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Problem 20)

Problem 21)

A)

The velocity function is:

The acceleration function is:

B)

Step-by-step explanation:

Problem 20)

We want to differentiate the equation:

We can take the natural log of both sides. This yields:

Since ln(aᵇ) = bln(a):

Take the derivative of both sides with respect to x:

Implicitly differentiate the left and use the product rule on the right. Therefore:

Simplify:

Simplify and multiply both sides by y:

Since y = (cos x)ˣ:

Problem 21)

We are given the position function of a particle:

A)

Recall that the velocity function is the derivative of the position function. Hence:

Differentiate:

The acceleration function is the derivative of the velocity function. Hence:

Differentiate:

B)

The position at t = 0 will be:

The velocity at t = 0 will be:

And the acceleration at t = 0 will be:

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x