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marissa [1.9K]
3 years ago
14

What is the fifth term of the sequence whose first term is 10 and whose common ratio is 1/2?

Mathematics
1 answer:
Alborosie3 years ago
4 0

Answer:

\frac{5}{8}

Step-by-step explanation:

The n th term of a geometric sequence is

a_{n} = a₁(r)^{n-1}

where a₁ is the first term and r the common ratio

here a₁ = 10 and r = \frac{1}{2}, thus

a_{5} = 10 × (1/2)^{4} = 10 × \frac{1}{16} = \frac{5}{8}

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Oksana_A [137]

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13.54

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In Scott’s backyard, he has a windmill that makes 5 ¾ of a turn every hour. How many turns does it make for 1 ½ hours?
DanielleElmas [232]

Answer: 8 5/8 turns

Step-by-step explanation:

Hi, to answer this question we have to simply to multiply the number of turns that the windmill makes per hour (5 3/4) by the time asked (1 ½ hours).

Mathematically speaking:

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3 years ago
An object moves in simple harmonic motion with period 8 seconds and amplitude 6 cm. At time t = 0 seconds, its displacement d fr
Vladimir79 [104]

In the equation model, the simple harmonic motion is d=6sin(πt/4)-6 if the object moves in simple harmonic motion with a period of 8 seconds and amplitude of 6 cm.

<h3>What is simple harmonic motion?</h3>

Simple Harmonic Motion is described as a motion in which the restoring force is proportionate to the body's displacement from its mean position.

We have:

Amplitude A = 6 cm

Time period = 8 seconds

T = 2π/w

8 = 2π/w

w = π/4

Its displacement d from rest is -6 cm, and initially, it moves in a positive direction.

d(0) = -6 cm at t = 0

The equation becomes:

\rm d = 6sin(\dfrac{\pi}{4}t)-6

Thus, in the equation model, the simple harmonic motion is d=6sin(πt/4)-6 if the object moves in simple harmonic motion with a period of 8 seconds and amplitude of 6 cm.

Learn more about the simple harmonic motion here:

brainly.com/question/17315536

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Step-by-step explanation:

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B

Step-by-step explanation:

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