Question

a cepheid variable star is a star whose brightness alternately increases and decreases. suppose that cephei joe is a star for which the interval between times of maximum brightness is 4.4 days. its average brightness is 4.5 and the brightness changes by /-0.4. using this data, we can construct a mathematical model for the brightness of cephei joe at time t, where t is measured in days:

Answer 1

After one day, the rate of increase in Delta Cephei's brightness is;0.46

We are informed that the function has been used to model the brightness of the star known as Delta Cephei at time t, where t is expressed in days;

B(t)=4.0+3.5 sin(2πt/5.4)

Simply said, in order to determine the rate of increase, we must determine the derivative of the function that provides

B'(t)=(2π/5.4)×0.35 cos(2πt/5.4)

Currently, at t = 1, we have;

B'(1)=(2π/5.4)×0.35 cos(2π*1/5.4)

Now that the angle in the bracket is expressed in radians, we can use a radians calculator to determine its cosine, giving us the following results:

B'(1)=(2π/5.4)×0.3961

B'(1)≈0.46

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