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The rate of change is 16.8 million tons per year
<em><u>Solution:</u></em>
Given that, the world catch of fish in 1950 was 12 million tons and in 1955 it was 96 million tons
<em><u>The average rate of change is given by formula:</u></em>
Value in 1950 = 12 million tons
Value in 1955 = 96 million tons
Change in value = value in 1955 - value in 1950
Change in value = 96 million - 12 million = 84 million tons
Number of years = 1950 to 1955 = 5 years
<em><u>Substitute the given values in formula,</u></em>
<em><u></u></em><em><u></u></em>
Thus rate of change is 16.8 million tons per year
The formula for the radius r in terms of x . and for the maximum areas is x=2/+4
Given that,
y forms a circle of radius r
y=2r
r=y/2
(2-y)- forms Square Side x
(2-y) = 4x
x=(2-y)/4
Now Sum of Area's=Area of Square +Area of Circle
Sum = r² + x²
Substitute the r and x values in above equation,
A(y)= y²/4+(y-2)²/ 16
To maximize Area A(y)
A'(y)= 0
2y/4 + 2(y-2)/16 =0
y/2 + (y-2)/8 =0
y = 2/
+4
Y max will be max, x to be maximum.
for maximum sum of areas,
x=2/+4
Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/+4
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