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jeka57 [31]
2 years ago
15

The following diagram represents all of the stages of a shrinking iceberg. The iceberg is circular, and when it started out, it

had a radius of 100 feet. The iceberg shrank to a radius that was 75% of its original size every hour. Each circle in the drawing represents the size of the iceberg in each of the successive hours it was shrinking. Using this information, answer the questions having to do with the image:
a. Is this a geometric series or an arithmetic series? Explain why you chose this answer.
b. Describe the steps you would use to calculate the radius of the 6th circle.
c. Assuming this pattern continued forever, what would be the total length if you added all of the circles’ radii* together? Explain your answer.

Mathematics
1 answer:
S_A_V [24]2 years ago
8 0

A <em>geometric progression</em> is a <u>sequence</u> that involves a rate, causing a change in the <u>subsequent</u> values of the <em>sequence</em> with respect to the given rate.

The <u>answers</u> to the given question are as follows:

a. It is a<em> geometric progression</em>.

b. <u>Radius</u> of the 6th circle ≅ 23. 73 ft.

c. The <em>total length</em>, l, can be determined by: l = ∑0.75R_{i}, i = 1 to n.

<em>Geometric progression</em> involves a <u>change</u> in the subsequent values of a given <u>sequence</u> due to a rate. So considering the given question, the circular iceberg <em>melts</em> at a certain <u>rate</u> per hour. Thus its <em>radius</em> decreases at the given <em>rate</em> per hour.

a. Therefore it can be deduced that the question is on<em> geometric progression</em>.

b. To determine the radius of the 6th circle, the:

radius of the 1st circle = 100 ft

radius of the 2nd circle = 0.75 x 100

                                        = 75 ft

radius of the t3rd circle = 0.75 x 75

                                        = 56.25 ft

radius of the 4th circle = 0.75 x 56.25

                                         = 42.1875 ft

radius of the 5th circle = 0.75 x 42.1875

                                        = 31.640625 ft

radius of the 6th circle = 0.75 x 31.640625

                                      = 23.73046875 ft

Thus the<u> radius</u> of the 6th circle is approximately <em>23. 73 ft</em>.

c. Since the process is assumed to continue forever, let the <u>number</u> of hours required to be represented by<u> n</u>, and each <em>radius</em> of the iceberg be represented by<em> R</em>.

So then, we can say that the <em>total length</em>, l, of all the circles' radii is will be given by:

              l = ∑0.75R_{i}, i = 1 to n

For more clarification on geometric progression, visit: brainly.com/question/26147596

#SPJ1

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