For what values of theta (0
r=-3 + 4 cos(theta)? Note that the maximum r-value occurs at a point that is the maximum distance from the pole.

,

Step-by-step explanation:

The determination of the maximum can be done with the help of the First and Second Derivative Tests. The first and second derivatives of the function are, respectively:

First Derivative Test

Given the periodicity of the function, there are multiple solutions. The set of solutions is represented by:

,

Second Derivative Test

There are multiple solutions. If is an odd number, then cosine is negative and output is positive, which means that associated value is an absolute minimum. Otherwise, if is zero or an even number, the cosine is positive and output is negative, which means that associated value is an absolute minimum. Consequently, the values of so that is a maximum are:

,

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours

b

step-by-step explanation: