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Alex73 [517]
2 years ago
9

The floor of a new planetarium is a circle with a 13-yard diameter.A stage will occupy a quarter circle section of the floor.The

material for the stage will cost $31.47 per square yard. If no material is wasted when making the stage,how could you find how much the stage will cost? Use 3.14
Mathematics
1 answer:
Naddik [55]2 years ago
5 0

Answer:

<h3>$1,043.74</h3>

Step-by-step explanation:

Area of the circular floor = πr²

Since the stage only occupies a quarter circle section of the floor, then;

Area of the stage = πr²/4

Given

diameter of the floor = 13yd

radius = 13/2 = 6.5yd

Find the area of the stage;

Area of the stage = π(6.5)²/4

Area of the stage = 3.14(42.25)/4

Area of the stage = 33.16625yd²

If the material for the stage will cost $31.47 per square yard, this means;

1yd² = $31.47

33.16625yd² = x

Cross multiply

x = 33.16625*31.47

x = 1,043.74

Hence the stage will cost $1,043.74

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The coordinates of point F are (15/4 , -5/2)

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<h3>What is the coordinates  about?</h3>

From the image attached:

AB divided into 4 similar parts, hence

  • E is the mid-point of AB
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Note that the rule of the mid-point states that:

When M (x , y) is the mid-point of the segment of AB, where A (x1 , y1)  and B (x2 , y2), Then  x = (x1 + x2)/2 and that of  y = (y1 + y2)/2

Then lets solve for points E, F, D

Since A (-3 , -1) and B (6 , -3),

E is the mid-point of AB

Then  E =[(-3 + 6)/2, (-1 + -3)/2]

         = (3/2 , -2)

Since  F is the mid-point of EB,

         E (3/2 , -2) , B (6 , -3)

Then F = [(3/2 + 6)/2 , (-2 + -3)/2]

       = (15/4 , -5/2)

Since D is the mid-point of AE, A (-3 , -1), E (3/2 , -2)

Then  D = [(-3 + 3/2)/2 , (-1 + -2)/2]

           = (-3/4 , -3/2)

Note also that:

 BC is said to be an  horizontal segment due to the fact that B and C have similar y - coordinate and G can be found on BC.

Since the y-coordinate of G is similar to y-coordinate of B and C

Then  y-coordinate of G is =  -3

Since DG ⊥ BC

Then DG =  vertical segment

So  G has similar x-coordinate of D

Then  The x-coordinate of G = -3/4

The  G = (-3/4 , -3)

Learn more about coordinate from

brainly.com/question/12481034

#SPJ1

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