Question

A cubical water tank has edge 5m long. Find the volume of water in the tank if 1/5th of the tank is empty.

Write down the equation of the line whose gradient is 3/2 and which passes through P, where P divides the line segment joining A(-2,6) and B(3,-4) in the ratio 2:3.

Pls consider and help..

Answer 1

Volume of full tank = 5^3= 125 m^3
If 1/5 of it is empty, then 4/5 of it is full
What is (4/5)(125) ?

#2
Let P be (x,y) so that AP is the shorter segment
to get the x:
(x+2)/(3-x) = 2/3
3x + 6 = 6 - 2x
5x = 0
x = 0
to get the y:
(y-6)/(-4-y) = 2/3
3y - 18 = -8 - 2y
5y = 10
y = 2
So point P is (0,2) , looks like the y-interept of our required line, so the equation is

y = (3/2)x + 2