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Karolina [17]
3 years ago
11

Which algebraic rule describes the transformation? A) (x, y) → (−x, y) B) (x, y) → (x, −y) C) (x, y) → (−x, −y) D) (x, y) → (−y,

−x)
Mathematics
2 answers:
SOVA2 [1]3 years ago
8 0
The correct Answer is letter D.
Vaselesa [24]3 years ago
6 0
The answer is D) (X,Y) ---(-y-x)



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Answer:

Step-by-step explanation:

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Consider the top half of a sphere centered at the origin with radius r, which can be described by the equation

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\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx

Converting to polar coordinates will help make this computation easier. Set

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\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta

You should get

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