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

gabi_thomas

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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
 
y is inversely proportional to the square root of x

Okay, this means:

y=kx\displaystyle \displaystyle y=\frac{k}{\sqrt{x}}

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

This allows us to write:

c=k9    k=3c\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?
 
Okay, this means:

y=kx\displaystyle \displaystyle y=\frac{k}{\sqrt{x}}



This allows us to write:

c=k9    k=3c\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
 
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i understand that k=3c ,but am not sure where to go after that?

The next step is to take:

y=kx\displaystyle \displaystyle y=\frac{k}{\sqrt{x}}

And plug in x=25\displaystyle x=25 and y=c16\displaystyle y=c-16...what do you get:
 
The next step is to take:

y=kx\displaystyle \displaystyle y=\frac{k}{\sqrt{x}}

And plug in x=25\displaystyle x=25 and y=c16\displaystyle y=c-16...what do you get:

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