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2 years ago

F(x)=[[2x]] picewise functions

Mathematics

1 answer:

Lena [83]2 years ago

6 0

Answer:

zknj;zhb

Step-by-step explanation:

zJ NKml

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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

erma4kov [3.2K]

Answer:

$\frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}$

Step-by-step explanation:

Given

5 tuples implies that:

$n = 5$

$(h,i,j,k,m)$ implies that:

$r = 5$

Required

How many 5-tuples of integers $(h, i, j, k,m)$ are there such that $n\ge h\ge i\ge j\ge k\ge m\ge 1$

From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.

Also considering that repetition is allowed: This implies that, a number can be repeated in more than 1 location

So, there are n + 4 items to make selection from

The selection becomes:

$^{n}C_r => ^{n + 4}C_5$

$^{n + 4}C_5 = \frac{(n+4)!}{(n+4-5)!5!}$

$^{n + 4}C_5 = \frac{(n+4)!}{(n-1)!5!}$

Expand the numerator

$^{n + 4}C_5 = \frac{(n+4)!(n+3)*(n+2)*(n+1)*n*(n-1)!}{(n-1)!5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5*4*3*2*1}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}$

<u><em>Solved</em></u>

6 0

2 years ago

Which rational graph has a minimum near x=-2 and a horizontal asymptote at y=1?

Arada [10]

Answer:

Graph A.

Step-by-step explanation:

The graph has a local minimum around x=-2 since it slightly curves downwards around this region. Moreover, the graph of the rational function has a horizontal asymptote at y=1 since the graph approaches this horizontal line but never touches nor crosses it

7 0

3 years ago

Please help what is the equation

Elanso [62]

let us take any two points here (5,20) and (7,30)

now let us use slope formula to get its slope

$slope=\frac{y2-y1}{x2-x1}$