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DedPeter [7]
1 year ago
11

consider a wire 2 ft long cut into two pieces. one piece forms a circle with radius r and the other forms a square with side len

gth x. (a) determine a formula for the radius r in terms of x .
Mathematics
1 answer:
makkiz [27]1 year ago
4 0

The formula for the radius r in terms of x . and for the maximum areas is x=2/\pi+4

Given that,

y forms a circle of radius r

y=2\pir

r=y/2\pi

(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 = \pir² + x²

Substitute the r and x values in above equation,

A(y)= y²/4\pi+(y-2)²/ 16

To maximize Area A(y)

A'(y)= 0

2y/4\pi + 2(y-2)/16 =0

y/2\pi + (y-2)/8 =0

y = 2\pi/\pi+4

Y max will be max, x to be maximum.

for maximum sum of areas,

x=2/\pi+4

Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/\pi+4

Learn more about Area :

brainly.com/question/28642423

#SPJ4

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1) given function

y = - 2 ^ ( -x + 2) + 1

2) domain: domain is the set of the x-values for which the function is defined.

The exponential function is defined for all the real numbers, so the domain of the given function is all the real numbers.

3) x-intercept => y = 0

=> y = - 2 ^ ( -x + 2) + 1 = 0 => 2^ ( -x + 2) = 1

=> - x + 2 = 0 => x = 2

The x-intercept is x = 0

4) y-intercept => x = 0

=> y = - 2 ^ ( -x + 2) + 1= - 2 ^ ( 0 + 2)  1 = - (2)^(2) + 1 =- 4 + 1 = - 3

=> The y-intercept is - 3

5) limit when x -> negative infinite

Lim f(x) when x -> ∞ = - ∞

6) limit when x -> infinite

Lim f(x) when x - > infinite = 1

=> asymptote = y = 1

7) range is the set of values of the fucntion: y

Given that the function is strictly decreasing from -∞ to ∞, the range is from - ∞ to less than 1

Range (-∞,1)


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