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lilavasa [31]
3 years ago
8

Look at the model. Name three equivalent fractions for the part that is shaded

Mathematics
1 answer:
Ymorist [56]3 years ago
7 0

Answer:

1. 2/6

2. 1/3

3. 3/9

Step-by-step explanation:

I've learned this before

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Elodia [21]

Answer:

264 inches

Step-by-step explanation:

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4 years ago
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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6
Anettt [7]
Splitting up the interval [0, 6] into 6 subintervals means we have

[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]

and the respective midpoints are \dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2. We can write these sequentially as {x_i}^*=\dfrac{2i+1}2 where 0\le i\le5.

So the integral is approximately

\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2

Recall that

\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6
\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2
\displaystyle\sum_{i=1}^n1=n

so our sum becomes

\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)
=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2

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Step-by-step explanation:

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2 years ago
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