Answer:
36 milliliters of rain.
Step-by-step explanation:
The rate at which rain accumluated in a bucket is given by the function:

Where r(t) is measured in milliliters per minute.
We want to find the total accumulation of rain from <em>t</em> = 0 to <em>t</em> = 3.
We can use the Net Change Theorem. So, we will integrate function <em>r</em> from <em>t</em> = 0 to <em>t</em> = 3:

Substitute:

Integrate:

Evaluate:

36 milliliters of rain accumulated in the bucket from time <em>t</em> = 0 to <em>t</em> = 3.
<u>Given</u><u> </u><u>:</u><u>-</u>
- Line p has an equation of y = 5/3x - 4 .
- Line q includes point (-10,-3) and is perpendicular to the line p .
<u>To </u><u>Find</u><u> </u><u>:</u><u>-</u>
<u>Solution</u><u> </u><u>:</u><u>-</u>
The equation of the line p is ,
y = 5/3x - 4
On comparing to slope intercept form of the line which is y = mx + c , we have ,
m = 5/3
Now as we know that the product of slopes of two perpendicular lines is -1 . So the slope of the perpendicular line will be ,
Now here the line q passes through the point (-10,-3) . So on using the point slope form of the line we get ,
y - (-3) = -3/5[ x-(-10)]
y +3 = -3/5(x+10)
y+3 = -3/5x - 6
y +9 = -3/5x
y = - 3/5x - 9
<u>Hence</u><u> the</u><u> required</u><u> answer</u><u> is</u><u> </u><u>y </u><u>=</u><u> </u><u>-</u><u>3</u><u>/</u><u>5</u><u>x</u><u> </u><u>-</u><u> </u><u>9</u><u> </u><u>.</u>