Exuru volume ( \( v \) ) of water in a tank is proportional to \( \sqrt{c} \) where \( c \) is the rate at which water is kept into the tank and constant is \( k \). 1. Find the value of \( k \) if \( v=60 \) and \( c \neq 536 \) ii. Use the value of \( k \) in i. to find the value of \( c \) when \( v \) is 90

To find the value of \( k \), we start with the relationship given: \[ v = k \sqrt{c} \] Given that \( v = 60 \) and \( c \neq 536 \), we rearrange the formula to solve for \( k \): \[ k = \frac{v}{\sqrt{c}} \] Substituting \( v = 60 \), we get: \[ k = \frac{60}{\sqrt{c}} \] Since we don't have the value of \( c \) directly, we can leave \( k \) as it is for now. Next, we want to find \( c \) when \( v = 90 \). We can assume the same expression holds: \[ 90 = k \sqrt{c} \] Now, substituting the expression for \( k \): \[ 90 = \frac{60}{\sqrt{c}} \sqrt{c} \] This simplifies to: \[ 90 = 60 \] Since we know that \( c \neq 536\), we can express \( k \) as \( k = \frac{90}{\sqrt{c'}} \) for a new \( c' \) and find an appropriate value for \( c \). With more known values or a clearer context such as specific values for \( c \), we can arrive at definitive numeric answers. In conclusion, more information regarding \( c \) would help find specific values for both \( k \) and \( c \).