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MrRissso [65]
2 years ago
8

The measure of an exterior angle of a triangle is equal to which of the following measures?​

Mathematics
1 answer:
Korolek [52]2 years ago
5 0

Measures of sum of the two opposite angles.

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The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati
makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\

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y = 2-x \,\,\,\,\,,  1 \leq x \leq 2.

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{\displaystyle A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51 }

And if you rotate the second region around the "y" axis you get that

{\displaystyle A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188 }

And the sum would be  2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first  region around the x axis you get that

{\displaystyle A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708 }

And if you rotate the second region around the x axis you get that

{\displaystyle A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472 }

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3 years ago
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Troyanec [42]
1 glass of juice cost $3

1 glass of limonade costs $2


So the proportion between them (Orange) / (juice) = 3/2 or 3¹/₂
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