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Naddika [18.5K]
3 years ago
14

???????????????????????

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
8 0

Answer: %15.6

your answer is %15.625. rounded to %15.6 because, the question says to round to the nearest tenth of a percent

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Find a power series representation of e^x sin(x)
liberstina [14]
The Taylor series is defined by:
f(x) = \sum \frac{f^n (a)}{n!} (x-a)^n

Let a = 0.
Then its just a matter of finding derivatives and determining how many terms is needed for the series.

Derivatives can be found using product rule:
f^n (x) = e^x g^{n-1} (x) + e^x g^n (x)  \\ g^0 (x) = sin x

Do this successively to n = 6.
f^1 (x) = e^x (sinx +cos x) \\ f^2 (x) = e^x (2cos x)  \\ f^3 (x) = e^x(2cos x - 2sin x)  \\ f^4 (x) = e^x (-4 sin x)  \\ f^5 (x) = e^x(-4sinx -4cos x) \\ f^6(x) = e^x(-8cos x)

Plug in x=0 and sub into taylor series:
e^x  sin x = x+x^2 +\frac{x^3}{3} -\frac{x^5}{30}-\frac{x^6}{90}...

If more terms are needed simply continue the recursive derivative formula and add to taylor series.
6 0
4 years ago
You roll a​ six-sided die. Find the probability of each of the following scenarios. ​(a) Rolling a 5 or a number greater than 3.
sertanlavr [38]

Answer:

Step-by-step explanation:

a.

let A= number 5

B=number >3

P(A)=1/6  {5}

P(B)=3/6  {4,5,6}

p(A∩B)=1/6   {5}

P(AUB)=P(A)+P(B)-P(A∩B)=1/6+3/6-1/6=3/6=1/2

b.

let  event C=number<5

D=even number

C=[1,2,3,4}

D={2,4,6}

C∩D={2,4}

P(C)=4/6

P(D)=3/6

P(C∩D)=2/6

P(C∪D)=P(C)+P(D)-P(C∩D)=4/6+3/6-2/6=5/6

c.

let event E=number 2

F= an odd number.

E={2}

F={1,3,5}

E∩F={}

P(E)=1/6

P(F)=3/6

P(E∩F)=0

P(E∪F)=P(E)+P(F)-P(E∩F)=1/6+3/6-0=4/6=2/3

7 0
3 years ago
500 reduced my 2 times my age is 300
never [62]

Answer:

Very interesting observation

~ Maria

Step-by-step explanation:

3 0
4 years ago
Read 2 more answers
​One-third of a number is 1 more than ​one-fourth of the same number.<br> What is the number?
konstantin123 [22]

Answer:

  12

Step-by-step explanation:

1/3 of 12 = 4

1/4 of 12 = 3

4 is 1 more than 3.

The number is 12.

_____

If this does not immediately come to mind, you can solve for the number, x:

  x/3 -x/4 = 1 . . . . the difference between 1/3 of x and 1/4 of x is 1

  x/12 = 1 . . . . . . . collect terms: (1/3 -1/4 = 4/12 -3/12 = 1/12)

  x = 12 . . . . . . . . multiply by 12

7 0
4 years ago
Evaluate 10^0 20 points
Karo-lina-s [1.5K]

Answer:

1

Step-by-step explanation:

8 0
3 years ago
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