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Anarel [89]
3 years ago
5

Express answer in exact form. Show all work for full credit.

Mathematics
1 answer:
Gennadij [26K]3 years ago
4 0

Answer:

Area segment = 3/2 π - (9/4)√3 units²

Step-by-step explanation:

∵ The hexagon is regular, then it is formed by 6 equilateral Δ

∵ Area segment = area sector - area Δ

∵ Area sector = (Ф/360) × πr²

∵ Ф = 60° ⇒ central angle of the sector

∵ r = 3

∴ Area sector = (60/360) × (3)² × π = 3/2 π

∵ Area equilateral Δ = 1/4 s²√3

∵ The length of the side of the Δ = 3

∴ Area Δ = 1/4 × (3)² √3 = (9/4)√3

∴ Area segment = 3/2 π - (9/4)√3 units²

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Brady made a scale drawing of a rectangular swimming pool on a coordinate grid. The points (-20, 25), (30, 25), (30, -10) and (-
djverab [1.8K]

Answer:

Length = 50 units

width = 35 units

Step-by-step explanation:

Let A, B, C and D be the corner of the pools.

Given:

The points of the corners are.

A(x_{1}, y_{1}})=(-20, 25)

B(x_{2}, y_{2}})=(30, 25)

C(x_{3}, y_{3}})=(30, -10)

D(x_{4}, y_{4}})=(-20, -10)

We need to find the dimension of the pools.

Solution:

Using distance formula of the two points.

d(A,B)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}----------(1)

For point AB

Substitute points A(30, 25) and B(30, 25) in above equation.

AB=\sqrt{(30-(-20))^{2}+(25-25)^{2}}

AB=\sqrt{(30+20)^{2}}

AB=\sqrt{(50)^{2}

AB = 50 units

Similarly for point BC

Substitute points B(-20, 25) and C(30, -10) in equation 1.

d(B,C)=\sqrt{(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}

BC=\sqrt{(30-30)^{2}+((-10)-25)^{2}}

BC=\sqrt{(-35)^{2}}

BC = 35 units

Similarly for point DC

Substitute points D(-20, -10) and C(30, -10) in equation 1.

d(D,C)=\sqrt{(x_{3}-x_{4})^{2}+(y_{3}-y_{4})^{2}}

DC=\sqrt{(30-(-20))^{2}+(-10-(-10))^{2}}

DC=\sqrt{(30+20)^{2}}

DC=\sqrt{(50)^{2}}

DC = 50 units

Similarly for segment AD

Substitute points A(-20, 25) and D(-20, -10) in equation 1.

d(A,D)=\sqrt{(x_{4}-x_{1})^{2}+(y_{4}-y_{1})^{2}}

AD=\sqrt{(-20-(-20))^{2}+(-10-25)^{2}}

AD=\sqrt{(-20+20)^{2}+(-35)^{2}}

AD=\sqrt{(-35)^{2}}

AD = 35 units

Therefore, the dimension of the rectangular swimming pool are.

Length = 50 units

width = 35 units

7 0
3 years ago
Will mark u as BRAINLIEST plz help
ale4655 [162]

Answer:

Im not sure

Step-by-step explanation:

this is kinda hard

4 0
3 years ago
WILL MARK BRAINLIEST PLEASE HELP
IRINA_888 [86]

Answer:

(1,2)

Step-by-step explanation:

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6 0
2 years ago
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Question 9: emathintruction can you guys help me? .....
stira [4]

Answer:

Choice #1) multiplied by 3

4 0
3 years ago
HELP PLEASE!!!
TiliK225 [7]

Problem 1

Answer: Independent

The reason why is because each bag is separate from one another, so one event doesn't affect the other. If we know the result of what we pulled out of one bag, it doesn't change the probability of the other event.

======================================

Problem 2

Answer: Dependent

Assuming you do not put the first card back, then the probability of picking a King on the second draw will be different than if you picked a King on the first draw. With all 52 cards in the deck, the probability of getting a king is 4/52 = 1/13. It changes to 4/51 after we picked out an ace for the first card (and didn't put that first card back).

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