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otez555 [7]
3 years ago
15

What is the exponent on 10 when you write 5.3 in scientific notation

Mathematics
1 answer:
Alex3 years ago
8 0

It's 1. Because 5.3 can't be simplified to any other scientific notation. It's 5.3 x 10^1
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I need with this. Someone help please.
seraphim [82]

Answer:

In the ATTACHMENT

Step-by-step explanation:

For the first one, you can plug in multiple numbers of any kind for x and start to form you line.

For the second one, know that the y line is always horizontal. Find -3 on the plot that would be on the y-axis and put that horizontal line on it.

<em>Hope this helps!!</em>

4 0
3 years ago
What is the value of c in the equation below?
Flauer [41]

Answer:

are the values of a or b given?

Step-by-step explanation:

6 0
3 years ago
For the function defined by f(t)=2-t, 0≤t&lt;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
Paul bags of raisin bars in a pan shaped like a rectangle or prism the volume of the pan is 252 in.³ the length of the pants 12
e-lub [12.9K]

Answer:

The height of the pan is 2 inches.

Step-by-step explanation:

Given : Paul bags of raisin bars in a pan shaped like a rectangle or prism the volume of the pan is 252 in.³ the length of the pants 12 inches and it's with is 10\frac{1}{2} inches.

To find : What is the height of the pan ?

Solution :

The volume of a rectangle or prism is

V=l\times w\times h

Where, l=12 inches is the length

w=10\frac{1}{2} inches is the width

V=252 in.³ is the volume

h is the height

Substitute the value,

252=12\times 10\frac{1}{2}\times h

252=12\times \frac{21}{2}\times h

h=\frac{252\times 2}{12\times 21}

h=2

Therefore, the height of the pan is 2 inches.

7 0
3 years ago
Pls help asap! It’s due in one hour!!
AfilCa [17]
1. t = 7
2. t = 0
i think? although I’m not 100% sure
8 0
2 years ago
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