Find the midpoint of the line joining A (3,5) and B(1,3)

Mathematics

1 answer:

MaRussiya [10]3 years ago

3 0

Answer:

(-1 , -1)

Step-by-step explanation:

$x_1= 3 \\ y_1= 5 \\ x_2=1 \\ y_2= 3$

$midpoint \: = ( \frac{x_2 - x_1}{2} \: \frac{y_2 -y_1}{2} )$

$=( \frac{1 - 3}{2} \: \frac{3 - 5}{2} ) \\ = ( \frac{ - 2}{2} \: \frac{ - 2}{2} ) = \\ ( - 1 \: - 1)$

You might be interested in

MATH PLS HELP EXAMS PROBLEM 1!!!!!!

STALIN [3.7K]

Answer:

C) -12y-8y-4

Step-by-step explanation:

3 0

2 years ago

Set up but do not solve for the appropriate particular solution yp for the differential equation y′′+4y=5xcos(2x) using the Meth

taurus [48]

Answer:

So, solution of the differential equation is

$y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

Step-by-step explanation:

We have the given differential equation: y′′+4y=5xcos(2x)

We use the Method of Undetermined Coefficients.

We first solve the homogeneous differential equation y′′+4y=0.

$y''+4y=0\\\\r^2+4=0\\\\r=\pm2i\\\\$

It is a homogeneous solution:

$y_h(t)=c_1e^{-2i t}+c_2e^{2i t}$

Now, we finding a particular solution.

$y_p(t)=A5x\cos 2x\\\\y'_p(t)=A5\cos 2x-A10x\sin 2x\\\\y''_p(t)=-A20\sin 2x-A20x\cos 2x\\\\\\\implies y''+4y=5x\cos 2x\\\\-A20\sin 2x-A20x\cos 2x+4\cdot A5x\cos 2x=5x\cos 2x\\\\-A20\sin 2x=5x\cos 2x\\\\A=-\frac{x}{4} \cot 2x\\$

we get

$y_p(t)=A5\cos 2x\\\\y_p(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x\\\\\\y(t)=y_p(t)+y_h(t)\\\\y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$