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3 years ago

Find the 10th term 3,15,75,375

Mathematics

1 answer:

vova2212 [387]3 years ago

5 0

Answer:

5859375

Step-by-step explanation:

These are the terms of a geometric sequence with n th term

$a_{n}$ = $a_{1}$ $r^{n-1}$

where r is the common ratio and $a_{1}$ the first term

here r = $\frac{375}{75}$ = $\frac{75}{15}$ = $\frac{15}{3}$ = 5 and $a_{1}$ = 3, hence

$a_{10}$ = 3 × $(5)^{9}$ = 5859375

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Answer:

The answer is below

Step-by-step explanation:

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: A linear model with ordered pairs at 0, 60 and 2, 75 and 4, 75 and 6, 40 and 8, 20 and 10, 0 and 12, 0 and 14, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet. Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points) Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points) Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points) Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds.

Answer:

Part A:

Between 0 and 2 seconds, the height of the balloon increases from 60 feet to 75 feet at a rate of 7.5 ft/s

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Between 2 and 4 seconds, the height stays constant at 75 feet.

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Between 4 and 6 seconds, the height of the balloon decreases from 75 feet to 40 feet at a rate of -17.5 ft/s

Between 6 and 8 seconds, the height of the balloon decreases from 40 feet to 20 feet at a rate of -10 ft/s

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Hence it fastest decreasing rate is -17.5 ft/s which is between 4 to 6 seconds.

Part D:

From 10 seconds, the balloon is at the ground (0 feet), it continues to remain at 0 feet even at 16 seconds.

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