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vampirchik [111]
3 years ago
10

The perimeter of a square is 96 inches. if the side length is 2x + 4, what is the value of x and the length of each side?

Mathematics
1 answer:
andriy [413]3 years ago
4 0
Subtract 4 from 96 and divide by 2
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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
3 years ago
2x + 16y + z = 7<br> x+2y-z = -1
Georgia [21]

Answer:

ㅎ 포토 타임 왔습니다

Step-by-step explanation:

по поводу того что бы не можете дозвониться не смогла найти

5 0
1 year ago
20 PTS!! PLEASE HELP
Levart [38]

Answer:

It may be D, correct me if i'm wrong.

Step-by-step explanation:

We already know that the majority of students will go to a college based on somebody else going to that college. With that in mind, we can draw a cause-and-effect conclusion summarizing why they want to choose that college (Because there friend) and the effect as there friend goes to that college.

8 0
2 years ago
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What is the unit rate for 16 ounces (pint) at $3.93?
Juli2301 [7.4K]

Answer:

25 cents/ounce

Step-by-step explanation:

The unit rate means how much is one of the thing you are working with.  In this case, the unit rate of a pint (16 ounces) is how much just one ounce will cost.  So divide $3.93 by 16

$3.93/16 =  $0.245625

Since we're working with money, round to the nearest hundredth

Unit rate is $0.25 per ounce, or 25 cents per ounce

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3 years ago
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PLS HELP WILL MAKE FIRST RIGHT ANSWER BRAINLIEST ​
Amanda [17]

Answer: -8 is the answer.

Step-by-step explanation:

according to the question:

{{(8+4)*5}/(-10)}-2

= {[12*5}/(-10)]-2

= [60/(-10)]-2

= -6-2 = -8

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2 years ago
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