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4 years ago

A circle with circumference 8, has an arc with a 288 degree central angle. What is the length of the arc?

2 answers:

8 0

We know that
the circumference C=2*pi*r
C=8 units

if 360° (full circle) has a length of-----------> 8 units
288°---------------------------> x
x=288*8/360-------> x=6.4 units

the answer is
6.4 units

ValentinkaMS [17]4 years ago

8 0

Answer:
length of arc = 6.4 units

Explanation:
The length of the arc can be calculated using the following formula:
length of arc = 2π * radius * $\frac{angle}{360}$ 

Taking a look at the equation and comparing it with the given, we would find that:
2π*r is the equation for calculating the circumference.
We are given that the the circumference of the circle is 8 units
theta is the angle subtended by the arc = 288°

Substitute with the givens in the above equation to get the length of the arc as follows:
length of arc = 8 * $\frac{288}{360}$ 
length of arc = 6.4 units

Hope this helps :)

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Answer:

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Step-by-step explanation:

The diagnal length of the orchard is the hypotenuse of the triangal with side lengths of 36 and 18.

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Answer:

The expected value is $38.46.

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3 years ago

Which of the following describes theoretical probability?

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Assume that it costs Apple approximately E(x) 25,600 + 100x + 0.012 dollars to manufacture x 32GB iPods in a day. (a) The averag

uranmaximum [27]

Answer:

(a) $C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)x=1600, Minimum Average Cost Per iPod=$132

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

Step-by-step explanation:

Given that it costs Apple approximately $ C(x) to manufacture x 32GB iPods in a day, where:

$C(x)=25,600+100x+0.01x^2$

(a)The average cost per iPod when they manufacture x iPods in a day is given by:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}$

The average cost per iPod is therefore:

$C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)To minimize average cost of x iPods per day, we set the average cost per iPod=0 and solve for x.

$C'(x)=\dfrac{x^2-2560000}{x^2}=0\\x^2-2560000=0\\x^2=2560000\\x=\sqrt{2560000}=1600$

The resulting minimum average cost (at x=1600) is given as:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}\\\dfrac{25,600+100(1600)+0.01(1600)^2}{1600}\\=\$132$

Second derivative test

(c)The answer above is a critical point for the average cost function. To show it is a minimum, we calculate the second derivative of the average cost function.

$C''(x)=\dfrac{5120000}{x^3}$

At the critical point, x=1600

$C''(1600)=\dfrac{5120000}{1600^3}=0.00125$

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

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FrozenT [24]

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