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Ivan
3 years ago
10

Help me out here with this another equation the the sign on the left is the checking

Mathematics
1 answer:
omeli [17]3 years ago
5 0
Put the same variable on the same side first than solve

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PLZ HELP!!! Use limits to evaluate the integral.
Marrrta [24]

Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:

\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

r_i=\dfrac{2i}n

where 1\le i\le n. Each interval has length \Delta x_i=\frac{2-0}n=\frac2n.

At these sampling points, the function takes on values of

f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}

We approximate the integral with the Riemann sum:

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3

Recall that

\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4

so that the sum reduces to

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}

Just to check:

\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28

4 0
3 years ago
The volume of a rectangular prism has 5376 cubic inches the prism is 14 in long and 16 in wide how tall is the prism
Mkey [24]

Answer:

The height of the prism is 24\ in

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

V=LWH

In this problem we have

V=5,376\ in^{3}

L=14\ in

W=16\ in

substitute in the formula and solve for H

5,376=(14)(16)H

H=5,376/[(14)(16)]

H=24\ in

4 0
3 years ago
Nobody been getting my recent questions please answer this and msg r the last 3 too
lakkis [162]

Answer:

The value of the missing angle is 103.

Step-by-step explanation:

4 0
2 years ago
The diagram is not drawn to scale
Firlakuza [10]

Answer:

<h2 /><h3><em><u>3x-2 = 25 </u></em></h3><h3><em><u> 3x = 25+2 </u></em></h3><h3><em><u> 3x = 27</u></em></h3><h3><em><u> x =9</u></em></h3><h3><em><u>the</u></em><em><u> </u></em><em><u>answer</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>option</u></em><em><u> </u></em><em><u>c</u></em></h3>
6 0
3 years ago
0.003 divided by 8.1
dusya [7]

2700  is your answer

Step-by-step explanation:

7 0
3 years ago
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