![kamiyaharris1](/avatars/9531.jpg)
kamiyaharris1
28.11.2020 •
Mathematics
A rectangle has a perimeter of 100 inches, and
one side has length x. Express the area of the
rectangle as a function of x.
Use the function in part a to find the dimensions of the rectangle with permitter 100 inches and the largest possible area
Solved
Show answers
More tips
- S Science and Technology Why is there no gravity on other planets?...
- F Food and Cooking Deflope: What is it and how does it work?...
- B Business and Finance How to Create a Business Plan? Your Ultimate Guide...
- F Food and Cooking Unusually Delicious Shashlik - Follow the Etiquette of Proper Preparation!...
- C Computers and Internet Make Easy Accessible Screenshots on iPad in Just a Few Minutes...
- T Travel and tourism Lost in the Catacombs: What to Do?...
- F Family and Home Protect Your Home or Apartment from Pesky Ants...
- H Health and Medicine How to Treat Styes: Causes, Symptoms, and Home Remedies...
- L Legal consultation What Documents Are Required for a Russian Passport?...
- F Family and Home How to Properly Use a Water Level?...
Answers on questions: Mathematics
- M Mathematics Enter the next 3 terms from the geometric sequence below. 1 -2,1, 2...
- M Mathematics On a map, Peach Street is modeled by the equation 4x - y = 7. Apple Street is perpendicular to Peach Street and passes through the point (12, 2). Find the equation that...
- M Mathematics What is Hcf of 12,15,18?...
- M Mathematics What if I asked you to count the number of chairs in the Great Hall? Don t worry...that s not what I m going to ask you to do, but WHAT IF you were assigned to gather the...
- M Mathematics Oooooooooooooooooooopppppooooooooooooppppplllooooookk help...
- M Mathematics Refer to Table 28-6. What is the U-2 measure of labor underutilization?...
- M Mathematics Follow the steps to solve this equation. 3(2x + 6) – 4x = 2(5x – 2) + 6 1. Use the distributive property: 6x + 18 – 4x = 10x – 4 + 6 2. Combine like terms: 2x + 18 = 10x...
- M Mathematics Find te slope of the graph...
- M Mathematics Diego ran a race in 80 minutes. The race started at 11:38 a.m. What time did he finish the race? 12:18 a.m. 1:58 p.m. A 11:56 a.m. 12:58 p.m....
- M Mathematics B 2. The diagram shows three houses on a street. Find the distance from House A to House C 60ft + 90 ft- feet The ne trom House At House C...
Ответ:
a. A = 50x - x² b. length = 25 inches and width = 25 inches and the maximum area is 625 in²
Step-by-step explanation:
a. The perimeter of a rectangle P = 2(L + W) where L = length and W = width. Now, given that P = 100 inches and W = x, substituting these into the equation, we have
P = 2(L + W)
100 = 2(L + x)
dividing both sides by 2, we have
100/2 = L + x
50 = L + x
making L subject of the formula, we have
L = 50 - x
Now, the are of a rectangle A = LW. Substituting the values of L and W, we have
A = LW
A = (50 - x)x
A = 50x - x²
b. To find the largest possible area of rectangle with perimeter 100 inches, we differentiate A and equate it to zero to find the value of x that maximizes A.
So, dA/dx = d(50x - x²)/dx
dA/dx = d50x/dx - dx²/dx
dA/dx = 50 - 2x
dA/dx = 0 ⇒ 50 - 2x = 0
50 = 2x
dividing both sides by 2, we have
x = 50/2
x = 25
To find it this gives maximum value for A, we differentiate A twice.
d²A/dx² = d(50 - 2x)/dx
d²A/dx² = d50/dx - d2x/dx
d²A/dx² = -2
Since d²A/dx² = -2 < 0, so x = 25 gives maximum value for the area, A.
Since W = x = 25 in and L = 50 - x. So, L = 50 - 25 = 25 in
So, the maximum area A = LW = Lx = 25 in × 25 in = 625 in²
The dimension with perimeter 100 inches that give maximum area are length = 25 inches and width = 25 inches and the maximum area is 625 in²
Ответ:
The name of the red one is Raphael