The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.
In this question we shall use the first and second derivative tests to determine the optimal dimensions of a rectangular plot of land. The perimeter ([tex]p[/tex]), in feet, and the area of the rectangular plot ([tex]A[/tex]), in square feet, of land are described below:
[tex]p = 2\cdot (w+l)[/tex] (1)
[tex]A = w\cdot l[/tex] (2)
Where:
[tex]w[/tex] - Width, in feet.[tex]l[/tex] - Length, in feet.In addition, the cost of fencing of the rectangular plot ([tex]C[/tex]), in monetary units, is:
[tex]C = c\cdot p[/tex] (3)
Where [tex]c[/tex] is the fencing unit cost, in monetary units per foot.
Now we apply (2) and (3) in (1):
[tex]p = 2\cdot \left(\frac{A}{l}+l \right)[/tex]
[tex]\frac{C}{c} = 2\cdot (\frac{A}{l}+l )[/tex]
[tex]\frac{C\cdot l}{c} = 2\cdot (A+l^{2})[/tex]
[tex]\frac{C\cdot l}{c}-2\cdot l^{2} = 2\cdot A[/tex]
[tex]\frac{C\cdot l}{2\cdot c} - l^{2} = A[/tex] (4)
We notice that fencing costs are directly proportional to the area to be fenced. Let suppose that cost is the maximum allowable and we proceed to perform the first and second derivative tests:
FDT
[tex]\frac{C}{2\cdot c}-2\cdot l = 0[/tex]
[tex]l = \frac{C}{4\cdot c}[/tex]
SDT
[tex]A'' = -2[/tex]
Which means that length leads to a maximum area.
If we know that [tex]c = 8[/tex] and [tex]C = 4000[/tex], then the dimensions of the rectangular plot of land are, respectively:
[tex]l = \frac{4000}{4\cdot (8)}[/tex]
[tex]l = 125\,ft[/tex]
[tex]A = \frac{(4000)\cdot (125)}{2\cdot (8)} -125^{2}[/tex]
[tex]A = 15625\,ft^{2}[/tex]
[tex]w = \frac{15625\,ft^{2}}{125\,ft}[/tex]
[tex]w = 125\,ft[/tex]
The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.
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Write and then evaluate an expression for the following number line.
Answer:
Step-by-step explanation:
7. Juanita is painting her house. She can either
buy Brand A paint and a paint roller tray or
a
Brand B paint and a grid for the paint roller. For
how many gallons of paint would the price for
both options be the same? If Juanita needs 15
gallons of paint, which is the better option?
Step-by-step explanation:
brand a is better option why because we have paint and paint roller
If you buy 1 gallon can of paint both brands will cost $30 and brand B paint is a better option because it costs less.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Suppose y is the total cost and x is the gallons cases,
The equations according to the given condition are,
y = 27 x + 3
y = 2x +5
The values obtained after solving the above equation will be (1,30). As a result, 1 gallon of paint cost you $ 30.
For condition 2 Juanita needs 15 gallons of paint, x =15
For A, y = 408
For B, y = 380
The brands A and B cost $408 and $380.So the brand costs Juanita more.
Thus, if you buy 1 gallon can of paint both brands will cost $30 and brand B paint is a better option because it costs less.
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...........................
Answer:
i think its c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
because -100,-57/8,6
the absolute value of -6 is 6 and
-8 7/8 is 8×(-8)+7=-64+7/8=-57/8 because when negative plus positive we subtract and we take the sign of the larger number
8 9/10 - 3 2/3 = Plz answer
Concept:- In mixed fractions, we will have one whole number and a proper fraction. So, first we should convert them into improper fractions, which has the numerator greater than the denominator. After, converting to that we should convert the unlike fractions to like fractions by the method of LCM of denominators. Then, we can sub all the fractions so that we can get the answer.
Explanation:
{8(9/10)} - {3(2/3)}
Convert all mixed fractions to proper fractions.
= {(80+9)/10} - {(9+2)/3}
Now, add the both numerators.
= (89/10) - (11/3)
LCM of 10 & 3 is 30.
= {(89*3)/(10*3)} - {(11*10)/(3*10)}
Now, multiply the numerator and denominator of all fractions.
= (267/30) - (110/30)
Write all numerators with common denominator.
= {(267-110)/30}
Subtract the fraction and write it in simplest form.
= 157/30
Write the obtained answer in the form of mixed fraction.
= {5(7/30)}.
also read similar questions: 5/7 + 3 2/5 = 5/9 + 2 4/7 = 6 2/6 + 4/11 = 10 2/3 + 5 1/4 = 9 1/2 + ....
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Lord...... Help me god pleas I will be giving u guy's credit.
Answer:
a. 36
b. 8.5 (8 1/2)
c. 2/5
d. 6
e. 9
f. 8
Step-by-step explanation:
a. 36
b. 8.5 (8 1/2)
c. 2/5
d. 6
e. 9
f. 8
What is the answer to
2 3/8 - 1 5/8 =
Answer:
6/8
Step-by-step explanation:
you have to convert each fraction into an improper. because the denominators are already the same, you dont have to worry. once you have it as an impropper, you can now subtract it. 19/8 - 13/8 = 6/8
reduce if you can
If 15 points is 13 cents how much would 5000 be?
Answer: at least 50 dollars
Step-by-step explanation:
Step-by-step explanation:
15 points ⇒ 13 cents5000 points ⇒ xCross-multiply to find x:
x = 5000*13/15x = 4333 cents or $43.33What is 352,914 rounded to the nearest hundred thousand?
Answer:
40,000
Step-by-step explanation:
The value of 352914 to the nearest hundred thousand is 400,000
What is approximation?To approximate a number means to write a number near the original number that is a number, not exactly the original number. It may be a bit more or less than the original.
For example 345 is called three hundred and forty five, this means that 3 is hundred , 4 is tens and 5 is units. When approximating we round up the next number to 1 if ≥ 5 and to 0 if ≤ 5.
Therefore, 352914 approximated to the nearest hundred thousand will be 400, 000 because the number after 3 is 5 it will be rounded to 1 and added to 3.
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A furniture company charges 0.45 per pound
for shipping
Write an equation for the cost(y) of shipping
x pounds.
Use it to determine the cost of shipping a
12-pound chair.
The cost of the shipping a 12 pound chair is 5.4 all you need to do is 0.45 x 12 =5.4
0.45=Y 5.3=X
In a group of 34 students, 12 study both Art and Biology.
14 study Biology but not Art.
5 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
Answer:
3
Step-by-step explanation:
12+14+5=31
so therefor 34-31=3
I'm not too sure but, wouldn't you just do the following
12 + 14 + 5 = 31
which would mean 15 students do art??
How long will it take for an investment to triple in value if it earns 81% compounded continuously? Round your answer to three decimals.
A. 0.678 years
B. 0.856 years
C. 1.356 years
D. 1.366 years
The number of years it would take an investment to triple with continuous compounding is 1.356 years.
The formula for calculating future value of an investment when there is continuous compounding is FV = A x [tex]e^{r}[/tex] x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rateFV = future value FV / A = 3N = log(3) / log(e) / 0.81 = 1.356 years
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what is the prime number of 30 to 59
Answer:
the prime numbers between 30 and 59 are 31, 37, 41, 43, 47, 53
consider the following matrix. I need to know if the system has zero or infinite solutions or just one solution and if the matrix does/does not have an inverse.
Answer:
I think it would be no solution
Step-by-step explanation:
since there is the same slope, the line would never cross. Also the determinate is 0 or 1/0, so there would be no solution
What two numbers multiply to -15 and add to 8
If M is the midpoint of JK and N is the midpoint of JL, find the value of x.
Answer options:
11
13
9
12
10
Answer:10
Step-by-step explanation:
the quotient of 28
divided by four
increased by 3
Step-by-step explanation:
28 / 4 = 7
7 + 3 = 10
so, 10 is your answer
Answer:
Step-by-step explanation:
28 ÷ 4 = 7
7 + 3= 10
Harper was out at a restaurant for dinner when the bill came. She wanted to leave a tip of 16%. What number should she multiply the cost of the meal by to find the total plus tip in one step?
Answer:
Harper would take the Total Bill after tax and mutiply it by 0.16.
The formula for this would be
Total Bill = x
Tip = 16% -> 16/100 = 0.16
So
0.16x
The perimeter of the figure below is 32.6 m. Find the length of the missing side.
Answer: 4.6
Step-by-step explanation: let the missing length be x
2+2+4.8+4.8+4.8+4.8+.4.8+x=32.6
28+x=32.6
x=32.6-28
x=4.6
Rewrite each equation in standard form.
4 and 5 only
Answer:
4) 2=4x-3y
5) 51=21x-3y
Step-by-step explanation:
I gave it my best shot, I used fraction busters to cancel out the fractions and then I used simple math and distributive property. Hope it helps.
Maya is helping a gardener plant 300 bulbs. They plant 20% of the bulbs on Monday and 30% of the bulbs on Tuesday. Maya says this means they have planted 50 bulbs so far. Label and shade the model. Then use your model to explain why Maya's statement is not reasonable.
Answer:
because the total is 300 not 100 so 50 is not reasonable because that is the percentage they planted and since it is more than 100 then it should be a percent of 300 not 100. Maya is wrong about placing 50 bulbs instead they placed 150.
Step-by-step explanation:
5.
Use the quadratic model y = -4x^2 - 3x + 4 to predict y if x equals 5.
A. -89
B. -111
C. -411
D. -51
Answer:
B. -111
Step-by-step explanation:
y = -4x^2 - 3x + 4
x = 5
y = -4(5)^2 - 3(5) + 4
y = -4(25) - 15 + 4
y = -100 - 15 + 4
y = -111
...............................................................................................................................................
Please, write -4x^2 (not 04x2).
Then the quadratic model is y = -4x^2 - 3x + 4.
Now substitute 5 for x: y(5) = -4 (5)^2 - 3(5) + 4
Simplifying, y(5) = -4(25) - 15 + 4 = -100 - 11 = -111.
C plus 3/8 equals 1 1/3 what does C equal
ASAP
Answer:
Exact Form:
C=23/24
Decimal Form:
C=0.9583
Step-by-step explanation:
What is 2,000/3.67 estimate
Answer:
an estimate would be 2000/4 so it would be 500
Step-by-step explanation:
hope this helped <3
select all the ways you can describe the given polygon
Answer:
Isoceles and obtuse
Step-by-step explanation:
Need some help with these 2 math questions, They are related so best to finish one then work on the bisect. Thank you.
Answer:
∠RQT = 23.5
∠PQR = 133°
Step-by-step explanation:
Question 1Step 1 - Add angles together:
As all angles on a straight line must add up to 180°:
3x - 5 + x + 1 = 180
Add like terms together
3x + x - 5 + 1
4x - 4 = 180
Step 2 - Add 4 to both sides of the equation:
4x - 4 + 4 = 180 + 4
4x = 184
Step 3 - Divide both sides by 4:
[tex]\frac{4x}{4} = \frac{184}{4}[/tex]
x = 46
∠RQS = x + 1
∠RQS = 46 + 1
∠RQS = 47
Given the ray QT bisects ∠RQS, the angles must be the same on either side so:
47 ÷ 2 = ∠RQT
∠RQT = 23.5
Question 2As we know the value of x:
∠PQR = 3x - 5
Plug known values in:
3x - 5
3(46) - 5
138 - 5
∠PQR = 133°
This can also be calculated by subtracting known angle ∠RQS from 180:
180 - 47 = 133.
Hope this helps!
Plzzzzz help
Among the following rational numbers,
which has the greatest value?
A. 0.34
B. 0.34
C. 0.34
D. 0.343
E. 0.3409
Answer:
D. 0.343
Step-by-step explanation:
You can see the first three options as 0.340 so if you substract this number with 0.343 the remainder is positive 3.
This strategy also can be applied to the number 0.3409 but in this occasion the result is different:
[tex]0.343 - 0.3409 = 2.1\times 10^{-3}[/tex]
That is small number but still is positive that's meaning that between 0.343 and 0.3409 the greatest value is 0.343 .
Identify a pattern in each list of numbers. Then use this pattern to find the next number.
-3, 12, -33, 102, -303, ___
[tex]\begin{array}{cccccccc}\\ \underline{-3}&,&12&,&-33&,&102\\ \cline{1-7} &&(-3)(\underline{-3})+3&&(-3)(12)+3&&(-3)(-33)+3 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccc} -303&,&912\\ \cline{1-3} (-3)(102)+3&&(-3)(-303)+3 \end{array}[/tex]
Rachel's income for July is $3300. She spent $1000 for rent, $150 on student loans, $100 for a new
tablet, and $450 on groceries. How much of her monthly income is left?
Answer: 1300
Step-by-step explanation:
3300-1000=2000
2000-450=1550
1550-150=1400
1400-100=1300
Ryan solved the problem above. He says there are 6 groups of 6 students and 1 group of 5 students . What did Ryan do wrong?
Answer:
hello want to be friends so i can join you and you can join me
Use distributive property to remove the parentheses. Simplify your answer as much as possible please.
Answer:
28y^3 -35y^5
Step-by-step explanation:
= 7y^3(4) -7y^3(5y^2)
= 28y^3 -35y^5
_____
The applicable rule of exponents is ...
(y^a)(y^b) = y^(a+b)