I need help with a precalculus problem!!?

Question

A norman window has the shape of a rectangle surmounted by a semicircle. if the permeter is 30ft. , find a fuction that models the area of the window

Answer 1

If L is length of rectangular section, W is width, Wπ/2 is circumference of semicircle, then perimeter of whole window is

Three sides of rectangle + semicircle
2L + W + Wπ/2 = 30
2L = 30 - W-Wπ/2
L = 15 - W/2-Wπ/4

You can substitute for L in area formula so everything is in terms of one variable.

Area of window is

Area of rectangle plus area of semicircle
LW + π(W/2)^2/2=
(15 - W/2-Wπ/4)W+ (πW^2)/8=
15W-(W^2)/2-(W^2)π/4+(W^2)π/8=
15W-(W^2)(1/2-π/4) = Area (in terms of width of window)

I think. (I'm tired...)

Answer 2

You need more information to get exact answers.

However, if you let x=height of the window and y=length of the window, then the perimeter of the window that belongs to the semicircle is 1/2 * pi * y

This means the perimeter= 2*x + y + 1/2*pi*y = 2x + 2.57y
So, 30=2x + 2.57y

If we put x in terms of y: 2x = 30 - 2.57y
x = 15 - 1.285y

Then, the area= x*y + pi*(0.5y)^2
Area = (15 - 1.285y)*y + 0.79y^2= 15y - 1.285y^2 + 0.79y^2

Area = 15y -0.5y^2

(That is approximate since I rounded pi)

Answer 3

You would have to add the area of the rectangle to the area of the semicircle. Do you have any other info about the dimensions of the window?

Answer 4

ok, you have sqrt(x+a million) + a million = sqrt(2x) sq. the two aspects factors: x +a million + 2sqrt(x+a million) + a million = 2x it is comparable to 2sqrt(x+a million) = x - 2 sq. the two aspects back factors: 4(x+a million) = x^2 - 4x + 4 it is comparable to 4x + 4 = x^2 -4x + 4 furnish all of it to a minimum of one section factors: x^2 - 8x = 0 it is comparable to x(x - 8) = 0 as a result x = 0 and x = 8 are the suggestions 8 of course works mutually as plugging it back indoors the equation, yet you're waiting to be waiting to prefer to undergo in techniques that the sq. root of a million could desire to be -a million besides as a million mutually as plugging indoors the x=0. i desire this helps.

Answer 5

This is exactly why I am in a major that requires algebra2 as the highest level of math needed, and I struggled with that also.

Answer 6

My ex had a real problem with premature calculation too. He never got over it.

Answer 7

I'm in post calculus sorry .