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3 years ago

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Which expression will you generate if you apply the Distributive Property and combine the like terms in the expression x + 3y −

y + 3x + 2(2 + 4 + y)?
A: 5x+8y+15

B: 4x+4y+12

C: 4x+3y+24

D: x+3y+14

2 answers:

tresset_1 [31]3 years ago

8 0

apply the Distributive Property and combine like terms in the expression

x + 3y − y + 3x + 2(2 + 4 + y)

= 4x + 2y+ 12 + 2y

= 4x + 4y + 12

answer

B: 4x+4y+12

NeX [460]3 years ago

5 0

<span>apply the Distributive Property and combine like terms in the expression
</span><span>
x + 3y − y + 3x + 2(2 + 4 + y)
= 4x + 2y+ 12 + 2y
= 4x + 4y + 12

answer

</span>B: 4x+4y+12

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Solve the nonhomogeneous differential equation y′′+25y=cos(5x)+sin(5x). Find the most general solution to the associated homogen

Marrrta [24]

Answer:

$y(x)=c_1cos(5x)+c_2sin(5x)+0.1xsin(5x)-0.1xcos(5x)$

Step-by-step explanation:

The general solution will be the sum of the complementary solution and the particular solution:

$y(x)=y_c(x)+y_p(x)$

In order to find the complementary solution you need to solve:

$y''+25y=0$

Using the characteristic equation, we may have three cases:

Real roots:

$y(x)=c_1e^{r_1x} +c_2e^{r_2x}$

Repeated roots:

$y(x)=c_1e^{rx} +c_2xe^{rx}$

Complex roots:

$y(x)=c_1e^{\lambda x}cos(\mu x) +c_2e^{\lambda x}sin(\mu x)\\\\Where:\\\\r_1_,_2=\lambda \pm \mu i$

Hence:

$r^{2} +25=0$

Solving for $r$ :

$r=\pm5i$

Since we got complex roots, the complementary solution will be given by:

$y_c(x)=c_1cos(5x)+c_2sin(5x)$

Now using undetermined coefficients, the particular solution is of the form:

$y_p=x(a_1cos(5x)+a_2sin(5x) )$

Note: $y_p$ was multiplied by x to account for $cos(5x)$ and $sin(5x)$ in the complementary solution.

Find the second derivative of $y_p$ in order to find the constants $a_1$ and $a_2$ :

$y_p''(x)=10a_2cos(5x)-25a_1xcos(5x)-10a_1sin(5x)-25a_2xsin(5x)$

Substitute the particular solution into the differential equation:

$10a_2cos(5x)-25a_1xcos(5x)-10a_1sin(5x)-25a_2xsin(5x)+25(a_1xcos(5x)+a_2xsin(5x))=cos(5x)+sin(5x)$

Simplifying:

$10a_2cos(5x)-10a_1sin(5x)=cos(5x)+sin(5x)$

Equate the coefficients of $cos(5x)$ and $sin(5x)$ on both sides of the equation:

$10a_2=1\\\\-10a_1=1$

So:

$a_2=\frac{1}{10} =0.1\\\\a_1=-\frac{1}{10} =-0.1$

Substitute the value of the constants into the particular equation:

$y_p(x)=-0.1xa_1cos(5x)+0.1xsin(5x)$

Therefore, the general solution is:

$y(x)=y_c(x)+y_p(x)$

$y(x)=c_1cos(5x)+c_2sin(5x)+0.1xsin(5x)-0.1xcos(5x)$

6 0

3 years ago

What is 4 and 1 over 5 into a decimal

NeTakaya

It was 4.2 because 1/5 equals to .2

3 0

2 years ago

What is the width of a box when the length is x+2, the height is x+8, and the volume is x^3+9x^2+6x-16?

Nostrana [21]

(x+2)(x+8) = x^2 +10x +16

(x^2 + 10x + 16)(x-1) = x^3+9x^2+6x-16, so the other dimension is x-1

8 0

3 years ago

Read 2 more answers

A container weighs 23 2/5 pounds holds sports equipment. Of the equipment in the container 1/3 of the weight is baseball equipme

hram777 [196]

What we need to know is how much is 1/3 of 25 2/5.

We will be multiplying fraction by a fraction and for this, it's good to change mixed numbers into improper fractions:

25 2/5= $\frac{23*5+2}{5}= \frac{117}{5}$

and now we multiply it by 1/3:

$\frac{1}{3}\frac{117}{5}=\frac{39}{5}=7\frac{4}{5}$

and that's the answer: the basketball equipment weights 7 4/5 pounds.

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2 years ago

Need help on this question Plzzz

stepladder [879]

Answer:

B. -9, -5, -1

Step-by-step explanation:

<u>Solve the inequality:</u>

- a + 1/3 > 1/4
a < 1/3 - 1/4
a < 4/12 - 3/12
a < 1/12

Correct choice is B

4 0

2 years ago