Respuesta :
Answer:
15 Kg cm²
Step-by-step explanation:
Given that V varies inversely with P then the equation relating them is
V = [tex]\frac{k}{P}[/tex] ← k is the constant of variation
To find k use the condition
V = 360, P = 20, then
360 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )
k = 7200
V = [tex]\frac{7200}{P}[/tex] ← equation of variation
When V = 480, then
480 = [tex]\frac{7200}{P}[/tex] ( multiply both sides by P )
480P = 7200 ( divide both sides by 480 )
P = 15
If two variables vary inversely, then their product is constant:
[tex]x=\dfrac{k}{y}\implies xy=k[/tex]
So, since [tex](V,P)=(360,20)[/tex] is a valid couple, we know that for each other couple we must have
[tex]VP=360\cdot 20 = 7200[/tex]
So, given the new value for the volume, we have
[tex]480P=7200\iff P=\dfrac{7200}{480}=150[/tex]
