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Find the complementary function to the second order differential equation d^2y/dx^2 - 5dy/dx + 6x = x^2

Use the auxiliary equation k 2 -5k+6=0. Solving this gives roots k=2 and k=3, which are real and distinct roots. This means that the complementary function is of the form y=Ae^(k 1 x)+Be^(k 2 x), where k 1 a...
SM
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If y^3 = 8.08, approximate y.

Firstly, recognize that 2^3 is 8, so y must be close to 8.It will be helpful to then write y^3 as y^3= 8 + 0.08We can then factorize out 8.y^3=8(1+0.01)If we try and take the cube root of this expression.y=2...
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Answered by Sanjith H. • Maths tutor
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Explain the role of Miles Davis as a soloist and band leader in 'Round Midnight'.

From the outset of the piece we see Miles Davis as the leader of the quintet as his solo kicks off the track. The role that Davis has is to set the tempo for the rest of the piece as he is the first musician...
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Answered by Amber H. • Music tutor
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Explain how a fish is adapted for gas exchange?

A fish had gills, made up of gill filaments containing lamellae, which provide a very large surface area for oxygen to diffuse out of the water as it moves over them. The blood vessels are in very close prox...
Answered by • Biology tutor
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How do anti-bumping granules work?

Anti-bumping granules prevent explosive boiling, as they provide a large surface area for bubbles to form on.
Answered by • Chemistry tutor
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