Advanced Placement (AP) High School

A spring has a function a (t) = 4 cos (π/3 t) What is its period?

A.0s
B.2s
C.4s
D.6s

Answers

Answer 1

The period of the function is 6s. The correct option is (D).

Understanding Period of a Function

The period of a function is the time it takes for the function to complete one full cycle.

For a sine function, the period is given by:

T = 2π/ω

Also for cosine function, we can express the period as:

T = 2π/ω

where T is the period, and ω is the angular frequency.

The angular frequency is related to the frequency, f, by the equation

ω = 2πf.

Going back to the question given, the function is:

a(t) = 4 cos (π/3 t)

Since the angular frequency is ω = π/3, so the period is:

T = 2π/ω = 2π/(π/3) = 6

Therefore, the period of the function is 6 seconds, so the answer is D.

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Related Questions

If a fair die is rolled 5 times what is the probability rounded to the nearest thousand of getting at least 4 sixes

Answers

The likelihood of getting at least 4 sixes when a fair die is rolled five times, rounded to the nearest thousand, is probability - 3240/7776 = 41% [approx.]

The probability of an occurrence, as used in science, is a figure that expresses how likely it is to take place. A number between 0 and 1 or a percentage between 0% and 100% are both acceptable forms of representation in mathematical notation.

An event's likelihood increases with its probability. Depending on whether something is conceivable or not getting , an event's likelihood can range from 0 to 1.

In both A and B, there is a one in one chance that two linked occurrences, A and B, will occur simultaneously.

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Song: Lovers Rock - TV Girl

Why do you think the artist named the song what they did?

What is the attitude of the speaker/singer?

Identify important tools and turns

What do you think the main theme or message of the song is?

Answers

The artist named the song in the way they did to pass a metaphorical message.

Why do you think the artist named the song what they did?

The attitude of the singer is one of regret and one who wants to mend a relationship. Note that attitude is reflected in the tone of the lyrics.

The them of the song is Love Gone sour.

Note that Metaphors and tones are tools in literature that are used for expression of thought and communication of central idea.

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The European Union (EU) is an alliance among several countries in Europe. Which of the following is true about the EU? (1 point)
A- It is an economic superpower that rivals the United States.
B- The alliance has lifted trade boundaries, but the trade revenue has remained the same.
C- The European member countries entered the agreement with little hesitation.
D- The members have pledged military allegiance to one another.
E- Its global influence is parallel to Australia.

Answers

B- The alliance has lifted trade boundaries, but the trade revenue has remained the same is true about the EU.

How do price controls set by the federal government help consumers during a time of high inflation?

They set a maximum price for products or services and also set a minimum amount on how much an employee can be paid for work. The government sets a specific price on all products and services. The government sets a specific salary for all jobs. The government gives corporations money to keep prices low.

Answers

Price controls set by the federal government help consumers during a time of high inflation by setting a maximum price for products or services. This ensures that prices do not rise too high, making goods and services more affordable for consumers. By limiting price increases, price controls can help prevent runaway inflation, which can be damaging to the economy and to consumers' purchasing power. However, it's worth noting that price controls can also have negative effects, such as creating shortages or reducing incentives for businesses to produce goods or services. Therefore, price controls should be used cautiously and in combination with other economic policies to promote stability and growth. The government does not set a minimum amount on how much an employee can be paid for work or give corporations money to keep prices low as part of price controls.
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