Answer:
This conjecture is false
<u> Explanation:</u>
A Conjecture is only an educated guess which might or might not be true. When two angles are supplementary, it means their sum when added together is 180°. But as per this, conjecture both the angles are acute, which means both are less than 90°. This is not possible.
This can be explained with a counter example. It is an example that can be given to show that a particular conditional statement is false.
If both angles are acute means they are less than 90°.Like one angle is 80° and the other is 70°. Adding 80° and 70° we will get 150°, which is not supplementary.
Answer:
3y
Step-by-step explanation:
Answer:
n = - 3 and k = 100
Step-by-step explanation:
We are given that
......... (1) and we have to find k and n which are constants.
Now, from equation (1), we can write
![\frac{z_{1} }{z_{2} } = \frac{\frac{k}{x_{1} ^{n} } }{\frac{k}{x_{2} ^{n} }}](https://tex.z-dn.net/?f=%5Cfrac%7Bz_%7B1%7D%20%7D%7Bz_%7B2%7D%20%7D%20%3D%20%5Cfrac%7B%5Cfrac%7Bk%7D%7Bx_%7B1%7D%20%5E%7Bn%7D%20%7D%20%7D%7B%5Cfrac%7Bk%7D%7Bx_%7B2%7D%20%5E%7Bn%7D%20%7D%7D)
⇒ ![\frac{z_{1} }{z_{2} } = (\frac{x_{2} }{x_{1} } )^{n}](https://tex.z-dn.net/?f=%5Cfrac%7Bz_%7B1%7D%20%7D%7Bz_%7B2%7D%20%7D%20%3D%20%28%5Cfrac%7Bx_%7B2%7D%20%7D%7Bx_%7B1%7D%20%7D%20%29%5E%7Bn%7D)
Now, for z = 100, x =1 and for z = 25/2, x = 2
Hence, ![\frac{100}{\frac{25}{2} } = (\frac{1}{2} )^{n} = 2^{-n}](https://tex.z-dn.net/?f=%5Cfrac%7B100%7D%7B%5Cfrac%7B25%7D%7B2%7D%20%7D%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%20%29%5E%7Bn%7D%20%3D%202%5E%7B-n%7D)
⇒ ![2^{3} = 2^{-n}](https://tex.z-dn.net/?f=2%5E%7B3%7D%20%3D%202%5E%7B-n%7D)
⇒ n = - 3
Now, from equation (1) we get
![z_{1} = \frac{k}{x_{1} ^{-3} }](https://tex.z-dn.net/?f=z_%7B1%7D%20%3D%20%5Cfrac%7Bk%7D%7Bx_%7B1%7D%20%5E%7B-3%7D%20%7D)
⇒ ![100 = \frac{k}{1} = k](https://tex.z-dn.net/?f=100%20%3D%20%5Cfrac%7Bk%7D%7B1%7D%20%3D%20k)
⇒ k = 100 {Since, x = 1, when z = 100}
Therefore, n = - 3 and k = 100 (Answer)