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3 years ago

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The function yp=3x2+4x is a particular solution to the nonhomogeneous equation y′′−6y′+9y=27x2−18 Find the general solution of t

he nonhomogeneous equation y′′−6y′+9y=27x2−18. (Hint: you need yc.)

1 answer:

olya-2409 [2.1K]3 years ago

8 0

Answer:

$y(x)==(c_1+c_2x)e^{3x}+3x^2+4x$

Step-by-step explanation:

We are given that non-homogeneous equation

$y''-6y'+9y=27x^2-18$

Particular solution of given equation is given by

$y_p=3x^2+4x$

We have to find the general solution of the non-homogeneous equation.

Auxillary equation

$m^2-6m+9=0$

$m^2-3m-3m+9=0$

$m(m-3)-3(m-3)=0$

$(m-3)(m-3)=0$

$m=3,3$

$y_c=(c_1+c_2x)e^{3x}$

General solution is given by

$y(x)=y_c+y_p$

$y(x)==(c_1+c_2x)e^{3x}+3x^2+4x$

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A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If

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Answer:

a. The test statistic for this hypothesis would be z=1.71

b. Critical value at α = 0.10: z=1.282

c. Reject H0, the television network should not keep its current lineup.

d. H0: p ≤ 0.50; HA: p > 0.50

Step-by-step explanation:

We have to performa an hypothesis test on a proportion.

The claim is that the proportion of viewers that prefer the new show is bigger than 50% (meaning that most viewers prefer the new show).

The null hypothesis will state that both shows have the same proportion.

Then, the null and alternative hypothesis are:

$H_0: \pi\leq0.50\\\\H_a: \pi>0.5$

The sample proportion is p=0.53

$p=X/n=438/827=0.53$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.5*0.5}{827}}= 0.017$

Then, the z-statistic can be calculated as:

$z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.53-0.50-0.5/827}{0.017}=\dfrac{ 0.029 }{0.017} =1.706$

The critical value for a right tailed test at a significance level of 0.10 is zc=1.282. This value can be looked up in a standard normal distribution table.

As the statistic is bigger than the critical value, it lies in the rejection region. The null hypothesis is rejected. There is evidence to support the claim that the proportion of viewers which support the new show is larger than 0.50.

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<span>b. A linear equation with slope 5 and y-intercept 1 c. A linear equation with slope 2 and y-intercept 3 d. A linear equation with slope 3 and y-intercept 2

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a class has 20 trays of paint each trays has 6 colors 1 of the color is red what fraction of the colors in the 20 trays is red

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Answer: it is 1/6

You can solve by saying, 1 out of 6 in each tray is red, so my fraction should be 1/6.

It doesn't matter the amount of trays because the pattern is always the same.

But if you want to check it out you can do it in this way.

You know there is 1 red color per tray, if there are 20 then you'd have 20 of them, in each tray there are 6 colors so the total is 120.

Now you solve it if there are 20 red colors out of 120 them the answer is 20/120, thus you get 1/6

Step-by-step explanation:

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Answer:

$y=(x-4)(x-2)$

Step-by-step explanation:

Consider the given equation

$y=x^2-6x+8$

Factor form of a parabola: It displays the x-intercepts.

$y=a(x-p)(x-q)$ .... (1)

where, a is a constant and, p and q are x-intercepts.

So, we need to find the factored form of the given equation.

Splinting the middle term we get

$y=x^2-4x-2x+8$

$y=x(x-4)-2(x-4)$

$y=(x-4)(x-2)$ .... (2)

On comparing (1) and (2) we get

$p=4,q=2$

It means x-intercepts of the given parabola are 4 and 2.

Therefore, equivalent forms of the equation is y=(x-4)(x-2).

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In this question, each star equal to 4 students. If the people on 85 and 90 take the test again that means their number should be 14+4 people= 18 people.
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If you add the stars graph it will be easier. It should be clear that 85 will have 1 stars and 90 have 3.5 stars. Adding them up will be 1 stars + 3.5 stars= 4.5 stars

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