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wolverine [178]
3 years ago
15

Find the area of the region that lies inside the first curve and outside the second curve. r = 6 − 6 sin θ, r = 6

Mathematics
1 answer:
yan [13]3 years ago
8 0
Each curve completes one loop over the interval 0\le t\le2\pi. Find the intersections of the curves within this interval.

6-6\sin\theta=6\implies 1-\sin\theta=1\implies \sin\theta=0\implies \theta=0,\theta=\pi

The region of interest has an area given by the double integral

\displaystyle\int_\pi^{2\pi}\int_6^{6-6\sin\theta}r\,\mathrm dr\,\mathrm d\theta

equivalent to the single integral

\displaystyle\frac12\int_\pi^{2\pi}\bigg((6-6\sin\theta)^2-6^2\bigg)\,\mathrm d\theta

which evaluates to 9\pi+72.

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Len [333]

Answer:

I think D

Step-by-step explanation:

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2 years ago
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Pete can type 80 words in the same time that Ralph can type 50 words. If they type at those rates
tamaranim1 [39]

Answer:

After the extended period of time, Pete would have typed 6400  words.

Step-by-step explanation:

Given the data in the question;

In the same time;

number typed word of Pete = 80

type word of Ralph = 50

After a period time;

number of typed word of Pete = ?

number of typed word of Ralph = 4000

so, let x represent the number of typed word by Pete after an extended period.

so

80 words = 50 words

x words =    4000 words

we cross multiply

x × 50 = 4000 × 80

x = ( 4000 × 80 ) / 50

x = 320000 / 80

x = 6400

Therefore, After the extended period of time, Pete would have typed 6400  words.

3 0
3 years ago
The probability of an outcome that lies within 68% of the mean is a good indicator that it lies in which standard deviation?
kotegsom [21]
Yes the probability of an outcome that lies within 68% is a good indicator that lies in which standard deviation.

8 0
3 years ago
X/2-x=x/4+6<br> I need help but it’s not ASAP
Ivanshal [37]
Answer is -8
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7 0
2 years ago
If y= x+3/6-x, what is the value of y when x =7i?
djverab [1.8K]

Answer:

Option (2)

Step-by-step explanation:

Given :  y = \frac{x+3}{6-x}

If x = 7i

y = \frac{7i+3}{6-7i}

By simplifying denominator of the given rational expression,

y = \frac{7i+3}{6-7i}\times \frac{6+7i}{6+7i}

y = \frac{(7i+3)(6+7i)}{6^2-(7i)^2}

y = \frac{7i(6+7i)+3(6+7i)}{36-49i^2}

y = \frac{42i+49i^2+18+21i}{36+49} [Since, i² = (-1)]

y = \frac{63i-49+18}{85}

y = \frac{63i-31}{85}

y = -\frac{31}{85}+\frac{63}{85}i

Therefore, Option (2) is the correct option.

3 0
2 years ago
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