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erastova [34]
2 years ago
12

Approximate the area under the

Mathematics
1 answer:
taurus [48]2 years ago
4 0

Split up the interval [0, 3] into 3 equally spaced subintervals of length \Delta x = \frac{3-0}3 = 1. So we have the partition

[0, 1] U [1, 2] U [2, 3]

The left endpoint of the i-th subinterval is

\ell_i = i - 1

where i\in\{1,2,3\}.

Then the area is given by the definite integral and approximated by the left-hand Riemann sum

\displaystyle \int_0^3 f(x) \, dx \approx \sum_{i=1}^3 f(\ell_i) \Delta x \\\\ ~~~~~~~~~~ = \sum_{i=1}^3 (i-1)^3 \\\\ ~~~~~~~~~~ = \sum_{i=0}^2 i^3 \\\\ ~~~~~~~~~~ = 0^3 + 1^3 + 2^3 = \boxed{9}

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Answer:

C

Step-by-step explanation:

Translate the image 2 units right and 1 unit up. Then rotate the image 180°.

Take the coordinate W, it is at (2, 4).

Translate 2 units right (add 2 to the x coordinate) and 1 up (add 1 to the y coordinate)

(2, 4) ------> (2 + 2, 4 + 1) -------> (4, 5)

A rotation of 180° (doesn't matter the direction) makes the coordinates their opposites. Positives become negatives and negatives become positive.

(4, 5) -------> (-4, -5)

8 0
2 years ago
Henry is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 54 feet and its width is
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Answer:

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3 years ago
Solve for x: -4x – 12 > 36 A. x > -12 B. x > 12 C. x < -12 D. x < 12
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Step-by-step explanation:

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x < -48/4

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Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great rest of Black History Month! :-)  

- Cutiepatutie ☺️❀❤

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