Respuesta :

Answer:

[tex] P = \frac{3}{4}k [/tex]

Step-by-step explanation:

Inverse Varation

[tex] y=xk [/tex]

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Since the two quantities are named P and V, then we will replace x and y with P and V:

P = Vk

P=18 when V=24:

[tex] 18 = 24k [/tex]

[tex] \frac{18}{24} = k [/tex]

[tex] k = \frac{3}{4} [/tex]

Now we have the value of k, we can now express P in terms of V:

[tex] P = \frac{3}{4}V [/tex]

Answer:

P = [tex]\frac{432}{V}[/tex]

Step-by-step explanation:

Given that P is inversely proportional to V then the equation relating them is

P = [tex]\frac{k}{V}[/tex] ← k is the constant of variation

To find k use the condition P = 18 when V = 24, that is

18 = [tex]\frac{k}{24}[/tex] ( multiply both sides by 24 )

432 = k

P = [tex]\frac{432}{V}[/tex] ← equation of variation

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