All categories

3 years ago

What is the perimeter of a square which has the same area as a circle with circumference of 4π?

1 answer:

6 0

The circumference of a circle is given by: 2πr, where r is the radius of the circle. Equating 4π, we have 2πr = 4π so the radius of the circle is: r = 4/2 = 2. Then, the area of the circle is given by πr ^ 2 = π * (2 ^ 2) = 4π.Since the square and the circle have the same area, then: Let L be the side of the square, we have: L ^ 2 = 4π, clearing L = 2 * (π ^ (1/2))The perimeter of a square is the sum of its sides: P = L + L + L + L = 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π) ^ (1/2)) P = 8 * (π ^ (1/2))

You might be interested in

a supermarket sells 2 kg and 4 kg of sugar a shipment of 1100 bags of sugar has a total mass of 2900 kg. How many 2 kg bags and

Vaselesa [24]

There are 750 (2 kg) bags and 350 (4 kg) bags in the shipment

Step-by-step explanation:

The given is:

A supermarket sells 2 kg and 4 kg of sugar a shipment of 1100 bags of sugar
The total mass of the sugar is 2900 kg

We need to find how many 2 kg bags and 4 kg bags are in the shipment

Assume that x represents the number of 2 kg bags and y represents the number of 4 kg bags

∵ x is the number of 2 kg bags

∵ y is the number of 4 kg bags

∵ The total number of bags are 1100

- Add x and y, then equate the sum by 1100

∴ x + y = 1100 ⇒ (1)

∵ The total mass of sugar is 2900 kg

- Multiply x by 2 and y by 4 to find the mass of the bags, then

add the two product and equate them by 2900

∴ 2x + 4y = 2900 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2 to eliminate x

∴ -2x - 2y = -2200 ⇒ (3)

- Add equations (2) and (3)

∴ 2y = 700

- Divide both sides by 2

∴ y = 350

- Substitute the value of y in equation (1) to find x

∵ x + 350 = 1100

- Subtract 350 from both sides

∴ x = 750

There are 750 (2 kg) bags and 350 (4 kg) bags in the shipment

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

4 0

3 years ago

Find a positive and a negative coterminal angle for each given angle. 75 degrees

maxonik [38]

Answer:

Positive co terminal angle = -105°

Negative co terminal angle = 225°

Step-by-step explanation:

We have been given the angle 75° and we have to find one positive and one negative co-terminal angle.

In order to find the co terminal angle, we add and subtract 180° to the given angle.

Therefore, the negative co terminal angle is given by

75 - 180 = -105°

And the positive co terminal angle is given by

75 + 180 = 225°

8 0

3 years ago

Zack went on 6 hikes. The hikes were:

PilotLPTM [1.2K]

Answer:

3 miles

Step-by-step explanation:

Range is the biggest number minus the smallest number.

First put the distance in order from least to greatest.

4 miles, 4 miles, 5 miles, 6 miles, 6 miles, 7 miles.

Now subtract the greatest and least amounts.

7 - 4 = 3

8 0

2 years ago

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

bagirrra123 [75]

Answer:

In order to maximize profit, the company should sell each widget at $22.68.

Step-by-step explanation:

The amount of profit y made by the company for selling widgets at x price is given by the equation:

$y=-34x^2+1542x-10037$

And we want to find to price for which the company should sell in order to maximize the profit.

Since our equation is a quadratic with a negative leading coefficient, its maximum will occur at the vertex point.

The vertex of a quadratic is given by the formulas:

$\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -34, b = 1542, and c = -10037.

Find the x-coordinate of the vertex:

$\displaystyle x=-\frac{(1542)}{2(-34)}=\frac{771}{34}\approx \$22.68$

So, in order to maximize profit, the company should sell each widget at $22.68.

Extra Notes:

In order to find the maximum profit, substitute the price back into the equation:

$\displaystyle y\left(\frac{771}{34}\right)\approx\$7446.56$

4 0

3 years ago

I need helpp pleaseeeee

kati45 [8]

Answer/Step-by-step explanation:

The angles where two unequal sides of a kite meet are congruent to each other. Thus, these two opposite angles in a kite are equal to each other.

Therefore:

7. <E = <G

Sum of interior angles of a quadrilateral = 360

Thus,

<E = (360 - (150 + 90))/2

<E = 120/2

<E = 60°

<E = <G (set of congruent opposite angles of a kite)

Therefore,

<G = 60°

8. <H = <F (set of congruent opposite angles of a kite)

<F = right angle = 90°

Therefore:

<H = 90°

<G = 360 - (90 + 110 + 90) (sum of quadrilateral)

<G = 70°

9. Based on trapezoid midsegment theorem, the equation should be:

MN = (AB + DC)/2

Thus:

8 = (14 + DC)/2

8 * 2 = 14 + DC

16 = 14 + DC

16 - 14 = DC

2 = DC

DC = 2

10. A kite has only one set of opposite angles that are congruent to each other. The angles where the unequal sides meet, <B and <D, is the only set of angles that are congruent.

Therefore, m<A ≠ 50°

Rather, m<B = m<D = 120°

m<A = 360 - (120 + 120 + 50) (sum of quadrilateral)

m<A = 70°

8 0

3 years ago