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3 years ago

What is the equation of the line parallel to y=3x−4 that passes through the point (-2, 7)?

Mathematics

1 answer:

Sauron [17]3 years ago

5 0

Answer:

your answer is going to be y=3x-1

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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

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

So, solution of the differential equation is

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

7 0

3 years ago

On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine

Ilya [14]

I believe its 144ft. Since
<span>h(2) = [-16(2^2) + 64(2) + 80] ft = 144 ft</span>

7 0

3 years ago

A washing machine cost $ 750. Mr. James bought it at a 40% discount. How much was the discount ?

DENIUS [597]

Answer:

300$

Step-by-step explanation:

750*0.4=300

3 0

3 years ago

Read 2 more answers

Can you please help me with this problem? It shouldn't be to hard if you've done Algebra one.

seropon [69]

A) Y=0.12x and the Y value is dependent whole X value is independent
b) Just make a table and multiple each value by the equation
c) The domain would be the lowest and highest values of X and the range would be the lowest and highest values of Y (double check me on this to be sure)
d) A day = (0.12)(300)+(0.12)(750)+(0.12)(1050)
A week = (0.12)(300)+(0.12)(750)+(0.12)(1050) and multiply that by 7

5 0

3 years ago

The difference of two times a number and five is eight more than the number

Finger [1]

Add it then x it by 3

4 0

4 years ago