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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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With each candle having a volume of 216 cubic inches, I assign a radius to each: 0.5 in, 1.0 in, 1.5 in, 2.0 in, 2.5 in, 3.0 in, 3.5 in, and 4.0 in. Then, using the formula of the volume of a cylinder, which is:

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Hence, we will have the following heights (expressed to the nearest hundredths) for each of the radius: for 

r=2.5 in: h=11.01 in
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3 years ago
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vovikov84 [41]

Answer:

In the previous lesson, you learned how to graph points on the coordinate plane. We can connect two points with a straight line.

To graph the equation of a line, we plot at least two points whose coordinates satisfy the equation, and then connect the points with a line. We call these equations "linear" because the graph of these equations is a straight line.

There are two important things that can help you graph an equation, slope and y-intercept.

Slope

We're familiar with the word "slope" as it relates to mountains. Skiers and snowboarders refer to "hitting the slopes." On the coordinate plane, the steepness, or slant, of a line is called the slope. Slope is the ratio of the change in the y-value over the change in the x-value. Carpenters and builders call this ratio the "rise over the run." Using any two points on a line, you can calculate its slope using this formula.

Let's use these two points to calculate the slope m of this line.

A = (1,1) and B = (2,3)

Subtract the y value of point A from the y-value of point B to find the change in the y value, which is 2. Then subtract the x value of point A from the x value of point B to find the change in x, which is 1. The slope is 2 divided by 1, or 2.

When a line has positive slope, like this one, it rises from left to right.

WATCH OUT! Always use the same order in the numerator and denominator!

It doesn't really matter whether you subtract the values of point A from the values of point B, or the values of point B from the values of point A. Try it - you'll get the same answer both ways. But you must use the same order for both the numerator and denominator!

You can't subtract the y value of point A from the y value of point B, and the x value of point B from the x value of point A - your answer will be wrong.

Let's look at another line. This line has a negative slope, it falls from left to right. We can take any two points on this line and find the slope. Let's take C (0, -1) and D (2, -5).

Using these two points, we can calculate the slope of this line. We subtract the y value of point C from the y value of point D, and the x value of point C from the x value of point D, and divide the first value by the second value. The slope is -2.

Y-Intercept

There's another important value associated with graphing a line on the coordinate plane. It's called the "y intercept" and it's the y value of the point where the line intersects the y- axis. For this line, the y-intercept is "negative 1." You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This point will always have an x coordinate of zero. This is another way to find the y-intercept, if you know the equation, the y-intercept is the solution to the equation when x = 0.

Equations

Knowing how to find the slope and the y-intercept helps us to graph a line when we know its equation, and also helps us to find the equation of a line when we have its graph. The equation of a line can always be written in this form, where m is the slope and b is the y-intercept:

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Let's find the equation for this line. Pick any two points, in this diagram, A = (1, 1) and B = (2, 3).

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y = 2x –1

The line shows the solution to the equation: that is, it shows all the values that satisfy the equation. If we substitute the x and y values of a point on the line into the equation, you will get a true statement. We'll try it with the point (2, 3).

Let's substitute x = 2 and y = 3 into the equation. We get "3 = 3", a true statement, so this point satisfies the equation of the line.

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6 0
3 years ago
If a 3,500 investment earns 120 over 3 years, what is the annual rate?
Katarina [22]

Answer:

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Step-by-step explanation:

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