So, if it triples its length every ten minutes and you want to know its length in forty minutes, you multiply one millimeter by three, letting you know its 10 minute point (3 mm). Keep multiplying it by three until you get to the answer you need to! 3 x 3 = 9 (20 min), 9 x 3 = 12 (30 min), 12 x 3 = 36 mm (40 min). Hope I've helped!
Not equivalent expression is validated so I think it’s second one bye
Answer:
C. the diameter would be 10 making the answer 10pi
Step-by-step explanation:
the diameter would be 10 making the answer 10pi
2(5)pi
10pi
I assume there's a plus sign missing above...
Convert to polar coordinates, using
![\begin{cases}x(r,\theta)=r\cos\theta\\y(r,\theta)=r\sin\theta\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%28r%2C%5Ctheta%29%3Dr%5Ccos%5Ctheta%5C%5Cy%28r%2C%5Ctheta%29%3Dr%5Csin%5Ctheta%5Cend%7Bcases%7D)
Then the Jacobian is
![\dfrac{\partial(x,y)}{\partial(r,\theta)}=\begin{vmatrix}x_r&y_r\\x_\theta&y_\theta\end{vmatrix}=\begin{vmatrix}\cos\theta&\sin\theta\\r\sin\theta&-r\cos\theta\end{vmatrix}=-r](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%28x%2Cy%29%7D%7B%5Cpartial%28r%2C%5Ctheta%29%7D%3D%5Cbegin%7Bvmatrix%7Dx_r%26y_r%5C%5Cx_%5Ctheta%26y_%5Ctheta%5Cend%7Bvmatrix%7D%3D%5Cbegin%7Bvmatrix%7D%5Ccos%5Ctheta%26%5Csin%5Ctheta%5C%5Cr%5Csin%5Ctheta%26-r%5Ccos%5Ctheta%5Cend%7Bvmatrix%7D%3D-r)
Then
![\mathrm dA=\mathrm dx\,\mathrm dy=|-r|\,\mathrm dr\,\mathrm d\theta=r\,\mathrm dr\,\mathrm d\theta](https://tex.z-dn.net/?f=%5Cmathrm%20dA%3D%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D%7C-r%7C%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%3Dr%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta)
so the integral can be written as
![\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^5r\sin(r^2)\,\mathrm dr\,\mathrm d\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_R%5Csin%28x%5E2%2By%5E2%29%5C%2C%5Cmathrm%20dA%3D%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_1%5E5r%5Csin%28r%5E2%29%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta)
Let
![s=r^2](https://tex.z-dn.net/?f=s%3Dr%5E2)
, so that
![\dfrac{\mathrm ds}2=r\,\mathrm dr](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20ds%7D2%3Dr%5C%2C%5Cmathrm%20dr)
.
A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.
Step-by-step explanation:
The inequality is given as;
-3x-7<20 which can be solved as
-3x < 20+7 -----collecting like terms
-3x < 27 -------divide both sides by -3
x > -9 -----change the sign direction because you divided by
plotting the solution x > -9 on a graph tool gives
Learn More
solving inequalities by graph :brainly.com/question/11688212
Keywords : number line, open circle, solution, graph, inequality
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