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elena-s [515]
2 years ago
13

Roy made a pizza that is 12 inches in diameter. He knows he can eat about 84.8 in, at what angle should Roy cut the pizza in rad

ians? Round your answer to the tenths place.
Mathematics
1 answer:
kolbaska11 [484]2 years ago
8 0

Answer:

Cutting angle in radian θ = 3π / 2

Step-by-step explanation:

Given:

Diameter of pizza = 12 inch

He can eat = 84.8 inch²

Find:

Cutting angle in radian

Computation:

Radius of pizza = Diameter of pizza / 2

Radius of pizza = 12 / 2

Radius of pizza = 6 inch

Area of sector = [θ/360][πr²]

Area of sector = [θ/360][(π)(6)²]

84.8 = [θ/360][(π)(36)]

θ = 270°

θ = 270[π/180]

θ = 27π / 18

Cutting angle in radian θ = 3π / 2

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Let's work on the left side first. And remember that
the<u> tangent</u> is the same as <u>sin/cos</u>.

sin(a) cos(a) tan(a)

Substitute for the tangent:

[ sin(a) cos(a) ] [ sin(a)/cos(a) ]

Cancel the cos(a) from the top and bottom, and you're left with

[ sin(a) ] . . . . . [ sin(a) ] which is [ <u>sin²(a)</u> ]  That's the <u>left side</u>.

Now, work on the right side:

[ 1 - cos(a) ] [ 1 + cos(a) ]

Multiply that all out, using FOIL:

[ 1 + cos(a) - cos(a) - cos²(a) ]

= [ <u>1 - cos²(a)</u> ] That's the <u>right side</u>.

Do you remember that for any angle, sin²(b) + cos²(b) = 1  ?
Subtract cos²(b) from each side, and you have sin²(b) = 1 - cos²(b) for any angle.

So, on the <u>right side</u>, you could write [ <u>sin²(a)</u> ] .

Now look back about 9 lines, and compare that to the result we got for the <u>left side</u> .

They look quite similar. In fact, they're identical. And so the identity is proven.

Whew !





4 0
3 years ago
Read 2 more answers
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tensa zangetsu [6.8K]
0.63 is the correct answer
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2 years ago
For every 10 flowers,there are 36 butterflies resting on the flower with the same number on each flower .How many butterflies ar
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Answer:

I don't know if this is right or not, but here's what I think.

There are 36 butterflies on each flower.

Step-by-step explanation:

<u>Question:</u>

For each 10 flowers, there are <u>36 butterflies resting on the flower</u> with the same number on each flower. How many butterflies are on one flower​?

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2 years ago
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Underline all the ordered pairs (x,y) that are solutions to the equation y=2x+1.
Romashka [77]

Answer:

<u>(3,7)</u> (7,3) (−1,14) <u>(0,1)</u> <u>(12,25)</u>

<u>(5,11)</u> (0,12) (1,8) (12,0) <u>(−1,−1)</u>

Step-by-step explanation:

We have the following function:

y = 2x+1.

We are going to check if each ordered pair is a solution.

(3,7)

If when x = 3, y = 7, it is a solution.

y = 2x + 1 = 2(3) + 1 = 7

This ordered pair is a solution.

(7,3)

If when x = 7, y = 3, it is a solution.

y = 2x + 1 = 2(7) + 1 = 15

This ordered pair is not a solution.

(-1,14)

If when x = -1, y = 14, it is a solution.

y = 2x + 1 = 2(-1) + 1 = -1

This ordered pair is not a solution.

(0,1)

If when x = 0, y = 1, it is a solution.

y = 2x + 1 = 2(0) + 1 = 1

This ordered pair is a solution.

(12,25)

If when x = 12, y = 25, it is a solution.

y = 2x + 1 = 2(12) + 1 = 25

This ordered pair is a solution.

(5,11)

If when x = 5, y = 11, it is a solution.

y = 2x + 1 = 2(5) + 1 = 11

This ordered pair is a solution.

(0,12)

If when x = 0, y = 12, it is a solution.

y = 2x + 1 = 2(0) + 1 = 1

This ordered pair is not a solution.

(1,8)

If when x = 1, y = 8, it is a solution.

y = 2x + 1 = 2(1) + 1 = 3

This ordered pair is not a solution.

(12,0)

If when x = 12, y = 0, it is a solution.

y = 2x + 1 = 2(12) + 1 = 25

This ordered pair is not a solution.

(-1,-1)

If when x = -1, y = -1, it is a solution.

y = 2x + 1 = 2(-1) + 1 = -1

This ordered pair is a solution.

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3 years ago
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