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jolli1 [7]
3 years ago
14

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9,8) Midpoint (0,9)​

Mathematics
1 answer:
shepuryov [24]3 years ago
5 0

Answer:

(-9, 10)

Step-by-step explanation:

The location of the midpoint of a line with endpoint at (x_1,y_1) and (x_2,y_2) is given as (x, y). The location of x and y are:

x = \frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}

Given the endpoint (9,8) and Midpoint (0,9), the location of the other endpoint can be gotten from:

0=\frac{9+x_2}{2}\\ \\9+x_2=0\\\\x_2=-9\\\\Also,9=\frac{8+y_2}{2}\\ \\8+y_2=18\\\\y_2=18-8\\\\y_2=10

Hence the endpoint is at (x2, y2) which is at (-9, 10)

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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
Which choice is equivalent to the expression below? square root of negative 20​
morpeh [17]

Answer:

B

Step-by-step explanation:

The expression can be written as

\sqrt{-20}

The - can be taken out from under the radicand and a 2 can be factored out of the expression to leave you with the expression

2i\sqrt{5}

7 0
3 years ago
Read 2 more answers
I WILL GIVE BRAINLIEST!! PLEASE HURRY
crimeas [40]

Answer:

B. It rejects the concept of social class in the American system.

Explanation:

The Enlightenment of the American Colonies was a period in time where the people were encouraged to become their own nation. This period was represented by many speeches and pieces of writing that boasted freedom of speech, equality, freedom of the press, and religious tolerance.

This specific piece of writing focuses on the aspect of all people in the nation of America having protected freedoms and rights to become their own people.

5 0
3 years ago
My final balance after 48 months was $896.00. if i bring back originally put$800.00 into the bank, what was the interest rate?
fomenos
The interest rate is $96.00.
3 0
3 years ago
If x=6 and y=−4, evaluate the following expression:10−4xy​
Lana71 [14]

Answer:

10-(4×6×-4)

10+96

=106

Step-by-step explanation:

hope it helps

5 0
2 years ago
Read 2 more answers
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