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
Leto [7]
3 years ago
14

Point) a norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle exactly matches the wi

dth of the rectangle. find the dimensions w×hw×h of the norman window whose perimeter is 1000in.1000in. that has maximal area.

Mathematics
1 answer:
svetlana [45]3 years ago
6 0
Let d represent the diameter of the semicircle (and the width of the window). Then the length of the semicircular arch is π/2*d. The remaining perimeter available for the height of the rectangular shape is then
.. 1000 -(d +π/2*d)
and that amount will be divided between the two sides of the window.

Then the height of the rectangular section is
.. h = (1/2)*(1000 -d(1 +π/2))
.. = 500 -d(1/2 +π/4)
The total area of the window is ...
.. A = dh +(1/2)(π/4)d^2
.. = d(500 -d(1/2 +π/4)) +π/8d^2
.. = 500d +d^2*(π/8 -π/4 -1/2)
.. = d(500 -d(1/2 +π/8))

This downward-opening quadratic function has its vertex (maximum) at
.. d = 500/(1 +π/4) = 2000/(4 +π)

The corresponding rectangle height is
.. h = 500 -500/(1 +π/4)*(1/2 +π/4)
.. = 500(1 - (2 +π)/(4 +π)) = 500(4 +π -2 -π)/(4 +π) = 1000/(4 +π)

That is, the height of the rectangular section is 1/2 the diameter of the circular section, so the overall window has the same overall height and width.

The height and width of the window with maximum area are ...
  2000/(4+π) in ≈ 280.0 in


_____
The graph shows both the area function and the (d, h) dimensions of the rectangle.

You might be interested in
"A laboratory tested 73 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with LaTeX: \sigmaσ = 17.4
Scrat [10]

Answer:

The 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is between 226.01 and 233.99 milligrams.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96*\frac{17.4}{\sqrt{73}} = 3.99

The lower end of the interval is the sample mean subtracted by M. So it is 230 - 3.99 = 226.01

The upper end of the interval is the sample mean added to M. So it is 230 + 3.99 = 233.99.

The 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is between 226.01 and 233.99 milligrams.

4 0
3 years ago
Data was collected on the number of pets and the height of a random group of students. Identify the correlation you would expect
Ipatiy [6.2K]
No correlation
A scatterplot is used to represent a correlation between two variables. There are two types of correlations: positive and negative. Variables that are positively correlated move in the same direction, while variables that are negatively correlated move in opposite directions.
4 0
3 years ago
Will mark as brainliest plz helpp​
almond37 [142]

x - √3y - 4 = 0 → <u>Choice</u><u> </u><u>A</u>

Step-by-step explanation:

x - 4 = √3y

x - 4 <u>- √3y</u> = √3y <u>- √3y</u>

x - 4 - √3y = 0

x - √3y - 4 = 0

4 0
3 years ago
Two pairs of jeans cost $75 before tax. If the total tax paid for the two pairs of jeans was $6, what is the percentage of tax?
Eddi Din [679]
Take the tax (6$) and divide it by the pretax(75$) and take that number and multiply it by 100 and you get your percentage (8%)
4 0
3 years ago
Brian is riding his bike. He biked a distance of 14 miles at a rate of 14 miles per hour. Rearrange the distance formula, d = rt
Stells [14]

Answer:

C. 60 minutes

Step-by-step explanation:

if Brian biked 14 miles in 1 hour and 1 hour = 60 minutes then the answer is 60 minutes. hope this helps

5 0
3 years ago
Other questions:
  • What fraction of a pound is eighty pence
    9·2 answers
  • 11.3562 rounded to the nearest hundred
    7·2 answers
  • Pls help with these two math questions
    13·2 answers
  • If sec0+tan0=p,then find the value of cosec0.
    5·1 answer
  • (3-x)(x-5)<br> Hurry PLZ
    13·1 answer
  • Can you guys help me on this one please ?
    13·1 answer
  • A football team loses 4 yards on each 3 consecutive plays. Find the total change in yard from where the team started
    10·1 answer
  • Passes through (3,-6), slope = 2 -3
    13·1 answer
  • A circular rug has a radius of 4. 5 feet. What is the circumference of the rug? Use 3. 14 for Pi and round to the hundredths pla
    12·1 answer
  • Which expression is equivalent to –3(u+7)<br> PLEASE ANSWER THE QUESTION
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!