I need some math help

How to algebraically find the limit of a function as x approaches infinity?

Sauron [17]

Well... One way you can do this is by testing a set of arrays and see the trend. If I chose to find what y1 is in (100, y1) and what y2 is in (101, y2), I would find the difference between y2 and y1. If y2 - y1 is positive, this means there is a positive relationship and y is also approaching POSITIVE infinity. A negative relation means that it is approaching NEGATIVE infinity. However, it could be approaching a single number like "4" for instance, and you just need to plug in the right number of data sets to make that educated guess.

Formula Example:
5 + 1 / (x + 1) will always approach 5 because "1 / (x + 1) will approach 0".

Hope this helps.

5 0

3 years ago

IF the area of the frame was 64inches², what would be 2 possible sets of dimensions that could be used to make a frame with that

alina1380 [7]

To resolve this exercise you have to choose two numbers that when you multiply them, you get 64:

For Set 1: If you choose to make a square frame, you can calculate its dimensions by clearing the value of each sides of it from the formula of the area of a square:

A= L²
L= √A
L= √64 inches²
L= 8 inches

So, you have a square frame of 8 inches x 8inches = 64 inches²

Set 1: 8 inches x 8 inches

For set 2, you can make a rectangular frame with the following dimensions: 16 inches x 4 inches = 64 inches²

Set 2: 16 inches x 4 inches

7 0

3 years ago

Ms. Smith mixes orange juice with seltzer in a ratio of 3:1. If she uses 48 ounces of orange juice, how many ounces of seltzer d

vladimir2022 [97]

Answer:

16 oz

Step-by-step explanation:

the ratio is 3 oz of oj to 1 oz of seltzer.

I pretty much just divided 48 by 3.

I hope this is correct and I hope it helps you!

3 0

3 years ago

An=an-1+6an-2 <br> n>2 a0=3 a1=6

Svetach [21]

$\begin{cases}a_0=3\\a_1=6\\a_n=a_{n-1}+6a_{n-2}&\text{for }n>2\end{cases}$

Let the generating function for $a_n$ be

$A(x)=\displaystyle\sum_{n\ge0}a_nx^n$

Multiplying both sides by $x^{n-2}$

$a_nx^{n-2}=a_{n-1}x^{n-2}+6a_{n-2}x^{n-2}$

Summing both sides over the non-negative integers greater than or equal to 2 gives

$\displaystyle\sum_{n\ge2}a_nx^{n-2}=\sum_{n\ge2}a_{n-1}x^{n-2}+6\sum_{n\ge2}a_{n-2}x^{n-2}$
$\displaystyle\frac1{x^2}\sum_{n\ge2}a_nx^n=\frac1x\sum_{n\ge1}a_nx^n+6\sum_{n\ge0}a_nx^n$
$\displaystyle\frac1{x^2}\left(\sum_{n\ge0}a_nx^n-a_0-a_1x\right)=\frac1x\left(\sum_{n\ge0}a_nx^n-a_0\right)+6\sum_{n\ge0}a_nx^n$
$\displaystyle\frac1{x^2}\left(A(x)-3-6x\right)=\frac1x\left(A(x)-3\right)+6A(x)$
$A(x)=\dfrac{3x+3}{1-x-6x^2}$
$A(x)=\dfrac3{5(1+2x)}+\dfrac{12}{5(1-3x)}$

For $|x|$ , the two series converge to

$\displaystyle A(x)=\frac35\sum_{n\ge0}(-2x)^n+\frac{12}5\sum_{n\ge0}(3x)^n$
$\implies A(x)=\displaystyle\sum_{n\ge0}\dfrac{3(-2)^n+12(3)^n}5x^n$
$a_n=\dfrac{3(-2)^n+12(3)^n}5=\dfrac{3(-2)^n+4(3)^{n+1}}5$

5 0

3 years ago

Draw a circle shade one sixth of it what percentage of the circle is shaded

White raven [17]

Answer:

16.6%

Step-by-step explanation:

6 0

3 years ago