Suppose xy=4 and dy/dt=-2. Find dx/dt when x=-3

2 answers:

4 0

We are given with the expression xy = 4. The first derivative of the x is dx/dt while that of y is dy/dt. in this case using the multiplication rule of differentiation and that of constants, x dy/dt + y dx/dt = 0. when x= -3, y should be -4/3. Hence when dy/dt = -2, -3(-2) -4/3 *dx/dt = 0. dx/dt is equal to 9/2.

nirvana33 [79]3 years ago

3 0

Dy/dx = dy/dt * dt/dx

xy = 4

y + x(dy/dx) = 0 by implicit differentiation.

x(dy/dx) = -y

dy/dx = -y/x

dy/dx = dy/dt * dt/dx dy/dt = -2

-y/x = -2 * dt/dx

y/(2x) = dt/dx

dt/dx = y/(2x)

dx/dt = 2x/y

When x = -3, xy = 4, y = 4/x = 4/-3 = -4/3

dx/dt = 2*-3/(-4/3) = -6 *-3/4 = 18/4 = 9/2 = 4.5

dx/dt = 4.5

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46.67% probability that they flew with airline B.

Step-by-step explanation:

We have these following probabilities:

A 40% probability that a traveler chooses airline A.

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A 25% probability that a traveler chooses airline C.

If a passenger chooses airline A, a 10% probability that he arrives late.

If a passenger chooses airline B, a 15% probability that he arrives late.

If a passenger chooses airline C, a 8% probability that he arrives late.

If a randomly selected traveler is on a flight from Seattle which arrives late to Sydney, what is the probability that they flew with airline B?

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

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P(B) is the probability that he flew with airline B.

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