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If x = 3 cos ⁡ t and y = 5 sin ⁡ t , where t is a parameter, then 9 d 2 y d x 2 at t = - π 6 is equal to

Correct answer

40

Step-by-step solution

d y d x = d y d t d x d t = 5 cos ⁡ t - 3 sin ⁡ t = - 5 3 c o t t d 2 y d x 2 = - 5 3 ⋅ - c o s e c 2 t ⋅ d t d x = 5 3 1 sin 2 ⁡ t 1 - 3 sin ⁡ t = 5 9 8

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