Inverse proportion to the square root
Inverse proportion to the square root occurs when one quantity decreases as the square root of another quantity increases. This concept is often found in areas like physics, such as the relationship between pressure and volume in gases or certain diffusion processes. Understanding this relationship helps in solving problems where the change in one value slows down as another value increases. Jump to the questions
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Question
y is inversely proportional to √p
y is when p is
Find the equation for y and p
Step 1 - describe the relationship using the correct symbol
y ∝ 1 / √p
Step 2 - replace the symbol with the constant of proportionality, k
y = / √p
Step 3 - substitute the values from the question into the equation
= /
Step 4 - rearrange the equation to isolate k
× = k
Step 5 - determine the value of k
k =
Step 6 - write the final equation linking y and √p
y = / √p
Find y when p =
Step 1 - restate the equation
y = / √p
Step 2 - substitute the value you know
y = /
Step 3 - determine the final value of y (to 3 decimal places)
y =
Find p when y =
Step 1 - restate the equation
y = / √p
Step 2 - substitute the value you know
= / √p
Step 3 - rearrange the equation to isolate √p
/ = √p
Step 4 - determine the value of √p
√p =
Step 5 - calculate p
p =
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