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3 years ago

What is 1/6 divided by 4?

Mathematics

1 answer:

vladimir2022 [97]3 years ago

6 0

The answer is 0.04166666666

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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 anyone??? I need answers

Anna35 [415]

Kkkkkk(kkkkkkklkkkkkkkkkkkll

3 0

3 years ago

use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines abo

sukhopar [10]

Answer:

16π square units.

Step-by-step explanation:

Please refer to the graph below.

So, if we draw a representative rectangle, the width of the rectangle will be (x), and the height of the rectangle at each (x) will be given by f(x) - g(x).

By the shell method:

$\displaystyle V=2\pi\int_a^bp(x)h(x)\,dx$

We are integrating from x = 0 to x = 2. p(x) is x and h(x) is f(x) - g(x):

$\displaystyle V=2\pi\int_0^2(x)((8-x^2)-(x^2))\,dx$

Evaluate. Simplify:

$\displaystyle V=2\pi \int_0^2(8x-2x^3)\,dx$

Hence:

$\displaystyle V=2\pi\Big(4x^2-\frac{1}{2}x^4\Big|_{0}^{2}\Big)$

Evaluate:

$\displaystyle \begin{aligned} V &= 2 \pi \Big[(4(2)^2-\frac{1}{2}(2)^4)-(4(0)^2-\frac{1}{2}(0)^4)\Big]\\ &=2\pi(8) \\&=16\pi\text{ square units} \end{aligned}$

7 0

2 years ago

10 + (-3 3/8) Please explain of how i can do this

seropon [69]

Answer:

53/8 or 6.625

Step-by-step explanation:

10 + (-3 3/8)

Convert everything to a fraction having the same denominator.

-3 3/8

-24/3 - 3/8

-27/8

10

80/8

Combine: (80/8 - 27/8) = 53/8 or 6.625

7 0

2 years ago

Hay 31 estudiantes en una clase. Ocho (8) estudiantes miden más de 6 pies de altura. Diecisiete (17) estudiantes miden 5-6 "a 6'

Ipatiy [6.2K]

Answer:

4/3

Step-by-step explanation:

6 0

2 years ago