Answer:
ysME
Step-by-step explanation:
A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 25 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible? (Round your answers to two decimal places.)width ________ ftheight _______ ft
Answer:
[tex]Length =\frac{25}{4 + \pi}[/tex] and [tex]Width = \frac{50}{4+\pi}[/tex]
Step-by-step explanation:
This question is better understood with an attachment.
See attachment for illustration.
Given
Represent Perimeter with P
[tex]P = 25ft[/tex]
Required
Determine the dimension of the rectangle that maximizes the area
First, we calculate the perimeter of the rectangular part of the window.
From the attachment, the rectangle is not closed at the top.
So, The perimeter would be the sum of the three closed sides
Where
[tex]Width = 2x[/tex]
[tex]Length = y[/tex]
So:
[tex]P_{Rectangle} = y + y + 2x[/tex]
[tex]P_{Rectangle} = 2y + 2x[/tex]
Next, we determine the circumference of the semi circle.
Circumference of a semicircle is calculated as:
[tex]C = \frac{1}{2}\pi r[/tex]
From the attachment,
[tex]Radius (r) = x[/tex]
So, we have:
[tex]C = \frac{1}{2}2\pi * x[/tex]
[tex]C = \pi x[/tex]
So, the perimeter of the window is:
[tex]P = P_{Rectangle} + C[/tex]
[tex]P =2y + 2x + \pi x[/tex]
Recall that: [tex]P = 25[/tex]
So, we have:
[tex]25 =2y + 2x +\pi x[/tex]
Make 2y the subject
[tex]2y = 25 - 2x - \pi x[/tex]
Make y the subject:
[tex]y = \frac{25}{2} - \frac{2x}{2} - \frac{\pi x}{2}[/tex]
[tex]y = \frac{25}{2} - x - \frac{\pi x}{2}[/tex]
Next, we determine the area (A) of the window
A = Area of Rectangle + Area of Semicircle
[tex]A = 2x * y + \frac{1}{2}\pi r^2[/tex]
[tex]A = 2xy + \frac{1}{2}\pi r^2[/tex]
Recall that
[tex]Radius (r) = x[/tex]
[tex]A = 2xy + \frac{1}{2}\pi x^2[/tex]
Substitute [tex]\frac{25}{2} - x - \frac{\pi x}{2}[/tex] for y in [tex]A = 2xy + \frac{1}{2}\pi x^2[/tex]
[tex]A = 2x(\frac{25}{2} - x - \frac{\pi x}{2}) + \frac{1}{2}\pi x^2[/tex]
Open Bracket
[tex]A = 2x * \frac{25}{2} - 2x * x - 2x * \frac{\pi x}{2} + \frac{1}{2}\pi x^2[/tex]
[tex]A = 25x - 2x^2 - \pi x^2 + \frac{1}{2}\pi x^2[/tex]
[tex]A = 25x - 2x^2 - \frac{1}{2}\pi x^2[/tex]
To maximize area, we have to determine differentiate both sides and set A' = 0
Differentiate
[tex]A' = 25 - 4x - \pi x[/tex]
[tex]A' = 0[/tex]
So, we have:
[tex]0 = 25 - 4x - \pi x[/tex]
Factorize:
[tex]0 = 25 -x(4 + \pi)[/tex]
[tex]-25 =-x(4 + \pi)[/tex]
Solve for x
[tex]x = \frac{-25}{-(4+\pi)}[/tex]
[tex]x = \frac{25}{4+\pi}[/tex]
Recall that
[tex]Width = 2x[/tex]
[tex]Width = 2(\frac{25}{4+\pi})[/tex]
[tex]Width = \frac{50}{4+\pi}[/tex]
Recall that:
[tex]y = \frac{25}{2} - x - \frac{\pi x}{2}[/tex]
Substitute [tex]\frac{25}{4+\pi}[/tex] for x
[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\pi (\frac{25}{4+\pi})}{2}[/tex]
[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\frac{25\pi}{4+\pi}}{2}[/tex]
[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{25\pi}{4+\pi} * \frac{1}{2}[/tex]
[tex]y = \frac{25}{2} - \frac{25}{4+\pi} - \frac{25\pi}{2(4+\pi)}[/tex]
[tex]y = \frac{25(4+\pi) - 25 * 2 - 25\pi}{2(4 + \pi)}[/tex]
[tex]y = \frac{100+25\pi - 50 - 25\pi}{2(4 + \pi)}[/tex]
[tex]y = \frac{100- 50+25\pi - 25\pi}{2(4 + \pi)}[/tex]
[tex]y = \frac{50}{2(4 + \pi)}[/tex]
[tex]y = \frac{25}{4 + \pi}[/tex]
Recall that:
[tex]Length = y[/tex]
So:
[tex]Length =\frac{25}{4 + \pi}[/tex]
Hence, the dimension of the rectangle is:
[tex]Length =\frac{25}{4 + \pi}[/tex] and [tex]Width = \frac{50}{4+\pi}[/tex]
Evaluate the expression 54⁰
Answer:
1
Step-by-step explanation:
All numbers to the power of 0 are 1.
PLS GIVE BRAINLIEST
Read the passage below and summarise it in a minimum of 100 words:
Until a hundred years ago as humans, we had a simple, uncomplicated biological connect. It was a straightforward equation: we drew roughly 3,000 calories each of energy out of the Earth for our food and life’s sustenance. Today that number per capita has grown to 100,000 calories. We still need only 3,000 calories each to nourish life itself. All the rest of this energy is what we extract from the Earth for everything else besides keeping ourselves alive. In some countries, like the US; this per capita number runs at over 200,000 calories! Some of us are concerned about this.
We fret over what we could and should really be doing to soften this abuse of resources. Little things fox us in the welter of things that we get to read. What is sustainable development? How can it be started in our homes? Beyond the ceremonial planting of green arid getting people to run marathons of various lengths in support of the environment, is there- more that we can add to the abstract value of “sustainability”? What are the little things we can do in our day-to-day lives, to reduce demand for things that people make and market? Of course, we know that it helps to avoid a plastic bag when you can use a newspaper bag, or a brown bag, or even a jute bag which you can use for many more years, unlike a plastic bag which you throw away in less than a week or after a few uses.
However, there’s actually quite a bit more than you and I can do without compromise on comfort, with very little as cost incurred, with financial savings that you can gain on energy and water use, and with solutions that are very feasible and within your reach. It is possible to understand our ecological footprint and its disastrous consequences, not merely in terms of our own behaviour as consumers, but really in terms of the impact on the environment we make.
(Source: Building Green and Thinking Green, 2010)
Answer:
Find the summary below.
Step-by-step explanation:
The article compares the standard of healthy living some hundred years ago to what is obtainable in our world today. While the energy gained through food consumption some years ago was just adequate and at the right proportion, what is consumed today, supplies energy that is on an all-time high. This misuse of resources led to the development of sustainable development practices such as planting of trees, exercise routines which are done occasionally.
Another sustainable practice that can be done on a more regular basis is the use of jute or paper bags which are more biodegradable, instead of plastic bags. Finally, the article encourages the adoption of more sustainable practices because they can be more economical compared to the other practices that are presumed to be the status quo.
Ben and josh went to the roof of their 40-foot tall high school
b) A quadrilateral has no pairs of parallel sides.
What two shapes could it be?
Answer:
I need points
Step-by-step explanation:
None
Answer:
um maybe a trapezoid and a rhombus i think
The table shows the weights of apples at a grocery store
Answer:
c
Step-by-step explanation:
Find the slope for the line that passes thru the points (-2, 7) and (4, 18)
Answer:
[tex]m=\frac{11}{6}[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-2, 7)
Point (4, 18)
Step 2: Solve for slope m
Substitute: [tex]m=\frac{18-7}{4+2}[/tex]Subtract/Add: [tex]m=\frac{11}{6}[/tex]Answer:
dkdkfdodffffdsddddddddd
what is 3/4 and 5/12 simplified in fraction form plz idk
Answer:
Well 3/4 & 5/12 are already simplified and in fraction form, if youre
looking for decimal form its gonna be .75 &.41
Step-by-step explanation:
a = 65 – 100n
Find a
39
(04.04 LC)
On a coordinate grid, point T is at (2,-4) and point S is at (2,6). The distance (in units) between points T and S is
numbers, such as 2.)
Answer:
The distance between T and S is 10 units.
Step-by-step explanation:
Given the points
T(2, -4)S(2, 6)[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
The distance between T and S is:
[tex]=\sqrt{\left(2-2\right)^2+\left(6-\left(-4\right)\right)^2}[/tex]
[tex]=\sqrt{\left(2-2\right)^2+\left(6+4\right)^2}[/tex]
[tex]=\sqrt{0+10^2}[/tex]
[tex]=\sqrt{10^2}[/tex]
[tex]=10[/tex] ∵ [tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
Therefore, the distance between T and S is 10 units.
Find the probability of guessing correctly at least 6 of the 10 answers on a true-false examination.
Answer:
24%
i think
Step-by-step explanation:
Jade only need 3 1/4 cans of paint
Answer:
whats the question?
Step-by-step explanation:
Missy wants to find the surface area of a snack box in her pantry her work is shown below
Answer:
Step 2: Missy did not multiply the area of each face by 2 before adding.
Step-by-step explanation:
I took the test :)
The speed at which you can log into a website through a smartphone is an important quality characteristic of that website. In a recent test, the mean time to log into the JetBlue Airways website through a smartphone was 4.237 seconds. Suppose that the download time is normally distributed, with a standard deviation of 1.3 seconds. What is the probability that the download time is:
A. Less than 2 seconds?
B. Between 1.5 and 2.5 seconds
C. Above 1.8 seconds
D. 99% of the download times are slower (higher) than how many seconds?
E. 95% of the download times are between what two values, symmetrically distributed around the mean?
F. Suppose that the download times are uniformly distributed between 1 and 9 seconds. What are your answers to A through C?
Answer:
A.) 0.0426
B) 0.073121
C.) 0.96958
D.) 1.2 seconds
E.) 1.689 < x < 6.785
Step-by-step explanation:
Given a normal distribution :
Mean download time (m) = 4.237 seconds
Standard deviation (s) = 1.3 seconds
A.) Probability that download time is less than 2 seconds :
P(x < 2)
Obtain standardized score (Z) :
Z = (x - m) / s
Z = (2 - 4.237) / 1.3
Z = −1.720769
P(Z < - 1.7208) = 0.0426 (Z probability calculator)
B.) Between 1.5 and 2.5 seconds :
1.5 < z < 2.5
((x - m) / s) < z <((x - m) / s)
((1.5 - 4.237) / 1.3) < z < ((2.5 - 4.237) / 1.3)
−2.105384 < z < −1.336153
P(Z < - 2.10538) = 0.017629
P(Z −1.336153) = 0.09075
0.09075 - 0.017629 = 0.073121
C.) Above 1.8 seconds
P(x > 1.8)
Obtain standardized score (Z) :
Z = (x - m) / s
Z = (1.8 - 4.237) / 1.3
Z = −1.874615
P(Z > −1.874615) = 0.96958 (Z probability calculator)
D.) 99% of the download times are slower (higher) than how many seconds?
P(Z > x) = 99% = 0.99
Z value corresponds to -2.326
Z = (x - m) / s
-2.326 = (x - 4.237) / 1.3
-2.326 * 1.3 = x - 4.237
−3.0238 = x - 4.237
−3.0238 + 4.237 = x
x = 1.2132
x = 1.2 seconds
E. 95% of the download times are between what two values, symmetrically distributed around the mean?
For symmetric distribution around the mean ;
P(-Z<x<Z) = 0.95
Corresponds to a z value of 1.96
-1.96 * 1.3 = x - 4.237
-2.548 = x - 4.237
x = - 2.548 + 4.237
x = 1.689
1.96 * 1.3 = x - 4.237
2.548 = x - 4.237
x = 2.548 + 4.237
x = 6.785
1.689 < x < 6.785
How many solutions does this system have?
-x + 2y = 16
4x - 8y = -64
What is the solution to x-8>-3
Answer:x>5
Step-by-step explanation:
The correct answer is x=5
Here is the soulution:
Add 8 to both sides of the equation. x = −3 + 8
Add −3 and 8.
That equals x = 5.
Which answers are examples of inductive reasoning?
Select each correct answer.
John saw wild turkeys in his yard during the past 3 years. He will see wild turkeys in his yard next year.
All right triangles have a 90° angle. Triangle ABC is a right triangle. Therefore, triangle ABC has a 90° angle.
The cinema charges $5 to see a movie. Four friends are going to the cinema to see a movie. Therefore, altogether they will pay $20 to see the movie.
Mrs. Smith notices that the first 10 students who enter her class are female. Therefore, she expects that all the students in her class will be female.
A
John will see a wild turkey in his yard next year
John saw wild turkeys in his yard during the past 3 years. He will see wild turkeys in his yard next year.
and
Mrs. Smith notices that the first 10 students who enter her cla$s are female. Therefore, she expects that all the students in her cla$s will be female.
Step-by-step explanation:
Hello!
First off, what is inductive and deductive reasoning?
Inductive is when you infer off of your observations. For example, "the last three cars I passed by were white, therefore the next car will also be white". The inductive reasoning is usually a broad guess. This could be right, but it isn't factual.
Deductive is when you infer based off of facts, or confirmed information. For example, "If you get 60% on a quiz, you pa$s the quiz. John got 80% percent on his quiz, therefore he passed." It is a confirmed fact that 60% is the pas$ing grade so if John got a 80%, that is more than 60% and he passes.
I hope the examples made sense!
I wrote about explaining the options but brainly is being sensitive
I WILL GIVE BRAINLIEST
Rewrite 12x + 3y = 6 in slope-intercept form. Give the slope and y-intercept.
y =
m =
b =
Answer:
12x + 3y = 6 in slope-intercept form.y = -4x+2m = -4b =(0,2)help plz and it’s not 61.6 because that’s what someone has said
Answer: 250 total kids and 140 girls
Step-by-step explanation:
%56=girls that means %44= boys that means 110 is %44 of the number of kids is 110/44*100= 2.5*100=250kids 56%=girls that means %56 of 250 which is 140 girls
Which number line shows the solution to the inequality 5x + 3> - 17
Answer:
C would be the correct number line
Step-by-step explanation:
5x ≥ - 17 - 3
5x ≥ -20
5x/5 ≥ -20/5
x ≥ 4
Find the slope of the line (4,2) (-3,-2)
Answer:
m=4/7
Step-by-step explanation:
slope: y2-y1/x2-x1
help
Please!!!!!!!!
Will appreciate it :)
Answer:
-5(-6x² + x + 2)
Step-by-step explanation:
-5(-6x² + x + 2)
= (-5)(-6x²) + (-5)(x) + (-5)(2)
= 30x²-5x-10
Does anyone know the answer!!!!
What is the absolute value of the number indicated on the number line below?
A. -2/3
B. -3/5
C. 3/5
D. 2/3
Answer:
C.
Step-by-step explanation:
Answer:
I believe is B or -3/5
Good luck!
If $2,500 is invested at 12% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?
Answer: 3,583.32
Step-by-step explanation:
Use money chimp calculator
Mr.Clark takes 25 minutes to brush his teeth. Mrs. Clark spends
20% longer brushing her teeth. In total, how much time does Mrs.Clark spend brushing her teeth ?
Clark spend brushing her teet
Answer:
30
Step-by-step explanation:
25 times 1.2= 30
Answer:
30
Step-by-step explanation:
simplify 6³÷2³×9^-2
In order to become a member at a gym, there is a $75 startup fee. You then have to pay $15 per month. Write an equation in slope-intercept form modeling this situation where y represents the total cost and x represents the number of months spent at the gym
Answer:
y = 15x +75
Step-by-step explanation:
15 is the number of months and changes based on how many months
75 doesn't change, remains constant.
The sum of two numbers is 12.
When three times the first number is added to 5 times the second number, the result is 44.
Find the two numbers.
A 9 and 3
B) 8 and 4
C) 10 and 2
D) 7 and 5
Answer:
b
Step-by-step explanation:
8*3
=24
4*5
=20
20+24
=44
So far, a storm has traveled 35 miles in half an hour. If it is currently 5:00 pm and the storm is 105 miles away, what time will the storm reach you? Explain how you solved the problem.
Answer:
It will reach you at 6:30.
Step-by-step explanation:
THe storm traveled at 35 miles in half an hour. It is 105 miles away.
Divide 105 by 35 to get how many half hours it will take to rach you.
105 ÷ 35 = 3.
So, it will be 3 half hours or one hour and a half.
Add that time to the current time, which is 5:00.
It will be 6:30 when the storm reaches you.
hope this helped tell me if it is right.
[[[click on the image to make bigger]]]
I really need questions 2 and 4 for this!! please
Answer:
It equals pizza 3’5.42 inch
Step-by-step explanation: