1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SIZIF [17.4K]
3 years ago
8

A Norman window has the shape of a rectangle surmounted by a semicircle. Find the dimensions of a Norman window of perimeter 30

ft that will admit the greatest possible amount of light. (Round your answers to two decimal places.)
Mathematics
2 answers:
stepan [7]3 years ago
8 0
Let x be the width, which is equal to the diameter of the semi-circle.
Then the perimeter around just the semi-circle is (1/2) pi x.
Let y the height of the rectangular portion of the window.
Perimeter around just the rectangular portion of the window is x + 2y.
The total perimeter is (1/2) pi x + x + 2y = 30
Solve this equation for y:
2y = 30 - (1/2) pi x - x
y = 15 - (1/4) pi x - x/2
Then the area of the rectangular portion is xy.
The area of the semi-circle is (1/2) pi (x/2)^2.
The total area = A = (1/2) pi (x/2)^2 + xy
Substitute the expression for y found above into this last equation:
A = (1/2) pi (x/2)^2 + x(15 - (1/4) pi x - x/2 )
Simplify and combine like terms:
A = x^2(-pi - 4)/8 + 15x
Take the derivative and set it to zero:
A' = (1/4) (-4-pi)x + 15 = 0
Solve for x:
(1/4) (-4-pi)x = -15
Multiply by -4:
(4+pi)x = 60
Divide:
x = 60 / (4+pi) ≈ 8.4 ft
y = 15 - (1/4) pi x - x/2 = 30 / (4+pi) ≈ 4.2 ft
Serjik [45]3 years ago
7 0
Hope i hepled you on this question.
Download pdf
You might be interested in
If 2&gt; -a, then a &lt; -2.<br> True<br> False
Nonamiya [84]

Answer:

False

Step-by-step explanation:

Flip the equation.

−a<2

Divide both sides by -1.

a>−2

4 0
3 years ago
Given A(-3, 6) and B(0, 6), what are the coordinates of point P that lies on segment AB, such that AP:PB = 2:1? A: (2, -2) B: (-
DerKrebs [107]

Answer:

(-1 1/2, 6)

Step-by-step explanation:

The mid point between A(-3,6) and B(0,6) represents the coordinates of point P, which is (x,y)

Hence,the coordinates, that is, AP: x = (-3 + 0)/2 = -3/2 = -1 1/2

also, BP: y = (6 + 6)/2 = 6

Therefore, the coordinates of point P = ( -1 1/2, 6)  

7 0
2 years ago
If F ( x ) = 2 x - 1, find the zero of F -1( x ).<br><br> A) -1<br> B) 1/2<br> C) 1
tigry1 [53]

Answer:

A.

Step-by-step explanation:

7 0
3 years ago
Explain how you know 21 over 30 is greater than 2 over 3
Lisa [10]
<span>So we need to explain how we know 21/30 is greater than 2/3. Well lets expand 2/3 by multiplying the numerator and the denumerator by 10. That way we get 20 / 30. Since 21/30 has 1/30 more than 20/30 we can clearly see that 21/30 is greater than 20/30 or 2/3.</span>
4 0
3 years ago
What is the y-intercept of a line parallel to y = 3x - 4 that passes through the point (2,3)
MrRa [10]
Y-3=3(x-2)
y-3=3x-6 :-x=0
y-3=0-6
y=-6+3
y=-3
8 0
3 years ago
Other questions:
  • What are the solutions of 12 – x2 = 0?
    6·2 answers
  • The capsules and montage families love writing. Last year,each capsule wrote 4 essays, each montage wrote 6 essays, and both fam
    11·1 answer
  • 2 7/10+9 2/15 выполнить сложение
    5·1 answer
  • The diameter of the larger circle is 12.5 cm. The diameter of the smaller circle is 3.5 cm.
    7·1 answer
  • 4. Find the value of n that makes this equation true. (Use
    15·1 answer
  • Biught 820 books and 34 books on a shelf how many shelves
    9·1 answer
  • How far from the base of the house do you need to place a 15' laddder so that it exatly reaches tehe top of a 12' wall?
    6·1 answer
  • A playground slide has a price of $770. With sales tax, it will cost $847. What is the sales tax percentage?
    11·1 answer
  • Please help me!!! Joe and his family are touring Chicago. They want to visit the Willis Tower, hang out at Navy Pier, and shop o
    5·1 answer
  • Find the collame of boid of dimension 16cm X 10m x 6cm.​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!