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3 years ago

B/ Evaluate e^(πi/2)

Engineering

2 answers:

ivanzaharov [21]3 years ago

8 0

Explanation:

≈4.8

There really isn't an elegant way to express it. Just plug and chug for irrationals raised to other irrationals.

Lilit [14]3 years ago

7 0

You get a result immediately from Euler's formula:

e ^(i π/2) = cos(π/2) + i sin(π/2) = 0 + i * 1 = i

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If the specific surface energy for aluminum oxide is 0.90 J/m2 and its modulus of elasticity is (393 GPa), compute the critical

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Answer:

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Explanation:

given data

specific surface energy = 0.90 J/m²

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to find out

critical stress required for the propagation

solution

we will apply here critical stress formula for propagation of internal crack

( σc ) = $\sqrt{\frac{2E\gamma s}{\pi a}}$ .....................1

here E is modulus of elasticity and γs is specific surface energy and a is half length of crack i.e 0.3 mm = 0.3 × $10^{-3}$ m

so now put value in equation 1 we get

( σc ) = $\sqrt{\frac{2E\gamma s}{\pi a}}$

( σc ) = $\sqrt{\frac{2*393*10^9*0.90}{\pi 0.3*10^{-3}}}$

( σc ) = 27.396615 × $10^{6}$ N/m²

so critical stress required for the propagation is 27.396615 × $10^{6}$ N/m²

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