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aivan3 [116]
2 years ago
14

PLEASE HELP!!! VERY EASY MATH EXPLINATION NEEDED!!!

Mathematics
2 answers:
Marta_Voda [28]2 years ago
8 0

Answer:

18

Step-by-step explanation:

So lets go voer what we know:

There are 6 pieces of ribbon.

Each piece of ribbon is 1 yard long.

We need 1/3 of each ribbon(1/3 yard).

To find this, lets take our 6 pieces of ribbbon, and break them into 3 seperate pieces.

This is because we need ribbons that are 1/3 of a yard. 3 ribbons would make up a single yard.

So:

The 6 yards of ribbon x 3 ribbons that make up 1 yard

6*3

=

18

I hope this makes more sense, and helps you understand better. I can try to explain in a different way if this still doesn't make sense.

I hope this helps! :)

Mrrafil [7]2 years ago
4 0
Answer:

It’s D, 18 cuts

Step-by-step explanation:

She cut a 6 yard long ribbon into 1/3 yard pieces so you would have to divide to get the answer and the steps to dividing is

Stay the same, change the sign, flip it
so the 6 would stay the same, you would change the division sign to multiplication because division is the opposite of multiplication, and you would flip the 1/3 into 3/1 so

6 x 3/1 would be 18/1 which is just 18
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A Riemann Sum is the sum of areas under a curve. It approximates an integral. There are various ways the area under a curve can be approximated, and the different ways give rise to different descriptions of the sum.

A Riemann Sum is often specified in terms of the overall interval of "integration," the number of divisions of that interval to use, and the method of combining function values.

<u>Example Problem</u>

For the example attached, we are finding the area under the sine curve on the interval [1, 4] using 6 subintervals. We are using a rectangle whose height matches the function at the left side of the rectangle. We say this is a <em>left sum</em>.

When rectangles are used, other choices often seen are <em>right sum</em>, or <em>midpoint sum</em> (where the midpoint of the rectangle matches the function value at that point).

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The height of each rectangle is the function value at its left edge. In the example, we have defined the function x₁(j) to give us the x-value at the left edge of subinterval j. Then the height of the rectangle is f(x₁(j)).

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The second and third attachments show a <em>right sum</em> (r₂) and a <em>midpoint sum</em> (r₃). The latter is the best of these approximations.

_____

<u>Other Rules</u>

Described above and shown in the graphics are the use of <em>rectangles</em> for elements of the summation. Another choice is the use of <em>trapezoids</em>. For this, the corners of the trapezoid match the function value on both the left and right edges of the subinterval.

Suppose the n subinterval boundaries are at x0, x1, x2, ..., xn, so that the function values at those boundaries are f(x0), f(x1), f(x2), ..., f(xn). Using trapezoids, the area of the first trapezoid would be ...

  a1 = (f(x0) +f(x1))/2·∆x . . . . where ∆x is the subinterval width

  a2 = (f(x1) +f(x2))/2·∆x

We can see that in computing these two terms, we have evaluated f(x1) twice. We also see that f(x1)/2 contributes twice to the overall sum.

If we collapse the sum a1+a2+...+an, we find it is ...

  ∆x·(f(x0)/2 + f(x1) +f(x2) + ... +f(x_n-1) + f(xn)/2)

That is, each function value except the first and last contributes fully to the sum. When we compute the sum this way, we say we are using the <em>trapezoidal rule</em>.

If the function values are used to create an <em>approximating parabola</em>, a different formula emerges. That formula is called <em>Simpson's rule</em>. That rule has different weights for alternate function values and for the end values. The formulas are readily available elsewhere, and are beyond the scope of this answer.

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<em>Comment on mechanics</em>

As you can tell from the attachments, it is convenient to let a graphing calculator or spreadsheet compute the sum. If you need to see the interval boundaries and the function values, a spreadsheet may be preferred.

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