P3 - Edexcel question calculus

Liquid is poured into a container at a constant rate of 30 cm3 s−1. At time t seconds liquid is leaking from the container at a rate of 152V cm3 s−1, where V cm3 is the volume of liquid in the container at that time.
(a) Show that
−15dV/dT = 2V – 450.

Given that V = 1000 when t = 0,
(b) find the solution of the differential equation, in the form V = f(x).

Please help.

Reply 1

!Laxy!

Paxi

Liquid is poured into a container at a constant rate of 30 cm3 s−1. At time t seconds liquid is leaking from the container at a rate of 152V cm3 s−1, where V cm3 is the volume of liquid in the container at that time.
(a) Show that
−15dV/dT = 2V – 450.

Given that V = 1000 when t = 0,
(b) find the solution of the differential equation, in the form V = f(x).

Please help.

a) dV/dt = 30 - 2/15V

then just multiply by 15 and and then by minus 1 to get the answer

b) Seperate the variables so:

-15/2V - 450 dV = dt

then integrate to obtain: -15/2 ln 2V - 450 = t

use limits to find c which is: -15/2 ln 1550

thus: ln (2V - 450/1550) = -2/15t

Rearrange to give: V = 225 + 775e^-2/15t

Reply 2

Feria

2

Where did the 2/15V come from?

P3 - Edexcel question calculus

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