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3 years ago

Determine the period of the function g(x) = (cos ;)

Mathematics

1 answer:

Romashka [77]3 years ago

5 0

Answer:

6 $\pi$

Step-by-step explanation:

The period of a sinusoidal function in the form a * cos (b (x + h)) + m is $\frac{2\pi }{|b|}$ . Therefore, we can see that "b" in g(x) is 1/3 and 1/3 substituted into $\frac{2\pi }{|b|}$ is 2 $\pi$ /1/3 which is 6 $\pi$ .

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First: State the degree and tell which monomial (term) you determined to be the one as the greatest degree. Second: Classify eac

kobusy [5.1K]

Answer:

$1.\text{ }7x^4+5x^2+x-9$

The term with the greatest degree is $7x^4$

The polynomial has degree 4 and is classified as a quadratic polynomial of 4 terms.

$2.\text{ }7x^6-4x^3+1/x$

It is not a polynomial.

Explanation:

Polynomials are expressions with terms composed of monomials.

A monomial is an expression formed by the product of a coefficient (constant numbers, like 3, 4/5, or even a root), and a literal part.

The literal part may consist of one or more letters and each letter may be raised to a non-negative integer number (positive or zero).

Hence, for instance, (2/9)x²y⁵z⁴³ is a monomial.

The given expressions are:

$1.\text{ }7x^4+5x^2+x-9$

$2.\text{ }7x^6-4x^3+1/x$

$1.\text{ }7x^4+5x^2+x-9$

This expression is a polynomial formed by 4 terms or monomials.

The monomials are:

$7x^4,\\ \\ 5x^2,\\ \\ x,\text{ }and\\ \\ 9$

The degrees of each monomial are:

$7x^4,\text{ }degree\text{ }4\\ \\ 5x^2,\text{ }degree\text{ }2\\ \\ x,\text{ }degree\text{ }1,\text{ }and\\ \\ 9\text{ }degree\text{ }0$

Thus, the one with the greatest degree is $7x^4$ . It defines the degree of the of the polynomial; hence the polynomial has degree four and is classified as quartic polynomial of four terms.

$2.\text{ }7x^6-4x^3+1/x$

This is not a polynomial, because the letter in the last term, i.e. 1/x has a negative power:

$1/x=x^{-1}$

As stated above, the powers have to be positive integers or zero (for the constant term).

Some special names used to classify the polynomials are:

Degree 1 – linear

Degree 2 – quadratic

Degree 3 – cubic

Degree 4 – quartic

Degree 5 – quintic

You can find other classifications in your book or in the internet.

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