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

Answer:

y axis denotes the level of water in cylinder

x axis denotes the time

Step-by-step 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

$m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}$

Since  $(x_{1} ,y_{1}) =(1,0.80)$

           $(x_{2} ,y_{2}) =(2,0.65)$

Thus  slope (m) =

$m=\frac{0.65 -0.80}{2-1}$

$m=-0.15$

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

Answer 2

Level, x       1      0.8    0.65
time, y        0        1       2

The graph is not a straight line, it is curved. You can observe this only if you include the point (1,0), which is the level at the begining (100%)

The y - intercept is the full level, at the beginning of the experiment.