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Mazyrski [523]
3 years ago
8

Richard has two circular sprinklers to water his rectangular backyard as shown.

Mathematics
1 answer:
makvit [3.9K]3 years ago
8 0

Answer:

109.88 ft² (nearest hundredth)

Step-by-step explanation:

<u>Formulae</u>

  • Area of a rectangle = width × length
  • Area of a circle = πr²

To find the area of the lawn that is not watered, subtract the area of the 2 circles from the area of the rectangle.

From inspection of the diagram

  • width of rectangle = 2r
  • length of rectangle = 4r
  • area = 512 ft²

Substituting the values into the area of a rectangle formula, and solving for r:

⇒ 512 = 2r × 4r

⇒ 512 = 8r²

⇒ r² = 64

⇒ r = ±8

As distance is positive, r = 8 ft

Area of one circle = π8² = 64π  ft²

Therefore,

Area not watered = area of rectangle - 2 × area of circle

                             = 512 - 2(64π)

                             = 109.88 ft² (nearest hundredth)

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If the angle is preserved, which describes the effect of moving the plane closer to the cone's vertex? Check all that apply.
Sholpan [36]

Let's go though the choices.

Major axis will get shorter.  TRUE, CHECK ME

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Ellipse will become a circle.  FALSE

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Ellipse will degenerate to a point.  TRUE, CHECK ME

Eventually the plane gets to the vertex, at which point (ha!) we have a single point.

Nappes?  Is that a word?   FALSE

The plane needs a steeper angle, steeper than the generators, before it can pass through both halves.

The generators are the lines through the vertex that form the cone.  The plane isn't steep enough to hold any of them. FALSE

4 0
4 years ago
Given that m∠ABD = 84° and m∠BAC = 37°, what is the m∠ACD?
stich3 [128]

Answer: 84°

Step-by-step explanation:

Pardon my drawing, I know it;s not prefect, and I'm not sure how to draw a figure on Brainly, but this is the best I can do. For this problem, it is easier to draw it out so you can see that the angles look like. Just pretend the lines are filled in, and this is a perfect parallelogram.

       

      A   ________________ C

        /                                   /

      /                                  /

    /                                 /

B /_______________/ D

As you can see, the angles given in the problem gives us a parallelogram. Since we know m∠ABD is 84° and m∠BAC is 37°, we know that m∠ACD is 84°. If you draw diagonal lines, ∠ABD and ∠ACD are vertical angles. Vertical angles are congruent. Therefore, m∠ACD is 84°.

7 0
3 years ago
Determine whether the measures 2, √8, and √12 can be the measures of the sides of a triangle. If so, classify the triangle as ac
gtnhenbr [62]

Answer:

C

Step-by-step explanation:

First check if the triangle is right.

If the square of the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.

longest side = \sqrt{12} and (\sqrt{12} )² = 12

2² + (\sqrt{8} )² = 4 + 8 = 12

Thus the triangle is right → C

7 0
3 years ago
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kodGreya [7K]

Answer:

D

Step-by-step explanation:

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3 years ago
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Answer:

A

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