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3 years ago

9)

Mathematics

2 answers:

makkiz [27]3 years ago

7 0

Answer: C. c+9/3

Step-by-step explanation:

You add the unknow varible C. with 9 and that sum is gong to be dived by 3 so 3 would be put on the bottom as the denominator.

snow_lady [41]3 years ago

3 0

C.c+9:/3 I think pls mark me the brainlest

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3(x-6)^2+4 in standard form

Nataly_w [17]

Answer:

$3x^2-36x+112$

Step-by-step explanation:

6 0

3 years ago

For the function defined by f(t)=2-t, 0≤t<1, sketch 3 periods and find:

Oksi-84 [34.3K]

The half-range sine series is the expansion for $f(t)$ with the assumption that $f(t)$ is considered to be an odd function over its full range, $-1$ . So for (a), you're essentially finding the full range expansion of the function

$f(t)=\begin{cases}2-t&\text{for }0\le t$

with period 2 so that $f(t)=f(t+2n)$ for $|t|$ and integers $n$ .

Now, since $f(t)$ is odd, there is no cosine series (you find the cosine series coefficients would vanish), leaving you with

$f(t)=\displaystyle\sum_{n\ge1}b_n\sin\frac{n\pi t}L$

where

$b_n=\displaystyle\frac2L\int_0^Lf(t)\sin\frac{n\pi t}L\,\mathrm dt$

In this case, $L=1$ , so

$b_n=\displaystyle2\int_0^1(2-t)\sin n\pi t\,\mathrm dt$
$b_n=\dfrac4{n\pi}-\dfrac{2\cos n\pi}{n\pi}-\dfrac{2\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{4-2(-1)^n}{n\pi}$

The half-range sine series expansion for $f(t)$ is then

$f(t)\sim\displaystyle\sum_{n\ge1}\frac{4-2(-1)^n}{n\pi}\sin n\pi t$

which can be further simplified by considering the even/odd cases of $n$ , but there's no need for that here.

The half-range cosine series is computed similarly, this time assuming $f(t)$ is even/symmetric across its full range. In other words, you are finding the full range series expansion for

$f(t)=\begin{cases}2-t&\text{for }0\le t$

Now the sine series expansion vanishes, leaving you with

$f(t)\sim\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi t}L$

where

$a_n=\displaystyle\frac2L\int_0^Lf(t)\cos\frac{n\pi t}L\,\mathrm dt$

for $n\ge0$ . Again, $L=1$ . You should find that

$a_0=\displaystyle2\int_0^1(2-t)\,\mathrm dt=3$

$a_n=\displaystyle2\int_0^1(2-t)\cos n\pi t\,\mathrm dt$
$a_n=\dfrac2{n^2\pi^2}-\dfrac{2\cos n\pi}{n^2\pi^2}+\dfrac{2\sin n\pi}{n\pi}$
$a_n=\dfrac{2-2(-1)^n}{n^2\pi^2}$

Here, splitting into even/odd cases actually reduces this further. Notice that when $n$ is even, the expression above simplifies to

$a_{n=2k}=\dfrac{2-2(-1)^{2k}}{(2k)^2\pi^2}=0$

while for odd $n$ , you have

$a_{n=2k-1}=\dfrac{2-2(-1)^{2k-1}}{(2k-1)^2\pi^2}=\dfrac4{(2k-1)^2\pi^2}$

So the half-range cosine series expansion would be

$f(t)\sim\dfrac32+\displaystyle\sum_{n\ge1}a_n\cos n\pi t$
$f(t)\sim\dfrac32+\displaystyle\sum_{k\ge1}a_{2k-1}\cos(2k-1)\pi t$
$f(t)\sim\dfrac32+\displaystyle\sum_{k\ge1}\frac4{(2k-1)^2\pi^2}\cos(2k-1)\pi t$

Attached are plots of the first few terms of each series overlaid onto plots of $f(t)$ . In the half-range sine series (right), I use $n=10$ terms, and in the half-range cosine series (left), I use $k=2$ or $n=2(2)-1=3$ terms. (It's a bit more difficult to distinguish $f(t)$ from the latter because the cosine series converges so much faster.)

5 0

4 years ago

A passenger jet flies at an average speed of 548 miles per hour. At that speed, how many miles does the plane travel in 4 hours?

marishachu [46]

The plane travels 2192 miles.

You’re multiplying 548 x 4 because the plane travels 548 an hour.

4 0

3 years ago

Let the base of a solid be the first quadrant region bounded by y=1-((x^2)/4), the x- axis and the y-axis. Suppose that cross se

barxatty [35]

Answer:

bjttkkhdvehakasgsgsbdhdndns thats the answer pick me brainliest

4 0

3 years ago

Calculate the missing measure of the line?

labwork [276]

Your answer would be 18.1 cm.

To find this length you have to notice that AC is the hypotenuse of the right-angled triangle ACD. This means that we can find it by using Pythagoras' Theorem (a² + b² = c²), however we need to find the length CD.

We can also find the length CD using Pythagoras' Theorem, because the length CD is the same as the base of the triangle at the top if the shape was split into a rectangle and a triangle.

The height of this triangle would be 11 - 4 = 7 cm, which means we can find CD by doing:

16² - 7² = 256 - 49 = 207 = CD²

Now we can find AC by doing √(CD² + 11²) = √(207 + 121) = √368 = 18.1

I hope this helps! Let me know if you have any questions :)

7 0

3 years ago

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