Question

Given z=k/x^n find k and n if
X is 1 z 100
X is 2 z 25/2
X is 4 z ?
X is ? Z 3/25

Answer 1

Answer:

n = - 3 and k = 100

Step-by-step explanation:

We are given that $z = \frac{k}{x^{n} }$ ......... (1) and we have to find k and n which are constants.

Now, from equation (1), we can write

$\frac{z_{1} }{z_{2} } = \frac{\frac{k}{x_{1} ^{n} } }{\frac{k}{x_{2} ^{n} }}$

⇒ $\frac{z_{1} }{z_{2} } = (\frac{x_{2} }{x_{1} } )^{n}$

Now, for z = 100, x =1 and for z = 25/2, x = 2

Hence, $\frac{100}{\frac{25}{2} } = (\frac{1}{2} )^{n} = 2^{-n}$

⇒ $2^{3} = 2^{-n}$

⇒ n = - 3

Now, from equation (1) we get

$z_{1} = \frac{k}{x_{1} ^{-3} }$

⇒ $100 = \frac{k}{1} = k$

⇒ k = 100 {Since, x = 1, when z = 100}

Therefore, n = - 3 and k = 100 (Answer)