:
Answer:
$624.90
Step-by-step explanation:
The total cost is the integral of the marginal cost. Here, you're asked to approximate that integral using 5 equal-width rectangles. The area of each rectangle is the product of its height and width. The height is given by the function value at the left end of the interval.
The table shows the function values at the left end of each of the 5 intervals. The intervals have width 1600/5 = 320. The total estimated cost is the sum of products of 320 and each of the table values. (Of course, 320 can be factored out of the sum to make the math easier.)
The estimated cost is ...
320(58 + 50.576 + 41.104 + 29.584 +16.016) = 62,489.6 . . . cents
≈ $624.90 . . . . cost of manufacturing 1600 yards of fancy ribbon
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Answer:
1. A. 1
2. D.
Step-by-step explanation:
Properties used:
- Power of a Power Property
- Product Property
- Quotient Property
- Zero Exponent Property
1. First, let's deal with the numerator.
can be turned into
by using the Power of a Power Property.
And then use the Product Property,
So now, our fraction is this:
All number over itself in a fraction is equal to 1. But you can also do this the mathmatic way using the Quotient Property: or
. Which then you plug the numbers in:
. And since we know that in Zero Exponent Property:
, we can see that
. So either way, we get 1.
So the answer is 1, which is A
2. Power of a Power Property:
So plug the numbers in the property: =
Product Property:
We plug the equation in with turned into
---
So the answer is , which is D
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