A factory is discharging pollution into a lake at the rate of r(t) tons per year given below, where t is the number of years that the factory has been in operation. Find the total amount of pollution discharged during the first 7 years of operation. (Round your answer to two decimal places.)

The total amount of pollution discharged during the first 7 years of operation is 1.955 tons

Step-by-step explanation:

Given

Required

The total amount in the first 7 years

This implies that:

The total amount is calculated by integrating r(t) i.e.

So:

--------------------------------------------------------------

We have:

Differentiate

Rewrite as:

Solve for t

---------------------------------------------------------------------------

So:

Make t the subject

Integrate

Expand

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation:

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: