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ahrayia [7]
3 years ago
9

What formula should be used when factoring the expressionn x^3+27

Mathematics
1 answer:
kobusy [5.1K]3 years ago
5 0

x³ + 27 which can be written as x³ + 3³

It is in the form of a³ + b³ = ( a + b) ( a² - ab + b²)

so

x³ + 3³

= (x+ 3) (x² - x * 3 + 3²)

= ( x + 3 ) ( x² - 3x + 9)

Hope this helps you.

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Slope and y-intercept form from a table
dsp73

Answer:

The y-intercept is 3

Gradient: 4

11-3= 8

2-0= 2

8/2= 4

Hope this helped!

 

4 0
2 years ago
Find the sum or difference. a. -121 2 + 41 2 b. -0.35 - (-0.25)
s344n2d4d5 [400]

Answer:

2

Step-by-step explanation:

The reason an infinite sum like 1 + 1/2 + 1/4 + · · · can have a definite value is that one is really looking at the sequence of numbers

1

1 + 1/2 = 3/2

1 + 1/2 + 1/4 = 7/4

1 + 1/2 + 1/4 + 1/8 = 15/8

etc.,

and this sequence of numbers (1, 3/2, 7/4, 15/8, . . . ) is converging to a limit. It is this limit which we call the "value" of the infinite sum.

How do we find this value?

If we assume it exists and just want to find what it is, let's call it S. Now

S = 1 + 1/2 + 1/4 + 1/8 + · · ·

so, if we multiply it by 1/2, we get

(1/2) S = 1/2 + 1/4 + 1/8 + 1/16 + · · ·

Now, if we subtract the second equation from the first, the 1/2, 1/4, 1/8, etc. all cancel, and we get S - (1/2)S = 1 which means S/2 = 1 and so S = 2.

This same technique can be used to find the sum of any "geometric series", that it, a series where each term is some number r times the previous term. If the first term is a, then the series is

S = a + a r + a r^2 + a r^3 + · · ·

so, multiplying both sides by r,

r S = a r + a r^2 + a r^3 + a r^4 + · · ·

and, subtracting the second equation from the first, you get S - r S = a which you can solve to get S = a/(1-r). Your example was the case a = 1, r = 1/2.

In using this technique, we have assumed that the infinite sum exists, then found the value. But we can also use it to tell whether the sum exists or not: if you look at the finite sum

S = a + a r + a r^2 + a r^3 + · · · + a r^n

then multiply by r to get

rS = a r + a r^2 + a r^3 + a r^4 + · · · + a r^(n+1)

and subtract the second from the first, the terms a r, a r^2, . . . , a r^n all cancel and you are left with S - r S = a - a r^(n+1), so

(IMAGE)

As long as |r| < 1, the term r^(n+1) will go to zero as n goes to infinity, so the finite sum S will approach a / (1-r) as n goes to infinity. Thus the value of the infinite sum is a / (1-r), and this also proves that the infinite sum exists, as long as |r| < 1.

In your example, the finite sums were

1 = 2 - 1/1

3/2 = 2 - 1/2

7/4 = 2 - 1/4

15/8 = 2 - 1/8

and so on; the nth finite sum is 2 - 1/2^n. This converges to 2 as n goes to infinity, so 2 is the value of the infinite sum.

8 0
3 years ago
A sequence has the formula f(1)=4, f(4)= f(1) + f(n-1) for n&gt;1.
Olegator [25]
Im so not good with these problems if you need help go to ask.com

5 0
3 years ago
What's the opposite of-2 2/3
Citrus2011 [14]
The oppiste of -2 2/3 is 2 2/3
6 0
3 years ago
When the tortoise raced the hare, the former maintained a constant pace of one mile per hour throughout the race; while the latt
katen-ka-za [31]
<span>The tortoise is runing one mile per hour the entire race. The hare is runing 3/4 only the first half. If we multiply by 2 totis =2 miles and hare =1.50 the hare need to run 1/2 or .50 faster to beat the tortis.</span>
6 0
3 years ago
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