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Ksenya-84 [330]
3 years ago
15

Find the series shown.

Mathematics
1 answer:
solmaris [256]3 years ago
8 0

Answer:

C 11+13+15+17+...

Step-by-step explanation:

Consider the series

\sum\limits_{n=3}^{\infty}(2n+5)

The nth term of series is a_n=2n+5

The bottom index tells you that n starts changing from 3, so

a_3=2\cdor 3+5=11\\ \\a_4=2\cdot 4+5=13\\ \\a_5=2\cdot 5+5=15\\ \\a_6=2\cdot 6+5=17\\ \\...

Thus, the sum of all terms is

11+13+15+17+...

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Which of the following is the weight of the cargo in a truck if 1/3 of the weight is 516 Ibs?
Anni [7]

Answer:

1548 lb

Step-by-step explanation:

Let the truck's weight be w.

Then (1/3)w = 516 lb

Solve for the truck's weight by multiplying both sides of this equation by 3:

w = 1548 lb (Answer B)

8 0
3 years ago
Suppose the claim size of an auto collision insurance, X, is uniformly distributed on the interval $1,000 to $10,000. What is th
timurjin [86]

Answer:

35.35%

Step-by-step explanation:

If there were no deductibles, the expected claim payment would be:

E(X) = \frac{10,000 +1,000}{2} \\E(X) =\$5,500

If the collision insurance claim is under $2,000, then the insurer would not pay anything, but if X > $2,000, then the insurer would pay X - $2,000. The new expected value is:

E_2(X)=\frac{2,000-1,000}{10,000-1,000} *0+\frac{10,000-2,000}{10,000-1,000}*\frac{(2,000-2,000)+(10,000-2,000)}{2} \\E_2(X)=\frac{8}{9}*\frac{0+8,000}{2}\\ E_2(X)=\$3,555.56

The percentage reduction on the claim payment is:

P=(1-\frac{E_2(X)}{E(X)})*100 \\P=(1-\frac{3,555.56}{5,500})*100\\P=35.35\%

There was a 35.35% reduction.

8 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
3 years ago
Write a word problem where the answer is 27 ¼.
svetlana [45]

a farmer poured 20 gallons of milk in a huge hole

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Later that day, he brought 1/4 gallon

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The correct answer is B) 11 years
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