Question

An aspiring engineer wants to build a timer by taking a glass cylinder, filling it with water, suspending it in the air, and cutting a small hole in the bottom. He notes that at 1 p.m., the cylinder is 80% full, and at 2 p.m., it is 65% full. Draw a graph expressing this and interpret the meaning of the y-intercept.

Answer 1

y axis denotes the level of water in cylinder

x axis denotes the time

Explanation:

Given : At 1 p.m. cylinder is 80% full i.e. 0.80.

At 2 p.m. cylinder is 65% full i.e. 0.65.

Solution :

time(x) : 1 2

level (y) : 0.80 0.65

Using these points we can plot the graph (refer the attached figure)

In the figure y axis denotes the level of water in cylinder

x axis denotes the time

We can also find the equation of the graph by using two point slope form :

`y-y_(1) =m(x-x_(1))` ---a

Where m is the slope

`m=(y_(2) -y_(1))/(x_(2)-x_(1))`

Since
`(x_(1) ,y_(1)) =(1,0.80)`

`(x_(2) ,y_(2)) =(2,0.65)`

Thus slope (m) =

`m=(0.65 -0.80)/(2-1)`

`m=-0.15`

Now putting values in equation a

`y-0.80 =-0.15(x-1)`

`y-0.80 =-0.15x+0.15`

`0.15x+y-0.95=0`

Thus the required equation of the situation or the graph is

`0.15x+y-0.95=0`

THE GRAPH IS ATTACHED AND Y INTERCEPT DENOTES THE LEVEL OF WATER