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choli [55]
3 years ago
10

A triangular prism has a triangular face with a base of 7 millimeters and a height of 4.6

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
3 0
13.1 milliliters i think
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The coefficients a_0,a_1,a_2,a_3 could be chosen to be the coefficients in the Maclaurin series of \sin(x).

We have

y = \sin(x) \approx a_0 + a_1 x + a_2 x^2 + a_3 x^3 \\\\ \implies y(0) = 0 = a_0

y' = \cos(x) \approx a_1 + 2a_2 x + 3a_3 x^2 \\\\ \implies y'(0) = 1 = a_1

y'' = -\sin(x) \approx 2a_2 + 6a_3 x \\\\ \implies y''(0) = 0 = 2a_2

y''' = -\cos(x) \approx 6a_3 \\\\ \implies y'''(0) = -1 = 6a_3

It follows that a_0=0, a_1=1, a_2=0, and a_3 = -\frac16.

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