Solve the following two problems using Calculus. Show all of your work on a separate sheet of paper, making clear how you arrived at all your solutions. Please be aware that you are using similar thinking for both of these problems, but you are solving for maximum area in Part A and minimum cost in Part B. Enjoy
A. If the materials for the fence cost $12 per foot, find the dimensions of the
corral for the largest possible area that can be enclosed with $2400 worth of fence.
B. If he only requires an area of 288 square feet for his vegetable garden, find the minimum cost of putting up this fence, if the cost per foot is $10. Indicate the dimensions of the garden that will minimize the cost.
Answers
9514 1404 393
Answer:
A. 50 ft square
B. 12√2 ft square
Step-by-step explanation:
These problems are basically the same, so have the same solution. The rectangle with maximum area for a given perimeter will have the same shape as the one with minimum perimeter for a given area.
We can find it generically. Let p represent the perimeter of a rectangular area with one side that measures x. The area will be ...
A = x(p/2 -x) = -x^2 +(p/2)x
The area will be maximized when dA/dx = 0:
dA/dx = -2x +p/2 = 0
p/2 = 2x . . . . . add 2x
x = p/4 . . . . . . divide by 2
The other dimension is ...
p/2 -x = p/2 -p/4 = p/4
The dimensions of the maximum area for perimeter p are ...
p/4 × p/4 . . . . . . . a square
__
A.$2400 worth of fence at $12 per foot is 2400/12 = 200 ft of fence. The largest possible area that can be enclosed will have dimensions of 200 ft/4 = 50 ft square:
50 ft × 50 ft
__
B.The perimeter of the garden will be at its shortest when the shape of the garden is square.
√(288 ft²) = 12√2 ft
The dimensions of the garden that will minimize the cost are ...
12√2 ft × 12√2 ft
Related Questions
5 less than two times 'm'
Answers
Answer:
[tex]5 < 2m[/tex]
Step-by-step explanation:
Please mark as Brainliest if this answer helped you! :)
(if you need it written in numbers as an expression, I hope this will help! The other answer interpreted it as an inequality, so hopefully one of these gives you the answer you are looking for!)
5 less than two times 'm'
\/
two times 'm' minus 5
\/ \/
2m -5
\/
2m - 5
If x=8, find the value of y in the equation 4x-2y=28
Answers
Answer:
The answer is 2
Step-by-step explanation:
[tex]4x - 2y = 28 \\ 4 \times 8 - 2y = 28 \\ 32 - 2y = 28 \\ 32 - 28 = 2y \\ 4 = 2y \\ devided \: by \: 2 \\ then \\ y = 2[/tex]
The function g(x) = 8|x – 15| - 30 is a transformation of the parent function p(x) = x. Which of the following correctly describes the transformation of function p that generates function g?
A p is translated 30 units down, then has a vertical shrink by a factor of 8, and then is translated 15 units right.
B. p has a vertical shrink by a factor of 8, then is translated 15 units down, and then is translated 30 units left
c. p is translated 15 units left, then has a vertical stretch by a factor of 8, and then is translated 30 units up.
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
Answers
Using translation concepts, it is found that the correct option, which represents the transformation made to function [tex]g(x) = 8|x - 15| - 30[/tex], is given by:
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
The parent function is:
[tex]p(x) = |x|[/tex]
The first transformation was [tex]x \rightarrow x - 15[/tex], which means that it was shifted 15 units to the right.
Then, the function was multiplied by 8, which means that it was stretched vertically by a factor of 8.
Finally, 30 was subtracted from the function, which means that it was shifted down 30 units.
Hence, the correct option is given by:
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
A similar problem is given at https://brainly.com/question/18405655
Archimedes drained the water in his tub. The amount of water left in the tub (in liters) as a function of time (in minutes) is graphed. How much water was initially in the tub?
Answers
Answer:
y+zx=a (see below for variables
Step-by-step explanation:
You haven't attached an image, so I'll I assume you want the equation
y is amount of water, x is time, z is water drained per minute, and a is the original amount o water
y=a-zx
rearranging it for the original amount of water
y+zx=a
Answer:
360 liters
Step-by-step explanation:
The time when the draining began is the same as 0 minutes since the beginning of the draining. So we need to look for the point on the graph where Time is 0, which is the y-intercept. The point we are looking for is (0,360), which means that at the beginning of the draining, there were 360 liters of water in the tub.
Charles has read 180 pages of a book. This is of the total number of pages in the book. If p represents the number of pages in the book, what is p?
Answers
Answer:
More than 180. It needs more info to have an actual answer.
Answer: I believe it would be 180 considering he has 180 pages in a book and you wanna know how many pages he has it would be 180 hoped this helped love ✨
Step-by-step explanation:
Hhhhhhhhhhhhhhhhjjjjjj
Answers
Answer:
8.75 per hour
Step-by-step explanation:
Since it is a linear function we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 370-20)/(40-0)
=350/40
= 8.75
True or false? Please help.
Answers
Answer:
True
Step-by-step explanation:
Vertical angles are angles that essentially opposite of eachother. Vertical angles are a pair of opposite angles formed by intersecting lines.
Answer:
True
Step-by-step explanation:
Vertical angles are angles that essentially opposite of eachother. Vertical angles are a pair of opposite angles formed by intersecting lines.
3. What is 11% of $3,000? • A) $250 e B) $300 • C) $380 • D) $350
Answers
Answer:
$330.00
Step-by-step explanation:
Hey there!
The word ‘of’ in math means multiply
And
11% of 3,000
= 11/100 * 3,000
= 11/100 * 3,000/1
= 11(3,000)/100(1)
= 33,000/100
= 33,000 ÷ 100/100 ÷ 100
= 330/1
= 330
Therefore, the answer is most likely: 330
(NONE of the ABOVE)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
PLEASE DO!! will give brainliest
Which statement correctly describes the end behavior of the function f(x) = x2 – 2x + 8?
Answers
Answer:
3
Step-by-step explanation:
in both f approaches +infinity
Draw a Graph y=3/2x+2
Answers
The answer is in the graph.
Answer:in the picture
Step-by-step explanation:
please give me a brainliest answer
Find the difference in area between the circle and the triangle. possible answers are
- A=27pi
- A=4pi-8
- A=9pi-9/2radical 3
- A=16/3pi
- A=16
Answers
Answer:
jo in no w fo r intelligent bio logy class fo r girl cth-qoqo-xvc
Step-by-step explanation:
A=9pi-9/2radical 3
this is the answer
brainliest please
Express (x + 2)² + 9 = 0 in standard form
Answers
x^2 + 4x + 4 + 9 = 0
x^2 + 4x + 13 = 0
Answer:
x^2+4x+13=0
Step-by-step explanation:
I'm 100% certain this is right. Have a good day/night wherever you are! :D
NEVER GOING TO GIVE YOU UP NEVER GOING TO LET YOU DOWN NEVER GOING TO RUN AROUND AND DESERT YOU NEVER GOING TO MAKE YOU CRY NEVER GOING TO TELL A LIE AND HURT YOU OOOOOOOO GIVE YOU UP OOOOOO NEVER GOINT TO GIVE NEVER GOING TO GIVE
[tex]3642164 \times 363.6466 = 666[/tex]
[tex] \infty [/tex]
Answers
Answer:
thank you!
Step-by-step explanation:
Urgent.. Please somebody help me with this it due by tomorrow
Answers
Lauren bought x boxes of cookies to bring to a party. Each box contains 12 cookies.
She decides to keep two boxes for herself. She brings 60 cookies to the party. Write
an equation that can be used to find the number of boxes, x, Lauren bought.
Answers
Answer:
12x-2=60
Step-by-step explanation:
since there are 12 cookies per box, u could multiply it by x boxes, and since she kept 2 you would need to subtract it from your total.
what is 512 grams in pounds
Answers
Answer:
1.12877
Step-by-step explanation:
You could also round it to the nearest tenth and just say 1.1 pounds
Answer:
1.12877 pounds
Step-by-step explanation:
For an approximate result, divide the mass value by 454.
1 gram = 0.00220462 pounds
3
Abox of cereal states that there are 84 calories in a
4
-cup serving. What is the unit rate for calories
per cup? How many calories are there in 4 cups of the cereal?
Answers
Answer:
21 calories per cup
Step-by-step explanation:
4cups↔84calories
1cup ↔less
1/4x84=21calories
Jessie recently drove to visit her parents who live 570 miles away. On her way there her average speed was 25 miles per hour faster than on her way home (she ran into some bad weather). If Jessie spent a total of 19 hours driving, find the two rates (in mph). Round your answer to two decimal places, if needed.
Jessie's average speed to her parents' house: ___________ mph
Jessie's average speed from her parents' house: ___________ mph
Answers
Answer:
Step-by-step explanation:
Let v be her average speed from her parents house
Let t₁ be the time traveled to parents house
Let t₂ be the time traveled from parents house
t₁ + t₂ = 19
t₁ = 19 - t₂
as the distance does not change, we can equate two velocity•time statements
vt₂ = (v + 25)t₁
vt₂ = (v + 25)(19 - t₂)
vt₂ = 19v - vt₂ + 475 - 25t₂
2vt₂ = 19v + 475 - 25t₂
vt₂ = 570 and t₂ = 570/v
2(570) = 19v + 475 - 25(570/v)
1140 = 19v + 475 - 14,250/v
665 = 19v - 14,250/v
665v = 19v² - 14250
0 = 19v² - 665v - 14250
0 = v² - 35v - 750
quadratic formula
v = (35 ±√(35² - 4(1)(-750))) / 2
v = (35 ± 65) / 2
v = - 15 mph which we ignore as she did not spend hours driving backwards
or
v = 50 mph is average speed from parents house
v + 25 = 75 mph is average speed to parents house.
the trip to took 570/75 = 7.6 hrs
the trip from took 570/50 = 11.4 hrs. total of 19 hrs.
Wesley willed his estate to Margaret,
no b Betty Jo, and Johnny. He gave Margaret
$20,000. Betty Jo got 22 times as much as
Margaret. Johnny got 32 times as much
as Margaret. What was the total value of
the estate?
Answers
Answer:
1,100,000
Step-by-step explanation:
20000 + 22(20000) + 32 (20000)= 55 (20000)= 1,100,000
Answer:
1,100,000
Step-by-step explanation:
Please do 3 hurry!!!!
Answers
Here is the answer above. Click to view
5. The number that is to be divided in a division problem is the
_______________
Answers
Answer:
z I need this in essay form......
Phaeton, who has just discovered that is he is the son of the sun god, pays a visit to his father and makes a special request. In this passage consider how the author uses literary elements such as plot and language to reinforce the theme of the dangers of pride.
Answer:
dividend
Step-by-step explanation:
answer - dividend
Find YZ and XY so I can put em in the boxes :)
Answers
Answer:
........................
Last year Kaitlin opened an investment account with $7600. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in her account at the end of the year
Answers
The increase was: 494
Choose the scientific notation for 800.
O 8 x 10
O 8 x 102
O 8 x 103
O 8 x 100
Answers
Answer:
O [tex]8 * 10^2[/tex]
Step-by-step explanation:
Hope it helps
Peace out
^^ ^-^ :) ;) ~-~
3. Find the slope of the line passing through the points (-4,-8) and (2,-8)
2. Find the slope of the line passing through the points(6,6) and (6,-4)
Answers
Answer:
2. undefined
3. 0
Step-by-step explanation:
Formula : -
Slope = ( y2 - y1 ) / ( x2 - x1 )
3.
( x1, y1 ) = ( - 4, - 8 )
Here,
x1 = - 4
y1 = - 8
( x2, y2 ) = ( 2, - 8 )
Here,
x2 = 2
y2 = - 8
Slope = ( - 8 - ( - 8 ) ) / ( 2 - ( - 4 ) )
= ( - 8 + 8 ) / ( 2 + 4 )
= 0 / 6
Slope = 0
2.
( x1, y1 ) = ( 6, 6 )
Here,
x1 = 6
y1 = 6
( x2, y2 ) = ( 6, - 4 )
Here,
x2 = 6
y2 = - 4
Slope = ( - 4 - 6 ) / ( 6 - 6 )
= - 10 / 0
Slope = not defined
Note : -
Any number who denominator is 0 is undefined.
Alec is 3 years older than 11 times the age of his nephew Luke. If A represents Alec's age and L represents Luke's age, which equation is true?
Answers
Answer:
A = 11L + 3
Hope this Help
Jayden walked a total of 12x+5r-8 miles on Monday and Tuesday. If he walked 7x-10r miles on Monday, how
many miles did he walk on Tuesday?
Answers
Answer:
8 Miles on Tuesday
Step-by-step explanation:
Jahden walked (12x + 5r - 8) - (7x -10r) = 5x + 15r - 8 miles on Tuesday.
HELP!!!!! Someone answer ASAP PLEASE!!!!
Answers
Answer:
thay are independent
Step-by-step explanation:
I only know that they are independent but Don't really know how to explain and do step by step.
Answer:
a, =to 13 and B, is to 45 and C,13 D, 14 of tells
Which of the numbers below is greater than zero? Select all that apply.
A)0.8
B)4.5
C)14
D)−2.25
E)−0.5
Answers
how many feet in 2/5 of a mile
Answers
The answer is 2112.