Inverse Proportion: y is inversely proportional to the square root of x; When x=9 y=c

[gabi_thomas]

y is inversely proportional to the square root of x
When x=9 y=c ,where c is a constant
When x=25 ,y=c-16
Show that when x=36,y=20

 

[MarkFL]

y is inversely proportional to the square root of x

Okay, this means:

\(\displaystyle \displaystyle y=\frac{k}{\sqrt{x}}\)

When x=9 y=c ,where c is a constant

This allows us to write:

\(\displaystyle \displaystyle c=\frac{k}{\sqrt{9}}\implies k=3c\)

When x=25 ,y=c-16

Can you write what this gives us?

Show that when x=36,y=20

After the above step, you will have two equations in two unknowns...can you solve the system?

 

[gabi_thomas]

Okay, this means:

\(\displaystyle \displaystyle y=\frac{k}{\sqrt{x}}\)



This allows us to write:

\(\displaystyle \displaystyle c=\frac{k}{\sqrt{9}}\implies k=3c\)



Can you write what this gives us?



After the above step, you will have two equations in two unknowns...can you solve the system?

Ah ive done it!! I got k=120 , and therefore 20=120/sqrt 36

 

[MarkFL]

i understand that k=3c ,but am not sure where to go after that?

The next step is to take:

\(\displaystyle \displaystyle y=\frac{k}{\sqrt{x}}\)

And plug in \(\displaystyle x=25\) and \(\displaystyle y=c-16\)...what do you get:

 

[gabi_thomas]

The next step is to take:

\(\displaystyle \displaystyle y=\frac{k}{\sqrt{x}}\)

And plug in \(\displaystyle x=25\) and \(\displaystyle y=c-16\)...what do you get:

Ah ive got it! This gives us k=120, and 20=120/sqrt36! Thank you

 

[MarkFL]

Ah ive got it! This gives us k=120, and 20=120/sqrt36! Thank you

Yes, that's correct!