Length and width should the rectangle have so that its area is a maximum are 4.242 and 2.121 respectively.
From the question, we have
Area = A = xy
A = xsqr(9-x^2)
Taking the derivative and set = 0
A' = (x/sqr(9-x^2)(-2x) + sqr(9-x^2) = 0
A' = -x^2 + 9 -x^2 = 0
-2x^2 =-9
x^2 = 9/2
x = 3/sqr2 = (3/2)sqr2 = 4.242
y = sqr(9-x^2) = sqr(9-9/2) = 3sqr2/2 = 2.121
Dimensions of the rectangle are 4.242 and 2.121 respectively
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
Complete question:
A rectangle is bounded by the x-axis and the semicircle y = radical 9 − x^2 (see figure). What length and width should the rectangle have so that its area is a maximum?
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