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1 year ago

6

Consider the equation Y=x^2-3 a) using the given input, complete the table by entering the corresponding ordered pairs separated

commas x, -2, -1, 0,1,2 y,_,_,_,_,_ b) Graph the equation by plotting the vertex and one other point

1 answer:

Marysya12 [62]1 year ago

3 0

Answer: I don't know

Step-by-step explanation:

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What is the circumference of a circle having a radius of 56 mm<br>

MArishka [77]

Answer:

circumference is πd

d=112mm

22/7*112

=352mm

Step-by-step explanation:

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3 years ago

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Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7

Zolol [24]

$f(x)=\begin{cases}1&\text{for }-7$

The Fourier series expansion of $f(x)$ is given by

$\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7$

where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
$a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2$

The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
$a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}$
$a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}$

When $n$ is even, the numerator vanishes, so we consider odd $n$ , i.e. $n=2k-1$ for $k\in\mathbb N$ , leaving us with

$a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}$

Meanwhile, the coefficients of the sine series are given by

$b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx$
$b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)$
$b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{7(-1)^{n+1}}{n\pi}$

So the Fourier series expansion for $f(x)$ is

$f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7$

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3 years ago

Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the

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<span>the answer was 8(1.25)^x </span>

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3 years ago

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Two cars leave Denver at the same time and travel in opposite directions. One car travels 10 mi/h faster than the other car. The

MaRussiya [10]

The speed of one car is 'S'. The speed of the other car is (S + 10).

In 5 hours, the first car travels (5S) miles, and the other car travels 5(S + 10) miles.

Since they're going in opposite directions, the distance between them at any time
is the sum of the distance that each one has traveled.

500 = (5S) + 5(S + 10)

500 = 5S + 5S + 50

500 = 10S + 50

Subtract 50 from each side:

450 = 10S

Divide each side by 10

S = <u>45</u>

S + 10 = <u>55</u>

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4 years ago

There are four classes of third graders at Woodbury Elementary School. One class has 24 students, one has 26 students, another h

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<span>The answer to this problem is B. 24 + 26 + 31 + 22. </span>

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3 years ago

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