Which sequence is modeled by the graph below? coordinate plane showing the points 1, 1; 2, 2; 3, 4; and 4, 8

1 answer:

3 0

The points of the graph are: (1,1), (2,2), (3,4), (4,8).

Then the sequence is:

- for the x-coordinate: 1, 2, 3, 4, 5, 6, 7, ...

- for the y-coordinate: 1, 2, 4, 8, which is: 2^0, 2^1, 2^2, 2^ 3, ... so the next y-coordinates are 16, 32, 64, 128, ...

So, the sequence is: 1, 2, 4, ,8, 16, 32, .... 2^x.

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Approximately how many times as great is the volume of a grapefruit with a diameter 16 cm as the volume of a lime with a diamete

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Answer: The volume of the grapefruit is approximately 8 times as great as the volume of the lime.

Step-by-step explanation:

You need to use the formula for calculate the volume of a sphere. This is:

$V=\frac{4}{3}\pi r^3$

Where "r" is the radius.

<u>Volume of the grapefruit</u>

You know that its diameter is 16 centimeters.

Since the radius is half the diameter, you get that its volume is:

$V_g=\frac{4}{3}\pi (\frac{16\ cm}{2}) ^3\\\\V_g= 2,144.66\ cm^3$

<u> Volume of the lime</u>

According to the information given in the exercise, the diameter of the lime is 8 centimeters.

As it was explained above, the radius is half the diameter. Knowing that, you get that volume of the lime is the shown below:

$V_l=\frac{4}{3}\pi (\frac{8\ cm}{2}) ^3\\\\V_l= 268.08\ cm^3$

In order to find approximately how many times as great is the volume of theat grapefruit as the volume of that lime, you need to divide the volumes calculated above. Then:

$\frac{2,144.66\ cm^3}{268.08\ cm^3}\approx8\ times$