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3 years ago

Determine whether the function is periodic. If it is periodic, find the period.

Mathematics

1 answer:

kkurt [141]3 years ago

7 0

Answer:

The period is 2pi

Step-by-step explanation:

A function is said to be periodic if there exists a T for which f(x+T)=f(x). In this case, the function is f(x) =7sin^3(x).

The period of sin(x) = 2pi. Then, in this case, no matter if the sin is elevated to a power of three, the period will remain the same.

Let's prove it:

f(x) =7sin^3(0) = 0

f(0 + 2pi) = f( 2pi) = 7sin^3(2pi) = 0.

Then, there exists a T for which f(x+T)=f(x) and it's T=2pi.

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For an angle θ, tan(θ) is a negative number. Which quadrants might θ be in?

Klio2033 [76]

So for this question, we're asked to find the quadrant in which the angle of data lies and were given to conditions were given. Sign of data is less than zero, and we're given that tangent of data is also less than zero. Now I have an acronym to remember which Trig functions air positive in each quadrant. . And in the first quadrant we have that all the trig functions are positive. In the second quadrant, we have that sign and co seeking are positive. And the third quadrant we have tangent and co tangent are positive. And in the final quadrant, Fourth Quadrant we have co sign and seeking are positive. So our first condition says the sign of data is less than zero. Of course, that means it's negative, so it cannot be quadrant one or quadrant two. It can't be those because here in Quadrant one, we have that all the trick functions air positive and the second quadrant we have that sign. If data is a positive, so we're between Squadron three and quadrant four now. The second condition says the tangent of data is also less than zero now in Quadrant three. We have that tangent of data is positive, so it cannot be quadrant three, so our r final answer is quadrant four, where co sign and seek in are positive.

4 0

2 years ago

Read 2 more answers

Let X denote the time from the present until the stock market hits 25,000. If X ≤ 1, you win $10, 000X. If X > 1, you win not

const2013 [10]

Answer: $6321

Step-by-step explanation:

Expected value is given as exactly what you might think it means intuitively, the return you can expect for some type of action.

The basic expected value formula is the probability of an event multiplied by the amount of times the event happens:(P(x) * n).

he formula for the Expected Value for a binomial random variable is:

P(x) * X.

X is the number of trials and P(x) is the probability of success.

The formula for calculating the Expected Value where there are multiple probabilities is:

E(X) = ∑X * P(X)

The equation is basically the same, but here you are adding the sum of all the gains multiplied by their individual probabilities instead of just one probability.

Calculating the expected value of winning as follows:

Given,

Fx= e^-x, x is greater or equal to 0

Now, P less than or equal to zero =

[-e^-x] ^1

e^-0 - e^-1

= 1 - e^-1

= 0.6321

and P(x>1) = 1-0.6321= 0.3679

Therefore,Let y= amount of winnings.

Based on the above given information,

y= $10000 0

P(y)= 0.6321 0.3679

The expected value of winning:

E(y) = ΣyP(y)

E(y) = 10000 × 0.6321 + 0 × 0.3679

E(y) = $6321

Therefore, the expected value of winning is $6321

5 0

3 years ago

Samantha works at an animal shelter. She decides to track the total number of kittens that are brought in. The equation k=4w+3 r

mel-nik [20]

Answer:

Step-by-step explanation:

The equation $k=4w+3$ represents the total number of kittens, where $w$ represents <u>the number of weeks that have passed since Samantha started counting.</u>

This means options C and D are false, because they say <u>the total number of kittens that have come into the shelter</u>.

$w$ represents the number of weeks, weeks can be counted 0 weeks, first week, second week and so on, so option B is true (the domain is all whole numbers) because 0, 1, 2, 3, ... are whole numbers.

Number of weeks can't be a negative number. Since "real numbers" include negatives, therefore, we exclude option A.

7 0

3 years ago

Which statements accurately describe the function f(x) = 3(16)^3/4? Check all that apply.

uysha [10]

Answers:

These are the statements that apply:

The initial value is 3.

The range is y >0.

The simplified base is 8.

Explanation:

1) Given expression:

$f(x)=3(16)^{\frac{3}{4} x$

2) Check every statement:

a) The initial value is 3?

initial value ⇒ x = 0 ⇒

$f(0)=3(16)^{0}=3(1)=3$

∴ The statement is right.

b) The initial value is 48?

Not, as it was already proved that it is 3.

c) The domain is x > 0?

No, because the domain of the exponential functions is all the Real numbers.

d) The range is y > 0?

That is correct, the exponential function is continuous, and monotonon increasing.

The limit when x → - ∞ is zero, but y never reaches zero, and the limit when x → ∞ is + ∞, meaning that the range is y > 0.

e) The simplified base is 12?

This is how you simplify the base:

$3(16)^{\frac{3}{4} x}=3{{(16}^{(3/4)})}^x=3(16^{3/4}})^{x}=3((2^4)^{3/4})^x=3(2^3)^x=3(8)^x$

Which shows that the simplified base is 8 (not 12).

f) The simplified base is 8?

Yes; this was just proved.

6 0

3 years ago

Read 2 more answers

Based on the graph, which inequality is correct for a number that is to the right of -3?

Firdavs [7]

Answer:

4 > −3

Step-by-step explanation:

To find a number to the right of -3, it must be bigger than -3

The open part of the inequality faces the bigger number.

4 is bigger than -3

4>-3

3 0

3 years ago