The dimensions of the rectangular pigpen with the largest possible area are 50 ft×25 ft.
The area and perimeter of a rectangle in the study of differential calculus, specifically in optimization problems are functions of two variables that depending on what is requested in these problems can be objective functions or link functions between the variables.
We use what we know about the perimeter of the rectangle to find a condition equation that expresses the length a in terms of the width b.
P(a, b)=a+2b [Perimeter of the fence of the rectangular pigpen]
p(a, b)=2a+3b [Substitute P(a, b)=100]
100=a+2b
a=100-2b
We must find the largest area. Using the condition equation, find the area as a function of the variable b.
A(a, b)=ab [total area of the rectangular pigpen]
A(a, b)=(100-2b)b [Replace a=100-2b]
A(a, b) = 100b-2b²
Objective function Domain
A(a, b) = 100b-2b²
D={b∈R : b>0} [Domain of the objective function]
To find the extremes of the function we have to look for the critical points of the function and apply the second derivative test.
A(a, b) = 100b-2b²
A'(a, b) =100-4b [First derivative of the objective function]
A'(b)=0
100-4b=0
4b=100
b=25 [Critical point]
Applying sufficient condition for extremes
A'(b)=100-4b [First derivative of the objective function]
A''(b)=-4 [Second derivative of the objective function]
A''(b)=-4 [A''(b)<0∀b∈D]
b=25 [Maximum point of the objective function]
Calculate the dimension of the rectangular pigpen
b=25 [Width of the rectangular pigpen]
a=100-2(25)=50 [Length of the rectangular pigpen]
Therefore, the dimensions of the rectangular pigpen with the largest possible area are 50 ft×25 ft.
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Write the equation of the line that passes through the points (-1,3) and (-6, -7).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answer:
y - 3 = 2(x + 1)
Step-by-step explanation:
First, use rise over run to find the slope
(y2 - y1) / (x2 - x1)
(3 + 7) / (-1 + 6)
10 / 5
= 2
Now, plug in the slope and a point into the point slope formula:
y - y1 = m(x - x1)
y - 3 = 2(x + 1)
So, the equation in point slope form is y - 3 = 2(x + 1)
Who said "you plus me sadly can be dangerous" in Kill this love? Person that gets it right gets brainiest
Gary wants to buy a bike that is 30% off. The original price is $109.56. What is the amount of the discount?
Answer:
32.868
≈33 ( am not sure if it needs to be estimated)
Step-by-step explanation:
100%-> 109.56
30%-> 32.868
≈33
You can buy 2 tickets to school carnival for $9 total.
How many tickets can you buy for $27?
Answer:
6
Step-by-step explanation:
pls brainliest
9/2=4.5
27/4.5=6
The size of a computer class is limited to 15 people. If 3 seats are still available, to what percent of its capacity is the full classical
Step-by-step explanation:
80%full
20% is still available
Line AB and line BC form a right angle at point B. If A = (-3, -1) and B + (4, 4), what is the equation of line BC?
A.) x + 3y = 16
B.) 2x + y = 12
C.) -7x - 5y = -48
D.) 7x - 5y = 48
Answer:
C.) -7x - 5y = -48
Step-by-step explanation:
slope AB = (y2 - y1)/(x2-x1)
= {4-(-1)}/{4-(-3)} = 4+1/4+3 = 5/7
slope of BC = -1 ÷ 5/7 = -1 × 7/5 = -7/5
taking -7x - 5y = -48
-5y = 7x -48
y = 7x/-5 - 48
y = -7/5x -48
Jerilyn picked 40 apples in 5 minutes. What is the unit rate?
Answer:
Step-by-step explanation:
Total apples = 40
Time = 5 min
Unit rate = 40 ÷ 5 = 8 apples per min
Answer:
You can conclude that the per apple price unit rate is $0.60/1.
Step-by-step explanation:
Find the solution to each equation.
3k = 48
k=
7p = 147
p=
9m = 216
m =
8C = 184
C=
4g = 72
g=
Answer:
k = 16
p = 21
m = 24
c = 23
g = 18
Step-by-step explanation:
All you had to do was divide the product by the number with the variable
answer for brainlist
write the equation of the line with a slope of 8, through the point (7,1)
Answer:
Y = 8x - 55
Step-by-step explanation:
PLS I NEED HELP ASAP I DONT HAVE TIME IT ALSO DETECTS IF IT RIGHT OR WRONG.
Answer:
D = 272 ft
Step-by-step explanation: hope this helps. pls mark me brainliest
HELP PLZZZZZZZZZZZZZ ILL GIVE U A JUICE BOX
Answer:
c)
Step-by-step explanation:
[tex]\frac{1}{2}[/tex](12*g) - h = [tex]\frac{1}{2}[/tex](12 * [tex]\frac{1}{4}[/tex]) - [tex]\frac{1}{2}[/tex] = 1/2 * 3 - 1/2 = 3/2 - 1/2 = 1
8. Find the area of the square.
79.54
90.51
128
64
256
Answer:
c
Step-by-step explanation:
Write and solve an equation to determine the value of x in the figure. a. 3x 84; 252 b. 3x 84; 28 c. 3x 84; 84 d. 3x 84; 81
Answer:
by men
Step-by-step explanation:
Don't forget to wash your lunch dishes and buy the rice and potatoes I asked ;:)
4persent of 3000 is whatW
Answer:
120 is the answer to the question
HELP PLS
What is the value of the x variable in the solution to the following system of equations? (1 point)
4x + 2y = 6
x - y = 3
O-1
5
-2
2
Answer:
D hope this helps
Step-by-step explanation:
-y •2=-2
-2+2=0
4x+x=5x
6+3=9
5x=9
9 divided by 5
x=1.9
So there for I think the answer is 2 it’s closest to 1.9
please help me with this math question
Answer:
6^11
Step-by-step explanation:
You need to add but only the exponents
Exmple:
6 ^ 3+2+5+1 =6^11
1)Here you add 1 because the last number don't have exponet this case you need to add 1
2) Because just you see 6 here so you don't touched the 6 nothing just stay the base
Answer:
When is multiply is 362797056
Step-by-step explanation:
6 to the 3 power is 216
6 to the 2 power is 36
6 to the 5 power is 7776
times six
216times 36 = 7776
7776 times 6 times 7776 is 362797056
please help to solve this
Answer:
I can do the top 2
1. a = -11
2. z = 9/2 (or nine over two in word form)
Step-by-step explanation:
Hey can somebody get this for me been stuck for five min
Answer:
3
Step-by-step explanation:
it might be a semicolon instead of a comma I guess
I believe it is 1 because you might needa put a comma there.
At the beginning of the month Kiran had $24 in his school cafeteria account. Use a variable to represent the unknown quantity in each transaction below and write an equation to represent it. Then, represent each transaction on a number line. What is the unknown quantity in each case? 1. In the first week he spent $16 on lunches. How much was in his account then? 2. Then he deposited some more money and his account balance was $28. How much did he deposit? 3. Then he spent $34 on lunches the next week. How much was in his account then? 4. Then he deposited enough money to pay off his debt to the cafeteria, How much did he deposit? 5. Explain why it makes sense to use a negative number to represent Kiran's account balance when he owes money.
Answer: 8, 20, -6, 6
Step-by-step explanation:
1. you need to to subtract 24-16=8
2. then you subtract 28-8=20
3. Then you subtract 28-34= -6
4. At the end you just put in 6!
Have a great day!
Answer:
Because it means that person Deposited that much that they didn't have so meaning when they add new money the negative number something of the amount will be taken away.
An Example is a person has in their bank account 20 dollars. They Spent 25 dollars so then means they owe the bank 5 dollars so it's gonna be -5.
Step-by-step explanation:
Find tan A for the triangle below.
a 1.5
b. 0.667
C. 0.832
d. 1.202
Answer:
B
Step-by-step explanation:
on edge
Answer:b
Step-by-step explanation:
A group of agricultural students went on a field trip to the state fair. Each ticket to enter the fair was 9$ and the parking fee for the groups bus was 25$. How many students went on the field trip if the total cost was 313$?
Can someone help me please!!!
Answer:
Step-by-step explanation:
(0,8)(8,0)
find slope
m=-1
b=8
y=-x+8
Answer:
y= -1x+8
Step-by-step explanation:
slope is -1/1 and your y intercept is (0,8)
Which element, that is essential for human life, is found in large amounts in both Earth's atmosphere and oceans?
A) helium
B) oxygen
C) silica
D) calcium
Answer:
oxygen
Step-by-step explanation:
we breath it every day
A female cheetah left her cubs to hunt for food. She sprinted 30 m away from her den in two seconds. Next, she turned around and traveled 10 meters back toward her den in three seconds. She suddenly stopped and listened intently for 1 second. Then, she traveled 40 meters away from her den in four seconds.
What is her average velocity in m/s?
Answer:
Step-by-step explanation:
total distance = 30+10+40 = 80 meters
time = 2+3+4 = 9 seconds
average velocity = 80/9 = 8 8/9 meters per second.
Please help me with this!
Answer:
10 is real, rational, integer, whole, natural
5/6 is real, rational
sqrt of 24 is real, irrational
0 is real, rational, integer, whole
sqrt 81 is real, rational, integer, whole, natural
Step-by-step explanation:
Classification
If a = 3, work out 7a + 4
Answer:
25 is the answer
Step-by-step explanation:
7×3=21
21+4=25
Find the value of x.
Answer:
B.50
Step-by-step explanation:
140-40=100
2x=100
x= 100/2
x=50
HEY THERE! PLEASE ANSWER THE MATH QUESTION IN THE PHOTO! THE CORRECT ANSWER WILL BE MARKED AS BRAINLIEST ,GET POINTS AND I WILL ALSO FOLLOW YOU! THANKS! (if you can explain your answer)
xoxo
Answer:
a) 1/10
b) 2/10
c) 8/10
Answer:
a) 1/10
b) 2/10
c) 8/10
:))
He math team does practice drills that each last hour. In February the team did practice drills for a total of 24 hours. How many practice drills did the math team do in feburary
Answer: 24 drills
Step-by-step explanation:
The math team in question does math drills that last for an hour each time.
In February, a total of 24 hours were used to practice drills.
If the team takes an hour to do one drill, the drills that will be done in 24 hours are:
= Number of hours / Drills per hour
= 24 / 1
= 24 drills