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Kitty [74]
3 years ago
8

The diameter of a circle is 16 meters. What is the angle measure of an arc 6​ meters long?

Mathematics
1 answer:
noname [10]3 years ago
8 0

Answer:

42.99° or approx 43°

Step-by-step explanation:

Diameter of circle d = 16 m

Lenght of arc l= 6 m

Let the angle measure of the arc be \theta

By length of arc formula of a circle.

l =  \frac{ \theta}{360 \degree}  \times\pi d \\  \\ 6 = \frac{ \theta}{360 \degree}  \times 3.14 \times  \: 16 \\  \\  \theta =  \frac{6 \times 360 \degree}{3.14 \times 16}  \\  \\ \theta =  \frac{2160\degree}{50.24}  \\  \\ \theta = 42.9936306 \degree \\  \\ \theta = 42.99  \degree \approx \: 43  \degree

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Step-by-step explanation:

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Answer:

(x_1,y_1) = (1,5840)

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Step-by-step explanation:

Given:

x = weeks; y = copies

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(x_1,y_1) = (1,5840)

(x_2,y_2) = (5,13090)

Next, we calculate the slope (m) using:

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m = \frac{13090 - 5840}{5 - 1}

m = \frac{7250}{4}

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The equation is then calculated using:

y = m(x - x_1) + y_1

y = 1812.5(x - 1) + 5840

y = 1812.5x - 1812.5 + 5840

y = 1812.5x + 4027.5

To calculate the y intercept, substitute 0 for x

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Step-by-step explanation:

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A Ferris wheel has a diameter of 380 feet and the center of the wheel is 195 feet above the ground. The wheel makes a complete t
Aleksandr [31]

Answer:

<u><em>y = -190 cos(π t / 120) + 195</em></u>

Step-by-step explanation:

<em>General form of a sinusoidal function: y = A cos(Bt - C) + D </em>

<em> </em>

<em>Now generally a cosine function starts at the maximum value, so to start at the minimum value, flip the cosine function by making it negative. </em>

<em> </em>

<em>A is the amplitude of the curve and will be the radius of the ferris wheel. Therefore, A = 380 / 2 = 190 feet. </em>

<em> </em>

<em> 2π / B is the period of the curve and will be the time to complete one full rotation. The time to complete one full rotation is given as 4 minutes. Convert this into seconds to get period = 4 minutes * (60 seconds / minute) = 240 seconds. Therefore, B = 2π / period = 2π / 240 seconds = π / 120. </em>

<em> </em>

<em> C/B is the phase shift, or horizontal shift of the graph. Since the negative cosine function already starts at the minimum value, there is no phase shift so C/B = 0, meaning C = 0. </em>

<em> </em>

<em> D is the vertical shift and will be the height of the center of the ferris wheel. Therefore, D = 195 feet. </em>

<em> </em>

<em> Your final function will be:</em>

<u><em>y = -190 cos(π t / 120) + 195</em></u>

7 0
3 years ago
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