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2 years ago

Find the general solution of y''' + 6y'' + y' − 34y = 0 if it is known that y1 = e−4x cos(x) is one solution.

Mathematics

1 answer:

SashulF [63]2 years ago

3 0

Answer:

Step-by-step explanation:

Given is a differential equation of III order,

$y''' + 6y'' + y' - 34y = 0$

The characteristic equation would be cubic as

$m^3+6m^2+m-34=0$

By trial and error, we find that

$f(2) = 2^3+6(2^2)+2-34 =0\\$

Thus m=2 is one solution

Since given that $e^{-4x} cos x$ is one solution we get

m = -4+i and hence other root is conjugate $m=-4-i$

Hence general solution would be

$y=Ae^{2x} +e^{-4x} (Bcosx +C sinx)$

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A study of immunizations among school‑age children in California found that some areas had rates of unvaccinated school‑age chil

Rom4ik [11]

Answer:

Probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.

Step-by-step explanation:

We are given that a classroom of 20 children in one such area where 13.5% of children are unvaccinated.

If there are no siblings in the classroom, we are willing to consider the vaccination status of the 2020 unrelated children to be independent.

The above situation can be represented through binomial distribution;

$P(X=r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,......$

where, n = number of trials (samples) taken = 20 children

r = number of success = none of the 20 children

p = probability of success which in our case is probability that

children are unvaccinated, i.e; p = 13.5%

Let X = Number of children that are unvaccinated

So, X ~ Binom(n = 20, p = 0.135)

Now, Probability that none of the 20 children in such a classroom would be unvaccinated is given by = P(X = 0)

P(X = 0) = $\binom{20}{0} \times 0.135^{0} \times (1-0.135)^{20-0}$

= $1\times 1 \times 0.865^{20}$

= 0.055

Hence, the probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.

8 0

2 years ago

Simplify!!! I need help please

satela [25.4K]

Answer:

$\frac{4^{21}}{5^{6}}$

Step-by-step explanation:

$\frac{4^{7*3}}{5^{2*3}}=\frac{4^{21}}{5^{6}}$

3 0

2 years ago

Ellen thinks that if a line has no slope, then it never touches the y-axis. Which line proves that her statement is incorrect?

galina1969 [7]

Answer:

Option D

Step-by-step explanation:

A horizontal line has no slope. The equation 'y=1' graphs as a horizontal line. It passes (0,1). So, it touches the y-axis.

A line with an undefined slope does not touch the y-axis. It is vertical.

Option D should be the correct answer.

4 0

2 years ago

Craig has $1850 dollars in a bank account that he uses to make automatic payments of $400.73 on his car loan. If Craig stops mak

Ivenika [448]

Given:

Amount in the bank account = $1850

Monthly payment of can loan = $400.73

To find:

When would automatic payments make the value of the account zero?

Solution:

Craig stops making deposits to that account. So, amount $1850 in the bank account is used to make monthly payment of can loan.

On dividing the amount by monthly payment, we get

$\dfrac{1850}{400.73}=4.61657$

It means, the amount is sufficient for 4 payment but for the 5th payment the amount is not sufficient.

Therefore, the 5th automatic payments make the value of the account zero.

6 0

2 years ago

The Community Relief Fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 s

asambeis [7]

The question is incomplete:

The Community Relief Fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 sweaters, $5 books. They want to buy 200 items and send them to schools in earthquake-hit areas. They must order as many books as school bags and sweaters combined. How many of each item should they order?

Answer:

They must order 40 bags, 60 sweaters and 100 books.

Step-by-step explanation:

From the information provided, you can write the following equations:

x+y+z=200 (1)

20x+25y+5z=2800 (2)

z=x+y (3), where:

x=amount of bags

y=amount of sweaters

z=amount of books

Now, you can replace (3) in (1) and (2):

x+y+x+y=200

2x+2y=200 (4)

20x+25y+5(x+y)=2800

20x+25y+5x+5y=2800

25x+30y=2800 (5)

Then, you will have 2 equations:

2x+2y=200 (4)

25x+30y=2800 (5)

You can isolate x in (4):

2x=200-2y

x=100-y (6)

After this, you can replace (6) in (5):

25(100-y)+30y=2800

2500-25y+30y=2800

5y=2800-2500

y=300/5

y=60

Next, you can replace the value of y in (6) to find the value of x:

x=100-60

x=40

Finally, you can replace the value of x and y in (3) to find the value of z:

z=40+60

z=100

According to this, the answer is that they must order 40 bags, 60 sweaters and 100 books.

7 0

2 years ago