Find the dimensions of a rectangle divided into three equal rectangles of maximum area that has total perimeter (including the middle divider) of 120 feet.
Answers
Answer:
The dimensions of the rectangle with the maximum area are 15 feet by 30 feet
Step-by-step explanation:
Optimization
There is a rectangle of dimensions x and y as seen in the figure below.
The side of length y is divided into three equal parts to make three equal rectangles.
The area of the greater rectangle is:
A = xy
It has to be maximized given the condition that the total perimeter including the middle dividers is 120 feet.
The outer perimeter of the rectangle is 2x+2y. There are two additional lines with a length of x feet each. Thus, the total perimeter is:
P = 2x + 2y + 2x = 4x + 2y
It has to be equal to 120 feet:
4x + 2y = 120
Dividing by 2:
2x + y = 60
Solving for y:
y = 60 - 2x
Substituting into the area:
[tex]A = x(60 - 2x) = 60x - 2x^2[/tex]
[tex]A=60x - 2x^2[/tex]
Taking the first derivative:
A'=60 - 4x
Equating to 0:
60 - 4x = 0
Solving for x:
x = 60/4 = 15
Thus x = 15 feet
Since y = 60 - 2x = 60 - 30 = 30
Thus y = 30 feet
The dimensions of the rectangle with the maximum area are 15 feet by 30 feet.
Related Questions
Lamar is a football player. In his best play, he ran 48 yards with the football scoring a touchdown. One yard is equal to three feet. How many feet did Lamar run with the football to score the touchdown?
Answers
Answer:
144 feet
Step-by-step explanation:
multiply the number of yards by 3 to get the number of feet
brainliest please
happy holidays
Answer:
144
Step-by-step explanation:
1 yard = 3 feet
48 yards× 3 feet= 144 feet
Please hurry!!!!!
-2 1/2 divided by -8/21
On Monday, Alex ran 1 1/2 miles. On Tuesday she ran 2 1/4. How much further did she run on Tuesday?
A tank at the Atlanta Aquarium is 3/4 of the way full. If the tank holds 40
gallons of water, how much water would it take to fill the tank?
Answers
I use a calculator.5625
W= 4/p+2 solve for p
Answers
Answer:
(w-2)x4 = p (i think)
Step-by-step explanation:
Find the value of x in the parallelogram.
Answers
Step-by-step explanation:
Since the opposite angles of the parallelogram are equal,
3x+25=5x-5
30=2x
so, x =15
the value of x is 15
There is a bag of blue and white marbles. The probability of pulling out a blue marble is 2 3. Find the probability of pulling out a white marble as a fraction.
Answers
Answer:
1/3
Step-by-step explanation:
The Yankees won 125 games, the Red Sox won 97 games, and the Mets won 86 games.
What is the ratio of wins of the Yankees to the Red Sox to the Mets?
Answers
Answer:
127:97:86
Step-by-step explanation:
The yankees won 125 games
The Red Sox won 97 games.
The Mets won 86 games
Therefore the ratio of wins of the Yankees to the red Sox to the Mets can be shown as follows
127:97:86
Evaluate: 36 ÷ (6 × 3) + (12 – 9) 5 8 18 21
Answers
2 + (3)
5
A. 5
hope this helped
The correct option is a. 5. The solution to the mathematical expressions 36 ÷ (6 × 3) + (12 – 9) is 5.
To evaluate the expression, follow the order of operations (PEMDAS/BODMAS):
Step 1: Evaluate the multiplication within parentheses:
6 × 3 = 18
Step 2: Evaluate the subtraction within parentheses:
12 - 9 = 3
Step 3: Perform the division:
36 ÷ 18 = 2
Step 4: Perform the addition:
2 + 3 = 5
Therefore, the solution to the given expression is 5.
Learn more about mathematical expressions here:
https://brainly.com/question/33824341
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Javier used the expression below to represent his score in a game of mini-golf.
3x + x + 5 – 2x
If he simplifies the expression, which statements are true about the parts of the simplified expression? Select three options.
The constant is 2.
The coefficient is 2.
The constant is 5.
The coefficient is 5.
There are two terms.
Answers
Answer
The constant is 2, the coefficient is 2 , and the constant is 5
Step-by-step explanation:
Please mark me brainlest
Answer: I don't know what the answer is but the one on top is wrong just to let you know :D have a bless day hopefully you get this one right on you test
it would be really helpful if you mark me brainly :D you'll be the first.
Step-by-step explanation:
Choose all the values equal to -5/7
Answers
Answer:
A B E
Step-by-step explanation:
can anyone help me out plzz
Answers
please help it’s due in like 10 minutes, i’ll give you brain
Answers
Answer:
I think it's B, I might be wrong though
Answer:
A
Step-by-step explanation:
Answer question w/ shown work please!
1st gets BRAINLIEST!
Answers
Answer:
c
Step-by-step explanation:
Need help ASAP, will give Brainly!
Answers
Answer:
y=-5x+2
your welcomesss
Explanation:
Slope is negative five, then just add the y intercept
PLZ HELP! I REALLY NEED HELP ON THIS! WILL GIVE BRAINLEIST!!! PLZZZDetermine any data values that are missing from the table, assuming that the data represent a linear function.
X
ly
-1
5
17
0
2
a.
5
9
C. 13
d. 11
b.
Answers
Answer:
It is B and your welcome
Step-by-step explanation:
Which expression is equivalent to (–3y – x) – (5y – 8x)?
–8y – 8x
–8y + 7x
2y – 7x
8y + 8x
Answers
it took the test guessed and i got it right i remembered that this one question dint have an answer so if i got it right i would have answered it
Answer:
(B) -8y + 7x
Step-by-step explanation:
A side of the triangle below has been extended to form an exterior angle of 151°. Find the value of x.
Answers
Answer:
180°
Step-by-step explanation:
Order the steps to solve for x:
Answers
Answer:
lolo
Step-by-step explanation:
Choose the best answer.
What would your aunt's daughter be to you?
tia
prima
sobrina
hermana
Answers
Answer:
prima
Step-by-step explanation:
I
Find the line parallel to y = 5x + 2 that passes through the point (3,9).
Plz awnser ik failing will mark brainliest
Answers
Answer:
y = 5x - 6
Step-by-step explanation:
How many sandwiches could Jonny choose
Bread: white or wheat
Meat: beef, ham, or turkey
Cheese: Swiss or cheddar
Answers
What is the difference?
StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction
Answers
Answer:
It's D
Explanation:
Edg2020
The difference between the given fractions is (-2x+12)/(x²-16).
Given that, (x/x²-16) - (3/x-4).
We need to find the difference between the given fractions.
How to subtract the fractions?To subtract the fractions follow these steps:
If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators.To subtract fractions with unlike denominators, rename the fractions with a common denominator. Then subtract and simplify.Now, the LCM of denominators x²-16 and x-4 is x²-16.
Then, (x/x²-16) - (3(x+4)/(x-4)(x+4)
=(x/x²-16) - (3x+12)/(x²-16)
=x-(3x+12)/(x²-16)
=(x-3x+12)/(x²-16)
=(-2x+12)/(x²-16)
Therefore, the difference between the given fractions is (-2x+12)/(x²-16).
To learn more about the subtraction of fractions visit:
https://brainly.com/question/5220474.
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Please Help!!! Will Give Brainliest!!!
Evaluate the expression: v ⋅ w
Given the vectors: r = ; v = ; w = ?
Answers
Answer:
If you have a vector a = [ax ay az] and b = [bx by bz], both in x-y-z Cartesian space, the dot product a•b is given by:
a•b = axbx + ayby + azbz
So, you have v = [2 -8 -8] and w = [-2 6 -5].
So, v•w = (2)(-2) + (-8)(6) + (-8)(-5) = -4 - 48 + 40 = -12
Step-by-step explanation:
what is equivalent to 1:3
Answers
is there a distance time and rate calculator
Answers
Answer:
yea but its like 100 dollars
Step-by-step explanation:
Which of the following is a solution of y > |x| - 5?
Answers
Answer:
[tex]\boxed{(-4,~1)}[/tex]
.
Step-by-step explanation:
Just input the point to test the truth
Let's try (-4, 1) → x = -4 and y = 1
[tex]y > |x| - 5[/tex]
[tex]1 > |-4| - 5[/tex]
[tex]1 > -(-4) - 5[/tex]
[tex]1 > 4 - 5[/tex]
[tex]1 > -1 \to \bold{true}[/tex]
So, (-4, 1) is its solution
Answer:
(-4, 1)
Step-by-step explanation:
you can solve this quicly
Let y =tan(a).
dy
What is the value of at C=
da
Зп
?
4
Choose 1 answer:
1
1
2
Answers
Answer:
C. 2
General Formulas and Concepts:
Algebra I
Function NotationPrecalculus
Unit CircleCalculus
DerivativesDerivative NotationDerivative of tan(x) = sec²(x)Step-by-step explanation:
Step 1: Define
y = tan(x)
x = 3π/4
Step 2: Differentiate
Differentiate: y' = sec²(x)Step 3: Evaluate
Substitute in x: y'(3π/4) = sec²(3π/4)Evaluate: y'(3π/4) = 2what is the decimal number of 100/2
Answers
The equation of line L is 3x − 4y = 24. The line intersects the X − axis at A and the
Y − axis at B. Given that M is the point (4, −3) and O is the origion. Find
. The gradient of line L.
Answers
Answer:
The slope of the line = m = 3/4
Step-by-step explanation:
We know that the slope-intercept of line equation is
[tex]y=mx+b[/tex]
Here:
m is the slopeb is the y-interceptGiven the equation of line L
[tex]3x - 4y = 24[/tex]
Writing the equation in the slope-intercept form
[tex]3x - 4y = 24[/tex]
Add -3x to both sides
[tex]3x\:-\:4y+\left(-3x\right)=\:24+\left(-3x\right)[/tex]
[tex]-4y=\:-3x+24[/tex]
Divide both sides by -4
[tex]-\frac{4y}{4}=\:\frac{\left-3x+24\right}{-4}[/tex]
[tex]y=\frac{3}{4}x-6[/tex]
Comparing the equation with [tex]y=mx+b[/tex]
Therefore, the slope of the line = m = 3/4
The table shows the number of games a team won and lost last season. Wins and Losses Last Season Number of Games Wins 24 Losses 16 Greg has tickets to six of the team’s games this season. He is designing a simulation, using last year’s wins and losses, to predict whether the team will win or lose each of the games he attends. Which tool is most appropriate for use in a simulation that fits the data? a coin with one side representing a win and the other representing a loss a 6-section spinner with congruent sections, 4 representing a win and 2 representing a loss a 5-section spinner with congruent sections, 3 representing a win and 2 representing a loss an 8-sided die with 5 sides representing a win and 3 sides representing a loss The table shows the number of games a team won and lost last season. Wins and Losses Last Season Number of Games Wins 24 Losses 16 Greg has tickets to six of the team’s games this season. He is designing a simulation, using last year’s wins and losses, to predict whether the team will win or lose each of the games he attends. Which tool is most appropriate for use in a simulation that fits the data? a coin with one side representing a win and the other representing a loss a 6-section spinner with congruent sections, 4 representing a win and 2 representing a loss a 5-section spinner with congruent sections, 3 representing a win and 2 representing a loss an 8-sided die with 5 sides representing a win and 3 sides representing a loss
Answers
Answer:
C
Step-by-step explanation:
my brain is dead from reading but C is the best answer choice for this probably
Answer:
C
Step-by-step explanation:
product A
can be represented by the function f(x) = 0.69(1.03)x
product B
years : price in dollars
1 : 10,100
2 : 10,201
3 : 10,303.01
4 : 10,406.04
Which product recorded a greater percentage change in price over the previous year?
Answers
Answer:
f(x) = 0.69 (1.03)^x
in other words TO THE POWER x
that would be 0.69 when x = 0 years, now
0.69 * 1.03 after one year
0.69 * 1.03 *1.03 after two years
0.69 *1.03*1.03*1.03 after 3 etc
It is getting bigger. Every year you increase by .03 x which is 3%
B
the ratio is for example
10406.04/10303.01
= 1.01
check:
10303.01/10201 = 1.01 sure enough
so that is increasing by ONLY ONE percent per year
