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Orlov [11]
3 years ago
5

If one rooster can wake up 10 hens, then how many hens can 3 roosters wake up?

Mathematics
1 answer:
Tresset [83]3 years ago
3 0
I’m pretty sure the answer is 30... right? Because you’d multiply 10 and 3
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Equilateral triangle ABC has an area of \sqrt{3}√ ​3 ​ ​​ . If the shaded region has an area of \piπK − \sqrt{3}√ ​3 ​ ​​ , what
Liono4ka [1.6K]

Answer:

The value of k = 4/3

Step-by-step explanation:

* Lets explain how to solve the problem

- An equilateral triangle ABC is inscribed in a circle N

- The area of the triangle is √3

- The shaded area is the difference between the area of the circle

  and the area of the equilateral triangle ABC

- The shaded are = k π - √3

- We need to find the value of k

* <u><em>At first lets find the length of the side of the Δ ABC</em></u>

∵ Δ ABC is an equilateral triangle

∴ Its area = √3/4 s² , where s is the length of its sides

∵ The area of the triangle = √3

∴ √3/4 s² = √3

- divide both sides by √3

∴ 1/4 s² = 1

- Multiply both sides by 4

∴ s² = 4 ⇒ take √ for both sides

∴ s = 2

∴ The length of the side of the equilateral triangle is 2

* <u><em>Now lets find the radius of the circle</em></u>

- In the triangle whose vertices are A , B and N the center of the circle

∵ AN and BN are radii

∴ AN = BN = r , where r is the radius of the circle

∵ The sides of the equilateral angles divides the circle into 3 equal

   arcs in measure where each arc has measure 360°/3 = 120°

∵ The measure of the central angle in a circle equal the measure

  of the its subtended arc arc

∵ ∠ANB is an central angle subtended by arc AB

∵ The measure of arc AB is 120°

∴ m∠ANB = 120°

- By using the cosine rule in Δ ANB

∵ AB = 2 , AN = BN = r , m∠ANB = 120°

∴ (2)^{2}=r^{2}+r^{2}-2(r)(r)cos(120)

∴ 4=r^{2}+r^{2}-2(r)(r)(-0.5)

∴ 4=r^{2}+r^{2}-(-r^{2})

∴ 4=r^{2}+r^{2}+r^{2}

∴ 4=3r^{2}

- Divide both sides by 3

∴ r^{2}=\frac{4}{3}

- Take square root for both sides

∴ r = 2/√3

* <u><em>Lets find the value of k</em></u>

∵ Area circle = πr²

∵ r = 2/√3

∴ Area circle = π(2/√3)² = (4/3)π

∵ Area shaded = area circle - area triangle

∵ Area triangle = √3

∴ Area shaded = (4/3) π - √3

∵ Area of the shaded part is π k - √3

- Equate the two expressions

∴ π k - √3 = (4/3) π - √3

∴ k = 4/3

* The value of k = 4/3

7 0
2 years ago
So, here’s a math question for you: Suppose you set your confidence level at "I think I know it," which means that you’re initia
stiks02 [169]

Answer:

The answer is 20 points

Step-by-step explanation:

If the points is based on 100 by rating, and your confidence level of 'I think I know it' places you on the initial risk of 80 points as suggested, which eventually places you on the wrong side, you will be left with the following:

Total rating point of 100 minus initial risking points of 80. This leaves you with a second chance points of just 20.

6 0
3 years ago
A painter charges $10 per due for labowplum 25 for a felder rental when the paints house. The customer provides the paint the to
Deffense [45]
The answer is D, 22.5 hours !!
7 0
2 years ago
Using FOIL method. Multiply the terms. (X^2 -7)(x^2 -4)
murzikaleks [220]

Answer:

x^4-11x^2+28

Step-by-step explanation:

  1. Set it up

x^2(x^2-4) -7(x^2-4)

    2. Multiply

x^4-4x^2-7x^2+28

    3. Simplify

x^4-11x^2+28

4 0
3 years ago
Use the graph to find the limit (if it exists). If the limit does not exist, explain why.
Mandarinka [93]

Answer:

  the limit does not exist

Step-by-step explanation:

As x approaches π/2 from below, tan(x) approaches +∞. A x approaches π/2 from above, tan(x) approaches -∞. These two limits are not the same, so the limit is said not to exist.

___

For a limit to exist, it must be the same regardless of the direction of approach.

6 0
3 years ago
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