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2 years ago

Find the area of the shaded region. Round your answer to the nearest tenth.

Mathematics

1 answer:

Katen [24]2 years ago

7 0

Answer:

AREA is 9 to the power of 4

Step-by-step explanation:

Which is 9×9×9×9= the answer

Cause area = l×w×h

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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

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

8 0

2 years ago

Help please question is in picture

lisov135 [29]

The answer is A

Explanation:
Hope this helps

8 0

3 years ago

Read 2 more answers

Which value of the 9 ten times in the number 920

umka21 [38]

Answer:

9000. the value of 9 in 920 is 900. and ten times anything is basically just adding a 0. so ten times 900 is 9000.

Step-by-step explanation:

Please mark brainliest and have a great day!

3 0

3 years ago

What is the domain of the function y = 2 VX-5?

tresset_1 [31]

Answer:

R

Step-by-step explanation:

All linear functions have a range and domain of R [ALL REAL NUMBERS].

I am joyous to assist you anytime.

3 0

3 years ago

Show me the steps to solve and the solution y-2>1/2(x-2)

aev [14]

y-2>1/2(x-2) can be expanded as follows: y - 2 > (1/2)x - 1

Mult. all terms by 2 to remove the fractions:

2y - 4 > x - 2

Add 4 to both sides: 2y > x + 2

Div. both sides by 2: y > (1/2)x + 1 (answer)

4 0

3 years ago