Farmer Ed has 7000 meters of fencing and wants to enclose a rectangular plot that borders on a river. If farmer Ed does not fence the side along the river, what is the largest are that can be enclosed? ...?
Answers
Let
x--------> the length side of the rectangular plot (assume side along the river)
y------> the width side of the rectangular plot
we know that
the perimeter of the rectangular plot is equal to
[tex]P=x+2y[/tex]
[tex]P=7,000\ m[/tex]
so
[tex]7,000=x+2y[/tex]
Clear variable y
[tex]y=(7,000-x)/2[/tex] -------> equation [tex]1[/tex]
The area of the rectangular plot is
[tex]A=x*y[/tex] ------> equation [tex]2[/tex]
substitute equation [tex]1[/tex] in equation [tex]2[/tex]
[tex]A=x*[(7,000-x)/2][/tex]
[tex]A=x*[(7,000-x)/2]\\\\ A=3,500x-0.5x^{2}[/tex]
we know that
To find the larger area that can be enclosed------> Find the vertex of the quadratic equation
The quadratic equation is a vertical parabola open down
so
the vertex is a maximum
using a graphing tool
see the attached figure
the vertex is the point [tex](3,500,6,125,000)[/tex]
that means
For [tex]x=3,500\ m[/tex]
the largest area is [tex]6,125,000\ m^{2}[/tex]
Find the value of y
[tex]y=(7,000-3,500)/2=1,750\ m[/tex]
the dimensions of the rectangular plot are
[tex]Length=3,500\ m\\Width=1,750\ m[/tex]
therefore
the answer is
The largest area that can be enclosed is [tex]6,125,000\ m^{2}[/tex]
Related Questions
4x^2+4y^2=64
what are the domain and range
Answers
Looking at the graph, the smallest x can be is -4. The largest x can be is 4. So the domain in interval notation is [tex][-4,4][/tex]
Similarly the range in interval notation is also [tex][-4,4][/tex] because the lowest you can go is y = -4. The highest you can go is y = 4
Write a proportion that can be used to find the cost of 10 notebooks if 3 notebooks cost $1.98.
Answers
For 3 notebooks you pay $1.98 so the ratio is 1:0.66.
For 10 notebooks, then we could scale the ratio and it will become 10:6.60. So they will cost you $6.60.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
If 6 is 24% of a number, what is 40% of the same number?
(A) 8
(B) 10
(C) 15
(D) 20
Answers
To find 40% of the number where 6 is 24%, we first determine the whole number by dividing 6 by 0.24 to get 25. Then we calculate 40% of 25, which is 10.
If we know that 6 is 24% of a number, we can find the whole number by dividing 6 by 0.24. Once we have the full number, we can calculate 40% of it. Let's do the calculation step by step.
Calculate the whole number using the given percentage: Whole number = 6 / 0.24.
Perform the division to find the whole number: Whole number = 25.
Calculate 40% of the whole number: 40% of 25 = 0.40 * 25.
Perform the multiplication to find 40% of the number: 40% of 25 = 10.
Therefore, 40% of the same number is 10.
find the missing angle of the triangle.
Answers
An increase in total assets can be financed by an increase in which of the following capital components:
a. debt
b. preferred stock
c. common equity
d. All of the above ...?
Answers
3^x : write in terms of base e and simplify! ...?
Answers
3x=e^ln3^x
=e^xln3
Let
[tex]y = {3}^{x} [/tex]
Writing the above exponential equation as a logarithmic equation, we obtain;
[tex] log_{3}(y) = x[/tex]
We can apply the change of base formula to obtain,
[tex] \frac{ log_{e}(y) }{ log_{e}(3) } = x[/tex]
Or
[tex] \frac{ ln(y) }{ln(3) } = x[/tex]
We can cross multiply to obtain;
[tex] ln(y) = x ln(3) [/tex]
Taking logarithm of both sides to base e, we obtain;
[tex] {e}^{ ln(y) } = {e}^{x ln(3) } [/tex]
This implies that,
[tex]y= {e}^{x ln(3) } [/tex]
But we know that,
[tex]y = {3}^{x} [/tex]
Hence
[tex] {3}^{x} = {e}^{x ln(3)} [/tex]
determine the differential equation giving the slope of the tangent line at point (x,y) for the given family of curves.
x^2+y^2=2cx ...?
Answers
can u show work 39472/78 ...?
Answers
78 x 5 = 390
Subtracting, then bringing down 7
47 is smaller than 78 so
78 x 0 = 0
Bringing down 2, we get 472
78 x 6 = 468
Subtracting, the remainder is 4
The answer is 506 with a remainder of 4.
Perform the operations, multiply, and simplify.-a^3b (3a^2 b^5 - ab^4 - 7a ^2
b.
Answers
3a^5.b^6-a^4.b^5-7a^5.b
Which answer describes the type of sequence?
1, 6, 7, 13, ...
A. geometric
B. neither arithmetic nor geometric
C. arithmetic
Answers
b: neither arithmetic nor geometric
The given sequence describes the type of sequence that is neither arithmetic nor geometric. which is the correct answer would be an option (B).
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is a particular order.
The sequence is given in the question following as:
1, 6, 7, 13, ...
We have to identify the type of given sequence
As per the given question, we have
1, 6, 7, 13, ...
For checking as an arithmetic sequence :
Common difference between 1 and 6 is d = 6 - 1 = 5
Common difference between 6 and 7 is d = 7 - 6 = 1
Since the common difference between consecutive terms is not the same, this means it's not an arithmetic sequence.
For checking as a geometric sequence :
Common ratio between 1 and 6 is r = 6/1 = 6
Common ratio between 6 and 7 is r = 7/6
Since the common ratio between consecutive terms is not the same, this means it's not a geometric sequence
Thus, the given sequence describes the type of sequence that is neither arithmetic nor geometric.
Learn more about arithmetic sequence here:
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Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .
Answers
"Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not exist, enter DNE.)
f (x) = cos(πx/2)
Answers
Answer: The derivate is f'(x) = -sin(πx/2)*(π/2)
Step-by-step explanation:
We want the value of the derivate at each point marked:
As you may know, the derivate of cos(x) is equal to -sin(x)
And in our case:
f(x) = cos(πx/2)
f'(x) = -sin(πx/2)*(π/2)
Where the rule used is that the derivate of f(g(x)) is equal to f'(g(x))*g'(x)
Now, as you may see, in both the marked points the curve changes of direction, so the tangent line in that point must be zero, letsinput the values of x in the derivate and see if this is true:
f'(0) = -sin(π*0/2)*(π/2) = -sin(0)*(π/2) = 0
f'(2) = -sin(π*2/2)*(π/2) = -sin(π)*(π/2) = 0
So this makes sense.
What is the inverse of f(x)=-3x^3 6?
Answers
When you multiply or divide an inequality by a ______ number, you must flip the inequality symbol.
Answers
your weekly wage is $400 what is your annual?
Answers
$400 x 52 = $28000
Three water pipes are used to fill a swimming pool. The 1st pipe alone takes 8 hours to fill the pool, the 2nd pipe alone takes 12 hours to fill the pool, and the 3rd pipe takes 24 hours to fill the pool. If all 3 pipes are opened at the same time, how long will it take all 3 together to fill the pool?
Answers
1st hour: 6/24
2nd hour: 12/24
3rd hour: 18/24
4th hour: 24/24
Transform the formula for the given variable: I=Prt solve for t
Answers
A jug of juice holds 8 cups. convert 8 cups to pints
Answers
8 cups convert to pints = 4 pints
Further explanation7 main quantities have been determined based on international standards, namely:
1. Length, meters (m)2. Time, second (s)3. Mass, kilograms (kg)4. Temperature, kelvin (K)5. Light intensity, candela (cd)6. Electric current, ampere (A)7. Amount of substance, mol (m)Volume is a derivative quantity derived from the length
The unit of volume can be expressed in liters or milliliters or cubic meters
The conversion is
1 cc = 1 cm³
1 dm = 1 Liter
1 mL = 1 cm³
1 L = 1 dm³
The other common units for US standart volume are :
Fluid OuncesCupsPintsQuartsGallonsThe conversion for all those units :
1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces
The conversion for pints and cups :
[tex]\large{\boxed{1\:pints=2\:cups}}}[/tex]
A jug of juice holds 8 cups
so 8 cups = 8 : 2 pints
8 cups = 4 pints
Learn moreA city that uses ten billion BTUs of energy
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what is the total mass in micrograms of cofactor
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A vineyard has 145 acres of Chardonnay grapes.
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Keywords: volume,pints, cups, a jug, juice
what is another name for plane Z?
Answers
___________________________
1) The "z-plane";
___________________________
2) The "complex plane";
___________________________
3) the "domain of the z-transform"
_____________________________
At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?
a. x + y < 12
b. x + y > 12
c. x + y ≤ 12
d. x + y ≥ 12
Answers
x + y > 12
The sign is greater (>) because it says "she bought more than. The sign isnt "equal and greater" because once again she says she bought more and it doesnt say she bought at least...
the answer is B hope it helps
At the bank brent exchanges $50 in bills for 50 one-dollars coins. the total mass of the coins is 405 grams. estimate the mass of 1 one - dollar coin.
Answers
Solve 16 1/2 ÷ 2 1/4
A:7 1/3
B:5 3/7
C:133/8
Answers
(33/2) / (9/4) =
33/2 * 4/9 =
132/18 =
7 1/3 <==
Solve the inequality.
p – 9 < –9
Answers
p-9 < -9
p-9+9 < -9+9
p <0
A movie store sells DVDs for $11 each. What is the cost of n DVDs? Identify the situation as discrete or continuous.
A) C= 11n; continuous
B) C= 11+n; discrete
C) C= 11+n; continuous
D) 11n; discrete
Answers
Answer:
Complete Quick Check of...
Lesson 4: Graphing a Function Rule
Algebra 1 A: Unit 5
Step-by-step explanation:
1.C) x,0,1,2,3, y,3,-1,-5,-9
2.A) True
3.D) $698.75
4.C) cant write it out.
5.D) C = 11n; discrete
:) hope this helps!
The folding chair has different settings that change the angles formed by its parts. Suppose m2 is 34 and m3 is 76. Find m1The diagram is not to scale.
A. 130
B. 110
C. 100
D. 120
Answers
first, the sum of angles in triangle is always 180°
so mx + m2 +m3 = 180°, so mx=1800-76-34=70°
but according to the figure m1 + mx=180°, so m1=180-mx=180-70=110°
the m1 = 110°
For a $1,000 loan at a rate of 16 3/4 % for 5 years, the simple interest is a. $83.75
b. $167.50
c. $500.00
d. $837.50
Answers
A box has a width 9 inches less than its height and a length 7 inches more than its height.
a. If h is the height of the box, write a polynomial that represents the volume of the box.
b. Use this polynomial to calculate the volume for h = 17 inches.
Answers
l=h+7
w=h-9
a.
volume is height x width x length
v=h*(h+7)*(h-9)
now we have to multiply these values
h*(h+7)=h^2+7h
(h^2+7h)*(h-9)=h^3-9h^2+7h^2-63h=h^3-2h^2-63h
b.
now we plug in h=17
v=17^3 -2(17)^2 -63(17) = which comes out to 2686
note: **i suggest going through these steps on your own mostly because it's late and i'm tired and that seems like an awfully large number so you may want to check it
for the parallelogram, if m<2+5x-28 abd m<4=3x-10, find m< 3. ...?
Answers
Final answer:
After finding the value of x by equating m<2 and m<4, we calculate m<4 and then use the property of supplementary angles in a parallelogram to find that m<3 is 163 degrees.
Explanation:
To solve for m<3 in the parallelogram with m<2 = 5x - 28 and m<4 = 3x - 10, we first find the value of x. Given that opposite angles in a parallelogram are equal (m<2 = m<4), we set the two equations equal to each other and solve for x:
5x - 28 = 3x - 10
5x - 3x = 18
2x = 18
x = 9
Now that we have the value of x, we can substitute it into the equation for either angle to find the measure of that angle. Since m<4 = 3x - 10:
m<4 = 3(9) - 10 = 27 - 10 = 17
In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Therefore, to find m<3, we subtract m<4 from 180 degrees:
m<3 = 180 - m<4
m<3 = 180 - 17 = 163
Thus, m<3 in the parallelogram is 163 degrees.
The measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 2x - 18 \).[/tex]
Explanation:In a parallelogram, opposite angles are equal. Therefore, we can set up an equation based on the given angle measures:
[tex]\[ m\angle 2 + m\angle 3 = 180^\circ \][/tex]
Substitute the given expressions for[tex]\( m\angle 2 \) and \( m\angle 4 \):[/tex]
[tex]\[ (2 + 5x - 28) + (3x - 10) = 180 \][/tex]
Combine like terms:
[tex]\[ 5x + 3x - 28 - 10 + 2 = 180 \][/tex]
[tex]\[ 8x - 36 = 180 \][/tex]
Add 36 to both sides:
[tex]\[ 8x = 216 \][/tex]
Divide by 8:
[tex]\[ x = 27 \][/tex]
Now that we have the value for x, substitute it into the expression for \( [tex]m\angle 3 \):[/tex]
[tex]\[ m\angle 3 = 2(27) - 18 \][/tex]
[tex]\[ m\angle 3 = 54 - 18 \][/tex]
[tex]\[ m\angle 3 = 36 \][/tex]
Therefore, the measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 36^\circ \).[/tex]
Simplify -3p3 + 5p + (-2p2) + (-4) - 12p + 5 - (-8p3). Select the answer in descending powers of p.
1 - 7p - 2p2 + 5p3
5p3 - 2p2 - 7p + 1
1 + 7p + 2p2 - 5p3
-5p3 + 2p2 + 7p + 1
Answers
-3p³ + 5p + (-2p²) + (-4) - 12p + 5 - (-8p³)
= -3p³ + 5p - 2p² - 4 - 12p + 5 + 8p³
= 8p³ - 3p³ - 2p² + 5p - 12p - 4 + 5
= 5p³ - 2p² - 7p + 1
Answer:
B. 5p³ - 2p² - 7p + 1
Step-by-step explanation:
Good luck! Hope it was found helpful to you!
what is the answer to n * $3.25 = 325.00 ?
Answers
let's solve your equation step-by-step
n(3.25)=325
Step 1: Simplify both sides of the equation
3.25n=325
Step 2: divide both side by 3.25
3.25n/3.25=325/3.25
n=100