To the nearest foot, what is the diameter of a circle whose circumference is 47.1 feet?

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 548 fee

aliina [53]

Answer: 274/3 and 137 ft

Step-by-step explanation:

Total fence used: 548 ft

So, perimeter will be 548 ft, including the fence that divides the land.

Consider the playground the drawing below.

__________x________

| |

| | y

| |

|__________________|

Let's consider that the playground is going to be divided parallel to y (and there's no problem, because if you choose parallel to x, the area will be the same). So, the perimeter (the sum of all sides) will be:

2x + 3y = 548

And the area

A = x.y

Isolating x, we have:

x = (548 - 3y)/2

Substituting the x in the Area equation:

A = (548 - 3y)/2 . y = 548y - 3y²/2 = 274y - 3/2y²

A = 274y - 3/2y²

So, it's a quadratic function. And, to find out the maximum area that the playground can have, we need to find the y-vertex of the parabola: y-vertex = Δ/4a

a = -3/2 b = 274 c = 0

Δ = 274² - 4.(-3/2).0 = 274² = 75076

Amax = -Δ/4a = -75076/4.(-3/2) = 75076/6 = 12512.7 ft²

y = -b/2a = -274/2.(-3/2) = 274/3 ft

x = (548 - 3y)/2 = (548 - 3.274/3)/2 = 274/2 = 137 ft

4 0

3 years ago

An anion with a -2 charge is found in which Group?

IgorLugansk [536]

Answer:

A and B any atom or group or atoms with a negative charge

5 0

2 years ago

Read 2 more answers

What is the length of DE

HACTEHA [7]

Answer:

DE = 20units

Step-by-step explanation:

In Δ ABC,

angle A is congruent to angle B.... (given)

therefore, ΔABC is an isoceles triangle.

therefore, CA = CB..... (side opposite to congruent angles are congruent in an isoceles triangle)

therefore, CB = 4 units

In ΔCDE,

angle D is congruent to angle E.... (given)

therefore, ΔCDE is an isoceles triangle.

therefore, CD = CE

therefore, CD = 8 units

ΔCDE ~ ΔCBA

therefore,

$\frac{cd}{cb} = \frac{ce}{ca} = \frac{de}{ab} \\ therefore \: \frac{8}{4} = \frac{8}{4} = \frac{de}{10 } \\ therefore \\ \frac{2}{1 } = \frac{de}{10 } \\ de \: = 2 \times 10 = 20units$

8 0

2 years ago

Find the approximate side length of a square game board with an area of 105 in2.

aleksley [76]

Answer:

Rounded to the nearest inch: 10

Rounded to the nearest tenth: 10.2

Rounded to the nearest hundredth: 10.25

Step-by-step explanation:

To find the area of a square, we multiply the side length by itself, or in other words, SQUARE the side length!

$A=s^2$

We are given the area, so plugging that into our equation looks like this:

$105=s^2$

To eliminate the exponent, take the square root of both sides of the equation!

$\sqrt{105}=s$

From here, there are a few paths to take, depending on what your teacher is looking for. I will evaluate the approximate of the square root by finding the nearest perfect squares.

The nearest perfect square less than √105 is √100, and the nearest perfect square greater than √105 is √121.

105 is closer to 100 than to 121, so √105 is closer to √100.

√100 is equal to 10, so the √105 is approximately 10 inches!

Using a calculator to check:

$\sqrt{105}=10.247$ inches

8 0

1 year ago

Tres veces un número x, restado de 18 es menor que -90

andrey2020 [161]

The answer is linked below

8 0

2 years ago