proportionalities

**andyboy179** · January 26th 2010, 10:30 AM

hi, this is my question:

In a balloon it was noticed the the pressure, in atmospheres was inversely proportional to the square root of the height, in metres. When the balloon was at a height of 25m, the pressure was 1.44atm.

would K= 7.2?

**e^(i*pi)** · January 26th 2010, 11:04 AM

Originally Posted by andyboy179

hi, this is my question:

In a balloon it was noticed the the pressure, in atmospheres was inversely proportional to the square root of the height, in metres. When the balloon was at a height of 25m, the pressure was 1.44atm.

would K= 7.2?

$P = \frac{k}{\sqrt{h}}$

$k =1.44 \times \sqrt{25} = 7.2$

**andyboy179** · January 26th 2010, 11:05 AM

thanks do u know what k would be in this:

the amount of waste which a firm produces, measured in tonnes per hour, is inversely proportional to the square root of the size of the filter beds, measured in metres squared. At the moment, the firm produces 1.25 tonnes per hour of waste, with filter beds of size 0.16 metres squared.

**andyboy179** · January 26th 2010, 11:12 AM

would K= 0.0128???

**e^(i*pi)** · January 26th 2010, 11:14 AM

Originally Posted by andyboy179

thanks do u know what k would be in this:

the amount of waste which a firm produces, measured in tonnes per hour, is inversely proportional to the square root of the size of the filter beds, measured in metres squared. At the moment, the firm produces 1.25 tonnes per hour of waste, with filter beds of size 0.16 metres squared.

The rates don't matter so treat them as if they were x and y. (technically only true for steady state but that's far too advanced for a simple proportion problem). The units only matter if you want to know the units of k.

The equation is $n = \frac{k}{\sqrt{A}}$

I get an answer of $k=\frac{1}{2}$

**andyboy179** · January 26th 2010, 11:18 AM

i don't understand it!!!

what is n, is it 1.25?

**e^(i*pi)** · January 26th 2010, 11:20 AM

Originally Posted by andyboy179

i don't understand it!!!

what is n, is it 1.25?

I got the wrong arithmetic before, the edited answer is now correct. Yes n is 1.25

I took n because it's a number, you could have picked y for example

**andyboy179** · January 26th 2010, 11:22 AM

ok, what is root with the a in it? is it 0.16? if so would square root of 0.16 be 0.4?

**e^(i*pi)** · January 26th 2010, 11:24 AM

Originally Posted by andyboy179

ok, what is root with the a in it? is it 0.16? if so would square root of 0.16 be 0.4?

A denotes the area of the filter beds. As you said it is 0.16 and so the square root is 0.4. Finding k in this case provides a good example of cancelling down too

$k = 1.25 \times 0.4 = \frac{5}{4} \times \frac{2}{5} = \frac{1}{2}$

**andyboy179** · January 26th 2010, 11:36 AM

also do you know what root5( 2+ root10)=?

**andyboy179** · January 26th 2010, 11:38 AM

would i be $proportionalities-untitled.jpg$

**e^(i*pi)** · January 26th 2010, 11:43 AM

Yes it would but didn't you ask that question before? Also if you have a new (especially unrelated) question it'd be best to make a new thread

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