Question

1.A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window find the dimensions of a Norman window of maximum area when the total permeter is 16ft.



2. A rectangle is bounded by the x axis and the semicircle
y=square root 25-x^2. what length and width should the rectangle have so that its area is a maxium.



3. A rectangle package to be sent by a postal service can have a maximum combined length and girth(perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent. ( Assume the cross section is square)


Hello to whomever is reading this I do not need the entire problem solved. I just struggle with findind the intial equation. I then know what to do after the equation is found. Can you please help me and let me know if there are any tricks of finding these equations. Thank you

Answer 1

Nevermind I got the first one just 2 and three please

Answer 2

I just struggle with findind the intial equation. I then know what to do after the equation is found>>
What you are finding difficult is analysis. You need to learn that skill.

a. make a sketch. Area total=area bottom rectangle + area top semicircle. Take that, and then you have your formula for total area. Of course, perimeter= 2h+1*w*1/2 PI *w check that.

b. make a sketch. You have the formula which the two uppermost corners of the rectangle happen, and with that, you know the x coordinates of the two bottom coordinates.
Rectangle dimensions: 2*xinterceptson curve+2*yinterceptsoncurve

areaRectangle=2x*y where y= 25-x^2
area rectangle= 2x*(25-x^2)
find max area.

Answer 3

#2 Let the rectangle extend from -x to +x, with height y. Then the area

a = 2xy = 2x√(25-x^2)
now find x such that da/dx = 0

#3 If the square cross-section has side x, and the package has length y, then the girth is 4x, and the volume is

v = x^2y = x^2(108-4x)