Consider the ellipse x^2+4y^2=1 in the xy plane.
a. of this ellipse is revolved about the x-axis, what is the equation of the resulting ellipsoid?
b. if this ellipse is revolved about the y-axis, what is the equation of the resulting ellipsoid?

  a.  x² +4y² +4z² = 1

  b.  x² +4y² +z² = 1

Step-by-step explanation:

a. In "intercept form", the given equation can be written as ...

  (x/1)² + (y/(1/2))² = 1

When the ellipse is revolved around the x-axis, the z-intercept will match the y-intercept, so the equation becomes ...

  (x/1)² + (y/(1/2))² + (z/(1/2))² = 1

  x² +4y² +4z² = 1

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b. Likewise, revolving the figure around the y-axis will make the z-intercept the same as the x-intercept. That equation is ...

  x² + 4y² +z² = 1

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See the attachments. The first shows revolution about the x-axis; the second shows revolution about the y-axis.

1353 people

Step-by-step explanation:

There are 26 letters in the English alphabet. Therefore there are 26*26 = 676 unique possible combinations there are for the baggage tagging. In the best case scenario, there are 676 different bags in which no bag have the same tagging initials on them. The 677th bag would have the same tagging initial on them as 1 of the previous 676 bag, making this the minimum number to guarantee 2 bags to have the same tagging initial.

Similarly, for the 3 bags to have the same tagging initials, the minimum number required would be 676*2 + 1 = 1353 bags or people