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steposvetlana [31]
3 years ago
9

What is .65% of 160? show your work?

Mathematics
1 answer:
photoshop1234 [79]3 years ago
7 0
65/100 ×160 =104 is the answer
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Graph the relation shown in the table. Is the relation a function? Why or why not?
dezoksy [38]

Answer:

Not a function fails the vertical line test

Step-by-step explanation:

This is not a function.  The value of x = -1  goes to two different values of y

This would fail the vertical line test

4 0
2 years ago
Read 2 more answers
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
A flagpole sits on top of a 25 foot tall building. The building is exactly 3 times the height of the flagpole, h, minus 5 feet.
Aleonysh [2.5K]
I got 6.66666 infinite, so 6.7
3 0
3 years ago
Read 2 more answers
I need helpppppppppppp
ratelena [41]
The answer to question 3 is D. 15(4a+3). And the answer to question 4 is A. 90. Have a great day
7 0
2 years ago
1. The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies
Lorico [155]
1.) <span>the ratio of the note A to middle C = 440.0 / 261.6 = 1.6820 ≈ 1.6818

2.) </span><span>the ratio of the note D to middle C = 293.7 / 261.6 = 1.1227

3.) </span><span>D# = 293.6 x 1.0595 = 311.1

4.) </span><span>the ratio of the frequency of G to C is 1 : 262/392 = 1 : 0.6683 ≈ 3 : 2

5.) </span><span>the ratio of the frequency of E to C = 1 : 262/330 = 1 : 0.7939 ≈ 5 : 4

6.) The </span><span>component in a musical note is referred to as the pitch of a sound is the frequency.</span>
8 0
2 years ago
Read 2 more answers
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