40.53 grams divided by 25.5ml rounded to the nearest hundredth

Mathematics

1 answer:

stiks02 [169]3 years ago

6 0

Hi!

Your answer should be: 2.00 (or 2).

Hope this helps!

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Find the radius and the center of the circle with the given equation x^2+y^2−8x−2y=48.

Semmy [17]

Step-by-step explanation:

x²+y²−8x−2y=48

the radius => √[(8/2)² + (2/2)² +48] =

√(16+1+48) =√65

the center => (8/2, 2/2)

=> (4, 1)

5 0

2 years ago

(6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Use an iterated integral to compute the vo

kipiarov [429]

Let $R$ be the ellipsoid with equation

$\left(\dfrac xa\right)^2+\left(\dfrac yb\right)^2+\left(\dfrac zc\right)^2=1$

so that the volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV$

Consider the augmented spherical coordinates given by the identities

$\begin{cases}x=ar\cos u\sin v\\y=br\sin u\sin v\\z=cr\cos v\end{cases}$

Computing the Jacobian, we find that the volume element is given by

$\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=abcr^2\sin v\,\mathrm dr\,\mathrm du\,\mathrm dv$

so that the volume integral can be written as

$\displaystyle\iiint_R\mathrm dV=abc\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\int_{r=0}^{r=1}r^2\sin v\,\mathrm dr\,\mathrm du\,\mathrm dv=\frac{4abc\pi}3$