MATHEMATICS HIGH SCHOOL

A particle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 4sin(t) - cos(2t), measured in feet. What is the acceleration of the particle at time t = 0 seconds?

Answers

Answer 1

Answer:

The acceleration of the particle at time t = 0 seconds is:

4 feet per square second.

i.e. 4 ft/s²

Step-by-step explanation:

We are given a position function in terms of the time t as:

$s(t)=4\sin (t)-\cos (2t)$

Now, we are asked to find the acceeleration of the particle at time t = 0 seconds.

We know that the acceleration of a particle is given by:

$a=(d)/(dt)v$

where v is the velocity of the particle which is calculated by:

$v=(d)/(dt)s$

Hence, we get:

$a=(d)/(dt)((d)/(dt)s)\n\ni.e.\n\na=(d^2)/(dt^2)s\n\ni.e.\n\na=s''(t)$

i.e. the acceleration of the particle is the double derivative of the position.

$s'(t)=4\cos (t)+2\sin (2t)$

and

$s''(t)=-4\sin (t)+4\cos (2t)$

i.e.

$a(t)=-4\sin (t)+4\cos (2t)\n\ni.e.\ at\ t=0\ we\ have:\n\na(0)=-4\sin 0+4\cos 0\n\ni.e.\n\na(0)=4$

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Identify the sample chosen for the study. The number of hours a group of 12 children in Mrs. Smith's kindergarten class sleep in a day. Answer2 Points The 12 children selected in Mrs. Smith's kindergarten class. All children in Mrs. Smith's kindergarten class. The number of hours children sleep.

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Answer:

The 12 children selected in Mrs. Smith's kindergarten class.

Step-by-step explanation:

A sample is a representative part of a population on which a research is carried out.

The study In Mrs Smith's class was to find out the number of hours the children in Kindergarten Sleep in a day. Out of the total number of students, 12 were selected for observation. The 12 childen selected is therefore a sample of the class.

Final answer:

The sample in the study refers to the 12 children in Mrs. Smith's kindergarten class. A sample is a subset of people selected from a larger group for study purposes. In this research, the data being analyzed only pertains to these selected individuals.

Explanation:

In this study, the sample chosen is the group of 12 children in Mrs. Smith's kindergarten class. This is because the data being collected and scrutinized is related to these particular individuals. In this context, 'sample' refers to the subset of people chosen from a larger group (the population) for research or study purposes. It is the set of individuals on which the study or experiment is conducted. In this case, the larger population could be considered all children in kindergarten, but the sample for the study is specifically the 12 children in Mrs. Smith's class, as the study only includes their sleep patterns.

Learn more about Sample in a study here:

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In a game for 24 groups, the average number of children was 16. When one more group of children was formed to join in the game, the average number of children became 18. The number of boys to girls who had just joined in the game was in the ratio 5:6. If there were 220 boys at first, how many more boys than girls were in the end?

Answers

Answer:

50 boys

Step-by-step explanation:

The number of groups = 24

The average number of children = 16

The new average number of children when one group is added = 18

The ratio of boys to girls in the group that just joined = 5:6

The initial number of boys = 220

Let the initial number of children

The initial total number of children = 24 × 16 = 384

The initial number of girls = 384 - 220 = 164

The final number of children = 25 × 18 = 450

The number of children in the group that joined in the game = 450 - 384 = 66

The ratio of boys to girls in the group = 5:6

Therefore, we get;

The number of boys = 66 × 5/11 = 30

The number of girls = 66 - 30 = 36

The number of boys at the end = 220 + 30 = 250

The number of girls at the end = 164 + 36 = 200

The number of more boys than girls at the end = 250 - 200 = 50

The number of more boys than girls at the end = 50 boys

CORRECT ANSWER WILL BE MARKED BRAINLIEST! plz help with question!Find the constant rate of change for the representation.
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Answer:

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