X = 6(2+3[2{7-3)+(4+1)-3]}
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.
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
Find the probability that an observation randomly selected from the normal distribution is between 75 inches and 81 inches.
Answer:
Happy birthday to you
Nobody like you
U look like a an animal go back to the zoo
Step-by-step explanation:
HINDI PO NAKATAWA
Solve for x. Help asap, please!
Answer:
[tex]x=4\frac{1}{8}[/tex]
Step-by-step explanation:
Step 1: Multiply (2x+5) by [tex]-\frac{3}{4}[/tex].
[tex]-\frac{3}{4}(2x+5)=-\frac{3}{4}*2x-\frac{3}{4}*5=-\frac{3}{2}x-\frac{15}{4}[/tex]
The equation becomes [tex]2\frac{1}{2}x-\frac{3}{2}x-\frac{15}{4}=\frac{3}{8}[/tex]
Step 2: Combine all terms that have a variable.
[tex]2\frac{1}{2}x-\frac{3}{2}x=\frac{5}{2}x-\frac{3}{2}x=\frac{2}{2}x=x[/tex]
The equation becomes [tex]x-\frac{15}{4}=\frac{3}{8}[/tex]
Step 3: Add [tex]\frac{15}{4}[/tex] to both sides of the equation.
[tex]x-\frac{15}{4}+\frac{15}{4}=\frac{3}{8}+\frac{15}{4}[/tex]
[tex]x=\frac{3}{8}+\frac{15}{4}=\frac{3}{8}+\frac{30}{8}=\frac{33}{8}=4\frac{1}{8}[/tex]
[tex]x=4\frac{1}{8}[/tex]
Mary found a pair of boots that cost $60 sales tax is 7% what is the total price Mary will pay for the boots?
Answer:
2 Hola cómo estás mi amigo
Answer:
sale price SP= cost + sales tax
SP= 60 + 7% of 60
SP= 60+4.2
SP= $64.2
help with question 4 please
Answer:
dont know
Step-by-step explanation:
sorry
3. They each have a brother who
weighs 40 units. Whose brother
weighs 40 pounds, and whose
weighs 40 kilograms? Explain your
reasoning
Lin's brother weighs 40 pounds, and Elena's brother weighs 40 kilograms, because kilograms are heavier than pounds and Elena's brother is bigger.
The number of marbles each sister gets when m marbles are shared equally among four sisters x = m/4
Answer:
m/4
Step-by-step explanation:
I need help answering this question please
b. What is the number that is halfway between the two values?
7 and 11
Submit
Answer:
9
Step-by-step explanation:
It would be 9 because 7 +2 is 9 and 11 - 2 is 9.
Isn't way to hard.
Good luck on whatever you are doing.
9514 1404 393
Answer:
9
Step-by-step explanation:
The midpoint between two values is their average. The average is half their sum.
(7 +11)/2 = 18/2 = 9
The number 9 is halfway between 7 and 11.
_____
Check
The distance from 7 to 9 is 9-7 = 2. The distance from 9 to 11 is 11-9 = 2. The distances are the same, so 9 is halfway between 7 and 11.
Mr. Braun has $75.00 to spend on pizzas and soda pop for a picnic. Pizzas cost $9.00 each and the drinks cost $0.75 each. Five times as many drinks as pizzas are needed. What is the maximum
number of pizzas that Mr. Braun can buy?
The maximum number of pizzas that Mr. Braun can buy is 5.
The equation that can be used to represent the total amount spent on soda pop and pizzas is:
$75 = 5x($0.75) + x($9)
Where:
x = number of pizzas that can be bought5x = total number of drinks that can be boughtIn order to determine the number of pizzas that can be bought, we have to solve for x
$75 = 3.75x + 9x
$75 = $12.75x
x = $75 / 12.75
x = 5.88
If 6 pizzas are bought, 30 drinks would be bought, the total cost would be:
6($9) + 30(0.75) = $76.50
If 5 pizzas are bought, 25 drinks would be bought, the total cost would be:
5($9) + 25(0.75) = $63.75
A similar question was answered here: https://brainly.com/question/13965560
What is 91835 rounded to the nearest Highest Place
Answer:
90,000
Step-by-step explanation:
A) 52°
B) 78°
C) 96°
D) 39°
What methods do you know that can be used to solve a quadratic equation?
Answer: If the quadratic equation has real, rational solutions, the quickest way to solve it is often to factorise into the form (px + q)(mx + n), where m, n, p and q are integers. This is especially true where the coefficient of x2 is 1.
Example 1 - Solve x2+7x+12=0
Step-by-step explanation:
that's the only one I remember
Answer:
factoring, using the square roots, completing the square and the quadratic formula.
Step-by-step explanation:
What is the value of 5 in 102,587?
Answer:
Value of 5 is 500
From right to left ones, tens, hundreds, thousands, ten thousands, hundred thousands
5 is in the hundredth place
HOPE THIS IS WORTH IT :)PLEASE HELP a great white shark loses an average of 2.7 teeth each year what is the change in the number of teeth a great white shark has in 5 years
13.5 teeth in five years
(3 x 62) - 25 + n = 166
Answer:
n = 5
Step-by-step explanation:
186 - 25 + n = 166
n + 186 - 25 = 166
n + 161 = 166
(n + 161) + (-161) = 166 + (-161)
n + 161 - 161 = 166 - 161
n = 5
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
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.
How many solutions does this equation have?
–7c = –7c + 3
Answer:
0
Step-by-step explanation:
If you move like terms to one side you'll get
-7c + 7c = 3
0c =3
0 = 3
cannot be true, so there are zero solutions
Explain how multiplying with 6 is like multiplying with 3.
Answer:
Step-by-step explanation:
lets say 6 times 6 =36
3 is a half of six so if you
6x6=36
3x6=18
-1/3x-1/6=2/9 solution
Answer:
-1 1/6
Step-by-step explanation:
Use a common denominator first to convert all the fractions so they can be easily added or subtracted.
Common denominator is 18 since 3, 6, and 9 can all evenly divide into 18
1/3 = 6/18
1/6 = 3/18
2/9 = 4/18
So now you have
-6/18x - 3/18 = 4/18
add 6/18x to both sides so you can make the number with the variable positive
6/18x - 6/18x - 3/18 = 4/18 + 6/18x simplifies to - 3/18 = 4/18 + 6/18x
subtract 4/18 from both sides
- 3/18 - 4/18 = 4/18 - 4/18 + 6/18x simplifies to - 7/18 = 6/18x
Divide both sides by 6/18 so x is alone on the one side
( - 7/18) / ( 6/18) = ( 6/18x) / ( 6/18) simplifies to ( - 7/18) / ( 6/18) = x
When you divide a fraction by a fraction, the bottom fraction gets flipped over then you multiply the two new fractions straight across
so the new equation looks like this
- 7/18 times 18/6 and you multiply -7 x 18 = -126 and the bottom is 18 times 6 = 108 you now have -126/108
x = -126/108 which simplifies to - 1 18/108 which can still be simplified more to -1 1 / 6 since 108 can be divided by 18 that gives you 6.
50,000 is 20% of what?
Answer:
250000
Step-by-step explanation:
20% of x is 50000
----------------------------
50000=20x/100
50000= x/5
5(50000) = x
250000 = x
 RST is a right triangle with RS = 12,
RT = 20, and ST = 16. What is sin R?
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \sf\longmapsto sinR=\dfrac{ST}{RT}[/tex]
[tex]\\ \sf\longmapsto sinR=\dfrac{16}{20}[/tex]
Option B
someoneplz help me plzzzzzzzzzzzz
Answer:
Whats the question ???
Step-by-step explanation:
What do you need help with?
NEDDDD ASAPPPPP!!!!!!!!!
Answer:
9
Step-by-step explanation:
4y + 6y = 90
10y =90
y = 90÷10
y = 9
Which table shows a proportional relationship between x and y?
A.
x y
2 4
3 6
4 9
B.
x y
3 4
9 16
15 20
C.
x y
4 12
5 15
6 18
D.
x y
1 4
2 8
3 15
Answer:
c is the answer
Step-by-step explanation:
Rashawn read 25 pages of his book each day until he finished the book. his book was 400 pages long. which sketch represents this situation?
Answer:
It took 16 days
Step-by-step explanation:
400/25=16
Can you help me on attached picture
A vector starts at point (-3, 4) and ends at point (6, -3). What is the magnitude of the vector? Answer to two decimal places.
Answer:
the magnitude of the vector is 11.40
MATH Topic - Coordinate system and Linear graphs Q.1) Complete the following tables and plot the points on the graph paper to represent the equations given below 1 2 3 X y=x+1 y=-3x (x, y) (x, y)
Step-by-step explanation:
Given Question
Complete the following tables and plot the points on the graph paper yo represents the equations given below :-
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = x + 1 & \sf & \sf & \sf \\ \\ \sf (x,y)& \sf & \sf & \sf \\ \end{array}} \\ \end{gathered} \\ [/tex]
and
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = - 3x & \sf & \sf & \sf \\ \\ \sf (x,y)& \sf & \sf & \sf \\ \end{array}} \\ \end{gathered} \\ [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
[tex]\rm \longmapsto\:y = x + 1[/tex]
On substituting x = 1, we get
[tex]\rm \longmapsto\:y = 1 + 1[/tex]
[tex]\rm \longmapsto\:y = 2[/tex]
On substituting x = 2, we get
[tex]\rm \longmapsto\:y = 2 + 1[/tex]
[tex]\rm \longmapsto\:y = 3[/tex]
On substituting x = 3, we get
[tex]\rm \longmapsto\:y = 3 + 1[/tex]
[tex]\rm \longmapsto\:y = 4[/tex]
Hence,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = x + 1 & \sf 2 & \sf 3 & \sf 4\\ \\ \sf (x,y)& \sf (1,2) & \sf (2,3) & \sf (3,4)\\ \end{array}} \\ \end{gathered}[/tex]
Now, draw a graph using the points (1 , 2), (2 , 3) & (3 , 4)
---------------------------------------------
Given equation is
[tex]\rm \longmapsto\:y = - 3x[/tex]
On substituting x = 1, we get
[tex]\rm \longmapsto\:y = - 3 \times 1[/tex]
[tex]\rm \longmapsto\:y = - 3[/tex]
On substituting x = 2, we get
[tex]\rm \longmapsto\:y = - 3 \times 2[/tex]
[tex]\rm \longmapsto\:y = - 6[/tex]
On substituting x = 3, we get
[tex]\rm \longmapsto\:y = - 3 \times 3[/tex]
[tex]\rm \longmapsto\:y = - 9[/tex]
Hence,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = - 3x & \sf - 3 & \sf - 6 & \sf - 9\\ \\ \sf (x,y)& \sf (1, - 3) & \sf (2, - 6) & \sf (3, - 9)\\ \end{array}} \\ \end{gathered}[/tex]
Now, draw a graph using the points (1 , - 3), (2 , - 6) & (3 , - 9)