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

Answers

Answer 1

Answer:

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


Related Questions

scientific notation for 1.0 ×10^6​

Answers

Answer:

1000000

Step-by-step explanation:

I'm not sure what you meant by "scientific notation". So uhh, I only solved the 1.0 times 10^6,

10^6=10×10×10×10×10×10

10^6=1000000

(Fun fact. If you ever see a power of 10, you don't actually need to solve it. Look at the power, and add the same amount of 0's. For example 10^2. Power sign is 2. 2 trailing 0's.)

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Step-by-step explanation:

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(Remember: electrons have a negative charge)

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Answer:

I think it would be -2 if it has a negative charge

Step-by-step explanation:

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Answers

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Step-by-step explanation:

Method elimination would be good for this system

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(1) + (2)

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(4, 1)

X= 4.25
Y= 0.75

4.25 +0.75 = 5
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Find the value of X and Y in this triangle.

Answers

Step-by-step explanation:

if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)

if leg b is unknown, then. b = √(c² - a²)

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Answer:

[tex] \sin(60) = \frac{45}{x} \\ [/tex]

[tex] x = \frac{45}{ \sin(60) } [/tex]

x=5 1.96

Step-by-step explanation:

[tex] \tan(30) = \frac{y}{45} [/tex]

[tex]y = 45 \tan(30) [/tex]

y=25.98

Noah pays $7.65 for a cappuccino on days he's running late to work. One week, he was late on Monday, Wednesday, and Friday. How much did he spend (in $) on cappuccinos that week? $

Answers

Answer:

Amount Noah spent on cappuccino for that week = $22.95

Step-by-step explanation:

Noah pays $7.65 for a cappuccino on days he's running late to work

Cost of cappuccino per day = $7.65

One week, he was late on Monday, Wednesday, and Friday.

That is 3 days in a week

How much did he spend (in $) on cappuccinos that week? $

Amount Noah spent on cappuccino = cost of cappuccino per day × 3 days

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= $22.95

Amount spent on cappuccino for that week = $22.95

Question is attached!​

Answers

Answer:

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Step-by-step explanation:

The correct answer is X= 3!

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Answers

Answer:

f(x) = [tex]\sqrt{x}[/tex]

Step-by-step explanation:

hope this helped :-)

You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish
Army in Sevilla in the year 1842. Outside your barracks window is a stack of
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Answers

Answer: The correct answer would be 164(c)

Step-by-step explanation:

You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish

Army in Sevilla in the year 1842. Outside your barracks window is a stack of

cannonballs, as shown in the illustration. On an idle afternoon you decide to

calculate the number of cannonballs in the stack. What is the number of

cannonballs?

650 is the number of cannonballs.  It typically fires a projectile propelled by an explosive chemical.

What is cannonballs?

A cannon constitutes a large-caliber gun that belongs to the artillery category. It typically fires a projectile propelled by an explosive chemical. Prior to the development of smokeless powder in the late 19th century, gunpowder (sometimes known as "black powder") served as the main propellant.

Depending on their intended purpose on the battlefield, different types of gun combine and balance these characteristics to differing degrees. Cannons differ in gauge, effective range, mobility, rate of fire, angle of fire, and firepower. A large artillery weapon is a cannon.

By utilizing the formula of a square pyramid,

n(n+1)(2n+1)/6

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12(13)(25)/6

2*13*25

=650

Therefore, 650 is the number of cannonballs.

To know more about cannonballs, here:

https://brainly.com/question/14330897

#SPJ7

Which graph represents a function?

Answers

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Answers

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Answers

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Step-by-step explanation:

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Answer:

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 4.1     7776 = 25•35

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The answer is 7776^2
_____
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Pls mark brainleist

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Answers

Answer:

The equation of line n is;

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Step-by-step explanation:

Here, we want to find the equation of line n

For the alternate interior angles to be congruent after drawing the transversal, then both lines must be parallel

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we need to get the y-intercept to write the complete equation

To get the y-intercept we simply substitute for (-4,-11)

Thus, we have

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y = -3x - 23

Click below for question!
THANKS FOR ALL YOUR HELP GUYS!

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Subtract the 2nd y from the first (2-9)

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Answers

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Step-by-step explanation:

Answer:

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Answers

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Answers

Answer:

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Step-by-step explanation:

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A person invests 5500 dollars in a bank. The bank pays 5.75% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14700 dollars?

Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Tara plans to put wallpaper on the walls of her room. She will not put the wallpaper across the doorway, which is 3 feet wide and 7 feet tall. Tara decides to get the same wallpaper for both rooms. Write the expression for the total amount of wallpaper she needs.

Answers

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Step-by-step explanation:

hope this helps

The formula for the volume of a cylinder is V = gran.
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O A. =
nar
B. n =
O c. h =
Vr2
O D. h=
372

Answers

Answer:

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Step-by-step explanation:

A grocery store clerk can scan 1 product every
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Answers

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