Answer:
Step-by-step explanation:
abc = 1
We have to prove that,
![\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2Ba%2Bb%5E%7B-1%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2Bc%5E%7B-1%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bc%2Ba%5E%7B-1%7D%7D%3D1)
We take left hand side of the given equation and solve it,
![\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2Ba%2B%5Cfrac%7B1%7D%7Bb%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2B%5Cfrac%7B1%7D%7Bc%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bc%2B%5Cfrac%7B1%7D%7Ba%7D%7D)
Since, abc = 1,
and c = ![\frac{1}{ab}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bab%7D)
By substituting these values in the expression,
![\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2Ba%2B%5Cfrac%7B1%7D%7Bb%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2B%5Cfrac%7B1%7D%7Bc%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bc%2B%5Cfrac%7B1%7D%7Ba%7D%7D%3D%5Cfrac%7B1%7D%7B1%2Ba%2B%5Cfrac%7B1%7D%7Bb%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2Bab%7D%2B%5Cfrac%7B1%7D%7B1%2B%5Cfrac%7B1%7D%7Bab%7D%2B%5Cfrac%7B1%7D%7Ba%7D%7D)
![=\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bb%7D%7Bb%2Bab%2B1%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2Bab%7D%2B%5Cfrac%7Bab%7D%7Bab%2B1%2Bb%7D)
![=\frac{1+b+ab}{1+b+ab}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%2Bb%2Bab%7D%7B1%2Bb%2Bab%7D)
![=1](https://tex.z-dn.net/?f=%3D1)
Which equal to the right hand side of the equation.
Hence, ![\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2Ba%2Bb%5E%7B-1%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2Bc%5E%7B-1%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bc%2Ba%5E%7B-1%7D%7D%3D1)
Answer:
The pairs ( 1 , 2 ) and ( 2 , 1 ) are not equal because their respective elements are not equal.
Step-by-step explanation:
The pair of elements which are in specific order is called an ordered pair. The pair ( 1 , 2 ) is not same as the pair ( 2 , 1 ). In the pair ( 1 , 2 ) 1 is in the first position and 2 is in the second position. In the pair ( 2 , 1 ), 2 is in the first position and 1 is in the second position.
Two ordered pairs ( a , b ) and (c , d ) are said to be equal if a = c and b = d. We write ( a , b ) = ( c , d ).
Hope I helped!
Best regards!!
Answer:
yes it does. good job on your A.
Step-by-step explanation:
The function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)
<h3>How to write a function of the length z in meters of the side parallel to the wall?</h3>
The given parameters are:
Perimeter = 210 meters
Let the length parallel to the wall be represented as z and the width be x
So, the perimeter of the fence is
P = 2x + z
This gives
210 = 2x + z
Make x the subject
x = 1/2(210 - z)
The area of the wall is calculated as
A = xz
So, we have
A = 1/2(210 - z) * z
This gives
A = z/2(210 - z)
Rewrite as
A(z) = z/2(210 - z)
Hence, the function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)
Read more about functions at
brainly.com/question/1415456
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The four sides to create the square