math
posted by Fabiola .
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 46 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
Enter your answers correct to two decimal places. Remember to take into account in your calculations that there is only half of a circle.
1.The length of the bottom of the rectangle is________ feet.
2.The length of each of the sides of the rectangle is ________feet.
I would let the bottom of the rectangle be 2x, that way you can let the radius of the circle be x, and avoid fractions.
Let the height of the rectangle by y.
Your main equation is
Area = xy = 1/2 Pi*x^2
but we know P=46
so 2x+2y + 1/2(2Pi*x) = 46
solve this for y, and substitute y in your Area equation
Differentiate,set equal to zero, and solve.
Good luck
Respond to this Question
Similar Questions

Math (:
My answer doesn't make sense. It's too big. A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman … 
Calculus
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30ft, find the dimensions of the window so that … 
Math
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 24 ft, find the value of x so that the greatest … 
Calculus
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 30 feet? 
Calculus
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus, the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 25 ft, find the dimensions of the window so that … 
Math
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus, the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30 ft, find the dimensions of the window so that … 
Calculus
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 33 feet? 
Calculus
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 49 feet? 
calculus
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 31 feet 
Calculus  Optimization
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 38 feet?