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3 years ago

Which represents the polynomial written in standard form? 4m – 2m4 – 6m2 + 9

2 answers:

4 0

-2m^4 - 6m^2 +4m +4
standard form for polynomials is written with the highest degree first followed by second highest and so on from there.

OlgaM077 [116]3 years ago

3 0

Answer:

Step-by-step explanation:

Alright, lets get started.

The given polynomial is : $4m-2m^4-6m^2+9$

In the standard form, the highest power term is written first

Then second highest power is written and follows the same rule further

Here the highest power term is $-2m^4$

The second highest power term is $-6m^2$

The third highest power term is $4m$

Last term is 9

So, the standard form is :

$-2m^4-6m^2+4m+9$ : Answer

Hope it will help :)

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4 years ago

Give the number to which the Fourier series converges at a point of discontinuity of f.

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Answer:

The Fourier series of f(x) converges to 3 at the points x= π+2kπ, where k is an integer.

Step-by-step explanation:

First, recall that the function f(x) is extended 2π periodic to the whole real line, in order to obtain a valid Fourier expansion. Remember that a Fourier series is formed by a sines and cosines, which are 2π-periodic.

So, the 2π-periodic expansion of f(x) is discontinuous at the points π+2kπ, in particular π and -π. Check the attached figure to a better understanding.

Now, the Dirichlet theorem on the convergence of a Fourier series tells us that the series converges to the function at the points of continuity, and at points of discontinuity the sum of the series is

$\frac{f(x_0+)+f(x_0-)}{2}$ .

Here we understand the notation $f(x+)$ and $f(x-)$ as

$f(x_0+) = \lim_{x\rightarrow x_0}f(x), x>x_0$

and

$f(x_0-) = \lim_{x\rightarrow x_0}f(x), x$ .

In this particular case

$f(\pi-) = \lim_{x\rightarrow \pi}(3-2x) = 3-2\pi, x$ .

For the limit $f(\pi+) = \lim_{x\rightarrow \pi}(3-2x)$ , with $x>\pi$ recall that our function is 2π-periodic, so the values of f near π, with x>π are the same when x is near -π and x>-π. Again, check the attached figure. So,

$f(\pi+) = \lim_{x\rightarrow \pi}(3-2x) = 3+2\pi, x$ .

Thus,

$\frac{f(\pi+)+f(\pi-)}{2} = \frac{3+2\pi +3-2\pi}{2} = \frac{6}{2} =3$ .

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3 years ago

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3 years ago

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3 years ago

For a fundraiser, Hailey raises $27, plus 1.50 for each lap she swims. What was the total amount raised by each swimmer after sw

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Question is Incomplete; Complete Question is given below;

For a fundraiser, Hailey raises $27, plus 1.50 for each lap she swims. Tariana raises $18, plus $3 for each lap she swims what is the total amount raised by each swimmer after swimming laps. after how many laps would the two swimmers have raised the same amount of money?

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If they swim 6 laps they would raise same amount of money.

The Total amount of money they raised is $36 after 6 laps.

Step-by-step explanation:

Let number of laps swim by the swimmers be x

Given:

Hailey raises $27, plus 1.50 for each lap she swims.

Hence It means amount raised by Hailey is the sum of $27 and 1.50 multiplied by Number of laps she swim.

Framing in equation form we get;

Amount of Money raised by Hailey = $27+1.5x$