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The area of an ellipse with axes of length
2a and 2b is ab.
The percent change in the area when a increases by
2.74% and b increases by 2.65% is

Respuesta :

janmilczek

Answer:

The area increases by 5.46261%

Step-by-step explanation:

Well firstly, the area of an ellipse is not ab, but it's proportional to ab ([tex]\pi ab[/tex] where a and b are the semi-minor and semi-major axes).

This tells us that when a increases by 2.74% and b increases by 2.65% the new area will be:

[tex]A = \pi \cdot (a \cdot 102.74\%)(b \cdot 102.65\%) = \pi a b \cdot 102.74\% \cdot 102.65\% = \pi ab \cdot 105.46261\%[/tex]

raphealnwobi

The percentage change in area of the ellipse is 5.5%

The area of an ellipse with an axes of length  of 2a and 2b is πab.

Area of ellipse = πab

Since a increases by  2.74%, hence a = (100% + 2.74%)a = 1.0274a

Also, b increases by  2.65%, hence b = (100% + 2.65%)b = 1.0265b

Therefore the new area = π * 1.0274a * 1.0265b = 1.055πab

The ratio in the area = 1.055πab/ πab = 1.055

The percentage change in area of the ellipse is 5.5%

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