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2 years ago

How many ways are there to arrange 5 people in 3 seats?

Mathematics

1 answer:

julsineya [31]2 years ago

7 0

assuming you can't repeat a person (duplicates?)

in the 1st chair, there are 5 possible people you can put there

in the 2nd chair, there are 4 possible people you can put there since 1 person already has a chair

in the 3rd chair, there are 3 possible people you can put there since 2 people already have chairs

so there are 5*4*3 or 60 ways to arrange 6 people in 3 seats

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The width of the field is 65 feet.

The length of the field is 780 feet.

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3 years ago

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2 years ago

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:

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

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2 years ago

The length of the rectangular tennis court at wimbledon is 6 feet longer than twice the width. if the court's perimeter is 240 f

KATRIN_1 [288]

Length (L): 2w + 6

width (w): w

Perimeter (P) = 2L + 2w

240 = 2(2w + 6) + 2(w)

240 = 4w + 12 + 2w

240 = 6w + 12

228 = 6w

38 = w

Length (L): 2w + 6 = 2(38) + 6 = 76 + 6 = 82

Answer: width = 38 ft, length = 82 ft

8 0

2 years ago