a farmer has 480 feet of fencing to construct two identical rectangular pens that will share one wall.ignore the gate. what are the dimensions of the pen that will maximize the area?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

To maximize the area of the two identical rectangular pens, we need to find the dimensions that will allow us to enclose the largest possible area using the given 480 feet of fencing.

Let's start by assigning variables to the dimensions of the rectangular pen. Let's say the length of the pen is "L" and the width is "W". Since the two pens share one wall, we can divide the available fencing equally between the two long sides and the two short sides.

The equation for the perimeter of a rectangle is: P = 2L + 2W.

In this case, we have two pens, so the total perimeter is 480 feet: 2L + 2W = 480.

We can simplify this equation by dividing both sides by 2: L + W = 240.

To maximize the area, we need to find the dimensions that satisfy this equation while maximizing the product of L and W, which represents the area.

Since the pens are identical, we can express one dimension in terms of the other. Let's solve the equation for L: L = 240 - W.

Now, substitute this expression for L in the equation for the area: A = L * W = (240 - W) * W.

To find the maximum area, we need to find the value of W that maximizes the expression (240 - W) * W.

One way to do this is by graphing the equation or using calculus, but since this is likely a high school-level problem, we can use the concept of symmetry.

Since the equation for the area is quadratic, the maximum area will occur at the midpoint of the symmetry axis. In this case, the symmetry axis is given by W = 240/2 = 120.

So, to maximize the area, each pen should have a width of 120 feet.

Substituting this value back into the equation for the perimeter, we can find the length of each pen: L + 120 = 240, L = 240 - 120 = 120.

Therefore, the dimensions of each pen that will maximize the area are 120 feet by 120 feet.

Keep in mind that this is just one possible answer, as there may be other valid dimensions that also maximize the area. However, for a symmetrical solution, both pens should have equal dimensions.

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Identify the terms and the like terms in this expression 7+ a - 2 + 3a + b

Answers

Answer:

its the second, third and fifth one

Step-by-step explanation:

cuz it just is

Answer:

2 and 5 are true.

The terms in the expression are 7, a, 2, 3a, b

a and 3a are like terms

Hope this helps! Please rate brainliest :)

Solve for X in 5x/10=2

Answers

5x=2*10
5x=20
x=20/5
x=4

Given Equation: 5x/10 = 2.
Steps:

Step 1: Multiply both sides of the equation by the L.C.M of the numerators of both sides of the equation ( 10 and 1). L.C.M is 10

(5x/10).10 = 2x10

5x = 20

Step 2: Divide both sides by the co-efficient of x i.e.5

(5x)/5 = 20/5

x = 4

I hope this helps

Find all solutions to the equation.

sin x = sqrt(3)/2

Answers

Answer:

$x=(\pi)/(3) and x=(2\pi)/(3)$

Step-by-step explanation:

We are given that $sin x=(\sqrt3)/(2)$

We have to find all solutions of the given equation

We know that $sin (\pi)/(3) =sin60^(\circ)=(\sqrt3)/(2)$

sin x is positive then the value of sin x will lie in I quadrant and II quadrant.The value of sin x is negative in III and IV quadrant .

We are given that sin x is positive then the solution will lie in I and II quadrant only.Therefore, the solution of sin x will not lie in III and IV quadrant .

$sin x =sin (\pi)/(3)$ ...(I equation )and $sin x =sin(\pi-(\pi)/(3))$ ...(II equation)

In II quadrant $\theta$ change into $(\pi-\theta )$

Cancel sin on both side of equation I

Then, we get

$x=(\pi)/(3)$

$sin x =sin ((3\pi-\pi)/(3))$

$sin x =sin (2\pi)/(3)$ ...(II equation )

Cancel sin on both side of equation II

Then we get

$x=(2\pi)/(3)$

Hence, the solutions of equation are

$x=(\pi)/(3) and x=(2\pi)/(3)$

The solutions of the equation are:

x = 60 degrees

x = 120 degrees

x = 420 degrees

x = 480 degrees, and so on.

We have,

The solutions to the equation sin(x) = √3/2 are any angles where the sine of the angle is equal to √3/2.

So,

sin 60 = √3/2

sin 120 = sin (π - 60) = sin 60 = √3/2

In trigonometry 180 is written as π.

Since (π - 60) is in the secondquadrant sin 60 is positive.

sin 420 = sin (360 + 60) = sin 60 = √3/2

In trigonometry 360 is written as 2π.

Since (2π + 60) is in the Firstquadrant sin 60 is positive.

Similarly,

sin 480 = sin (2π + 120) = sin 120 = sin (π - 60) = sin 60 = √3/2

Thus,

The solutions of the equation are:

x = 60 degrees

x = 120 degrees

x = 420 degrees

x = 480 degrees, and so on.

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Find the final sale price rounded to the nearest cent of a $239 television with a 10% discount.

Answers

Answer:

215

Step-by-step explanation:

239 x .10 = 23.9

239 - 23.9 = 215.1

then to round it would be 215!

Answer with solutions.Find the corresponding roots in the box for the given quadratic

equations and get the letters to decode the hidden message . You

may use the extracting the square root method

P:±6
M: ±7
C:5,6
A : 0
J:4,-1

Q:±√5
L:±11
H:±4
D:-4,1 I:±3

S:16,-6
Y: ±8
B:±4√2
E:±2
A:0,-4

U:6,0
U:±√10
N:6,-16
G:1,-1
T:±2√2

O:±6√2
V:±√3
I:±5
J:-7,-1
K:5,-2

W:±12
F:±2√3
X:±6
R:0,-6
•:9±√6
/4

Message : __________________________________

________________________________________

1. x2 = 49
2. x2 -27 =0
3. 3x2-36= 0
4. 9x2 = 0
5. 5x2- 15=0
6. 2x2- 144=0
7. ( x + 3)2 = 9
8. 4x2 -100 =0
9. 5x2 = 40

10. 3x2 -12 = 0

11. (x-5)2

Answers

The corresponding roots of the quadratic equations are given.

What are Quadratic Equations?

Quadratic expressions are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

1. x² = 49

Find the square root.

x = ±√49 = ±7

2. x² - 27 = 0

x² = 27 = 9 × 3

x = √27 = √(9×3) = √9 × √3 = ±3√3

3. 3x² - 36 = 0

3x² = 36

Divide 3 on both sides.

x² = 12

x = √12 = √(4 × 3) = ±2√3

4. 9x² = 0

x = 0

5. 5x² - 15 = 0

5x² = 15

x² = 3

x = ±√3

6. 2x² - 144 = 0

2x² = 144

x² = 72

x = √72 = √(36 × 2) = ±6√2

7. (x + 3)² = 9

x + 3 = √9

x + 3 = ±3

x = 3 - 3 = 0 and x = -3 - 3 = -6

8. 4x² - 100 = 0

4x² = 100

x² = 25

x = ±√5

9. 5x² = 40

x² = 8

x = √8 = √(4 × 2) = ±2√2

10. 3x² - 12 = 0

3x² = 12

x² = 4

x = ±2

11. (x - 5)² = 121

x - 5 = √121

x - 5 = ±11

x = 11 + 5 = 16 or x = -11 + 5 = -6

Hence the solutions are found.

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Triangle P=27,Q=40,P=33 law of sines round measures to the nearest tenth

Answers

For the law of sines, you would apply it in this particular problem like so:
Since P is 27, its angle is 33 and Q's length is 40; you would set it up like this
40/SinQ = 27/Sin33, multiply 40 with Sin33, then it would be 40Sin33, then divide it by 27. The result should be 40Sin33/27 = X

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