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
The store is 15 min. away from my house, it takes 30 min. to get to and from the store. How come my dad isn't back with milk yet
coldgirl [10]

Answer:

What dad?

Step-by-step explanation:

he ran away. or hes with somebody

8 0
2 years ago
Read 2 more answers
Solve the system of equations
Veseljchak [2.6K]

Answer:

Option c is right:

(-6 , 2)

Step-by-step explanation:

( -6 , 2)

7 0
2 years ago
Sarah's age is four more than twice her brothers age. Write two equivalent algebraic equations that can be used to find their ag
marissa [1.9K]

Answer:

Step-by-step explanation:

Let her brother's age be x

Sarah is 2x + 4

3 0
3 years ago
16% of ____ shirts are 44<br> How many shirts are there?
yawa3891 [41]
I don’t know, I forgot how to solve problems like this, look it up
5 0
3 years ago
Read 2 more answers
the ratio of sadia's age to her father's age is 3:6. The sum of their age is 96 .What is sadia's age?​
Mrrafil [7]

Answer:

sadia is 32

Step-by-step explanation:

sadia : father : total

3          6          9

Divide 96 by 9

96/9 = 32/3

Multiply each by 32/3

sadia :     father : total

3*32/3    6*32/3  9*32/3

32                 64          96

4 0
2 years ago
Other questions:
  • 8. Write the number in expanded form.<br> 674.281
    13·2 answers
  • Please help I'm stuck ?
    11·2 answers
  • Simplify the expression (3x^3 y^-2)^-4
    7·1 answer
  • What is 174/216 in simplify form
    5·2 answers
  • Find the value of x so that the line that passes through the points A(5,x) and B(2,-3) has a slope of 5/3
    9·1 answer
  • Is the simplified form of 2square root of 3 − 2square root of 3 rational?<br><br> Yes<br> No
    9·2 answers
  • What is the difference the simplest terms 2/3 - 3/5
    7·1 answer
  • Determine whether the following is a statistical question. How many teeth does Edna have in her mouth?
    12·2 answers
  • The table below shows the number of kilometers Jessica ran this weekend.
    9·2 answers
  • Give an example of a monomial and a binomial having degrees as 82 and 99, respectively.​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!