2. -8n - 17 + 19n

What is the approximate length of arc s on the circle below? 330 degrees central angle radius 12 feet

Aneli [31]

Answer:

$69.08\ ft$

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

$C=2\pi r$

we have

$r=12\ ft$

substitute

$C=2\pi (12)$

$C=24\pi\ ft$

step 2

Find the approximate length of arc s

we know that

The circumference of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the length of arc for a central angle of 330 degrees

$\frac{24\pi}{360}=\frac{x}{330}\\\\x=24\pi(330)/360$

$x= 22\pi\ ft$ ----> exact value

assume

$\pi =3.14$

$22\pi\ ft=22(3.14)=69.08\ ft$ ----> approximate value

3 0

3 years ago

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

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

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:

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

<u>Second derivative test</u>

(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.

3 0

3 years ago

What are two decimals whose product is close to 10?

Elanso [62]

3.162 and 3.162. (3.162 is the rounded square root of 10)

5 0

4 years ago

Can someone help me

Rama09 [41]

If x and y vary inversely, then xy = const.

x = 10, y = 8

$xy=10\cdot8\\\\xy=80\ \ \ \ |:x\\\\\boxed{y=\dfrac{80}{x}}$

4 0

3 years ago

A __________ is a claim or assertion either about one or more population or process characteristics (parameters) or else about t

Vladimir [108]

Answer:

statistical hypothesis.

Step-by-step explanation:

A statistical hypothesis has the central objective of assisting in a decision-making process about one or more populations in relation to the sample data, allowing the observance of whether the information found in the samples will support the statistical hypothesis.

It is necessary to know concepts of mathematical probability to perform the tests, the most used models for this purpose are the fisher method, by Neyman-Pearson and Bayes.

The variables used in a statistical hypothesis are: the Null Hypothesis, the one that is assumed to be the true one, the Alternative Hypothesis, the one that is used when there is no statistic to analyze the hypothesis given as true, the Type I Error, related to the probability of rejection of the null hypothesis, and the Type II Error, which is the probability of rejection of the alternative hypothesis if it is true.

6 0

3 years ago

2. -8n - 17 + 19n - 4 = -41