If the circumference of a circle is 36, what is the length of an arc of the circle intercepted by a central angle of 30 degrees?

Step-by-step explanation:

The formula for calculate the arc lenght is:

Where "r" is the radius and "" is the central angle of the arc in degrees.

The formula used to find the circumference of a circle is:

Where "r" is the radius.

Then, we can observe that the formula for calculate the arc lenght can be rewritten in this form:

Where "C" is the circumference of the circle.

Finally we need to substitute the central angle and the circumference into . Then the result is this:

the answer is ! ?

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt