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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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151. Find the perimeter of this triangle
Lena [83]

The perimeter is the sum of all the sides of the figure⇒

<em><u>151</u></em>

P=a+b+c+d...

P=(y+9)+(3y+3)+(4y+6)=y+9+3y+3+4y+6=8y+18

<u><em>152</em></u>

<u><em></em></u>P=a+b+c+d...\\P=(4a-100)+(2a-15)+(2a+40)=4a-100+2a-15+2a+40=\\=8a-75<u><em></em></u>

<u><em></em></u>

<u><em>153</em></u>

You forgot to attach a photo

6 0
3 years ago
Thea has a key on her calculator marked $\textcolor{blue}{\bf\circledast}$. If an integer is displayed, pressing the $\textcolor
worty [1.4K]

Answer:

$9$

Step-by-step explanation:

Given: Thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again such that the calculator displays final number as $243$.

To find: number that Thea originally entered

Solution:

The final number is $243$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $243$ must be $324$.

As previously the number was squared, so the number before $324$ must be $18$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $18$ must be $81$

As previously the number was squared, so the number before $81$ must be $9$.

3 0
3 years ago
Geometry...halp QwQ......
nignag [31]
I am pretty sure that it is C.
7 0
3 years ago
Y=4(-1)+3<br> Linear Equations
rewona [7]

Your equation states y = 4(-1) + 3

Since the parentheses touch the number 4 which means you multiply, we will start with that first.

4 × -1 or 4(-1)  (it means the same thing) would be -4

Now let us combine the equation.

y = -4 + 3

The addition property is included now,

-4 + 3 = -1

Therefore, your answer would be y = -1


Hope this helped! :D

7 0
3 years ago
Which macaw has a mass closest to 1 kilogram?
Nataliya [291]

Answer:

green winged

Step-by-step explanation:

coz 1 kg = 1000g

and 900 is closer to 1000

7 0
3 years ago
Read 2 more answers
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