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4 years ago

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Find the first four nonzero terms of the taylor series about 0 for the function f(x)=x4sin(6x). note that you may want to find t

hese in a manner other than by direct differentiation of the function.

1 answer:

ziro4ka [17]4 years ago

4 0

The quickest way to get the series is if you already know the series for sine:

$\sin6x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^n(6x)^{2n+1}}{(2n+1)!}$

Then just multiply the series by $x^4$ to get

$f(x)=x^4\sin6x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^n6^{2n+1}x^{2n+5}}{(2n+1)!}$

The first four nonzero terms are simply the first four terms:

$6x^5-\dfrac{6^3}{3!}x^7+\dfrac{6^5}{5!}x^9-\dfrac{6^7}{7!}x^{11}$

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there are 150 more passenger cars than trucks on the highway. for every 10 passenger cars there are 7 trucks. how many trucks ar

lora16 [44]

Answer:

500

Step-by-step explanation:

Given: P = 150 - T where P is passenger cars and T is trucks

10P = 7T ⇔ P = $\frac{7T}{10}$

Plug in equation 2 into equation 1:

$\frac{7T}{10}$ = 150 - T

Solving for T, we get 500

5 0

3 years ago

Read 2 more answers

Solve the system by elimination 1: x+5y-4z=-10, 2x-y+5z=-9, 2x-10y-5z=0 .. . 2. Solve the system by substitution: 2x-y+z=-4, z=5

Kryger [21]

1 )
1st and 2nd equation (multiply 1st by -2 ):
-2x - 10 y + 8 z = 20
2 x - y + 5 z = -9
---------------------------
- 11 y + 13 z = 11 / * ( -20 )
1st and 3rd:
- 2 x - 10 y + 8 z = 20
2 x - 10 y - 5 z = 0
-----------------------------
- 20 x + 3 z = 20 / * 11
----------------------------------
220 y - 260 z = -220
- 220 y + 33 z = 220
------------------------------
z = 0, y = -1, x = - 5
2 )
2 x - y + 5 = -4
- 2 x + 3 y - 5 = - 10
Substitution: y = 2 x + 9
- 2 x + 3(2 x + 9 ) = -5
4 x = - 32, x = -8, y = -7, z = 5
3 )
x + y + z = 11
1.5 x+3 y +1.5 z = 21
x = 2 y
------------------------
3 y + z = 11 / * (-2)
6 y + 1.5 z = 21
------------------------
- 6 y - 2 z = -22
6 y + 1.5 z = 21
------------------------
-0.5 z = -1, z = 2, y = 3, z = 6
Answer: the store used 6 pounds of peanuts, 3 pounds of almonds and 2 pounds of raisins.

8 0

3 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

So

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

-140 divided by 5 1/2 then rounded to the nearest 10th of a foot

storchak [24]

Answer:

Step-by-step explanation:

8 0

3 years ago

Find the product. (x-3)^2

r-ruslan [8.4K]

Greetings and Happy Holidays!

Find the Product:
$(x-3)^2$

Expand:
$=(x-3)(x-3)$

Use FOIL or other techniques to solve binomial multiplication:
$=x(x-3)-3(x-3)$

$=x^2-3x-3(x-3)$

$=x^2-3x-3x+9$

Combine like terms:
$=x^2-6x+9$

The Answer Is:
$\boxed{=x^2-6x+9}$

I hope this helped!
-Benjamin

3 0

3 years ago