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4 years ago

Simplify the expression cos(x)cot(x)+sin(x) a. 0 b. csc(x) c. tan(x) d. sec(x)

Mathematics

1 answer:

Ilia_Sergeevich [38]4 years ago

6 0

Answer:

csc(x)

Step-by-step explanation:

cos(x)cot(x)+sin(x)

We know that cot(x) = cos(x)/ sin (x)

cos(x)cos(x)/ sin(x)+sin(x)

cos^2 (x)/ sin + sin (x)

Getting a common denominator

cos^2 (x)/ sin + sin (x)* sin (x)/ sin(x)

(cos^2(x) + sin^2(x)) /sin(x)

We know that (cos^2(x) + sin^2(x)) = 1

1/sin (x)

1/ sin (x) =csc(x)

csc(x)

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Step-by-step explanation:

The complete question is:

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for random sampleof 1044 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.44 hours with a standarddeviation of 0.57 hour. (A.) A histogram of time spent eating and drinking each day is skewed right. Use the result to explain why a large samplesize is needed to construct a confidence interval for the mean time spent eating and drinking each day.A. The distribution of the sample mean will never be approx. normalB. The distribution of the sample mean will always be approx. normalC. Since the distribution of time eating and drinking each is normally distributedthe sample must be large so that the distribution of the sample mean will be apprx. NormalD. Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be large so that the distribution of the sample mean will be approx. normal.

(B) In 2010, there were over 200 million people nationally age 15 or older. Explain why this, along with the fact that that the data were obtained using a random sample, satisifies the requirements for constructing a confidence interval.A. The sampe size is greater than 5% of the population.B. The sample size is less than 10% of the populationC. The sample size is greater than 10% of the populationD. The sample size is less than 5% of the population.

(C.) Determine and interpret a 95% confidence interval for themean amount of time Americans age 15 older spend eating and drink each day.A. the nutritionist is 95% confident that the mean amount of time spent eatingand drinking per day is between blank and blank hours.B. the nutritionist is 95% confident that the amount of time spent eating or drinking per day forany individuals is between blank and blank hours.C. There is a 95% probability that the meant amount of time spent eating or drinking per day is between blank and blank hours.D. The requirements for constructing a confidence interval are not satisfied.

(D) Could the interval be used to estimate the mean amount of time a 9 year old spends eating and drinking each day?A. No, the interval is about individual time spent eating or drinking per day and cannot be used to find the mean time spent eating or drinking per day.B. No the intreval is about people age 15 or older. The mean amount of time spent eatinf or drinking per day for 9 year olds may differ.C. Yes, the interval is about individual time spent eating or drinking per dat and can be used to find the mean amount of time a 9 year old spends eating and drinking each day.D. Yes, the interval is about the mean amount of time spent eating or drinking per day for the 9 year olds.E. A confidence interval could not be constructed in part (C)D

A) a large sample size ensures normal distribution

B) a good sample size is around 10% of the population

C) confidence interval is a range of value and defines probability that mean of the population will lie with in the range

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Can someone please help me with my math homework?

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For asymptotes, we need to consider when a function becomes undefined.
Such examples include x = 0 as the denominator.

Vertical asymptotes are merely stated when an x-ordinate allows the function to become undefined. They are the easiest of the two to solve. Let's consider the first example:

$y = \frac{1}{x} - 3$

In this case, we know that x is the denominator. So when the x-ordinate hits 0, there are no y-values to associate with the function. Hence, we know there is a vertical asymptote at x = 0.

Horizontal asymptotes are defined when a certain value of y makes the function undefined. They are usually harder to find and can be time-consuming. The easiest way to identify horizontal asymptotes is by taking limits or dividing a function.

Notice how our first section is 1/x. For harder polynomic functions, we would do something called long division of polynomials. But for this instance, let's divide the top and bottom of the fraction by x and take the limit as x approaches positive and negative infinite.

After division, we would get something like this:

$y = \frac{1/x}{1} - 3$

Now, as x approaches positive infinity, our fraction would get closer and closer to zero, so at x = infinity, our y value would be -3
At x = negative infinity, our y value would remain as -3.

So at x = infinity, we would yield y = -3, which is our horizontal asymptote.

So, VA: x = 0
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