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2 years ago

Yesterday between nooN And midnight the temperature dropped by 29.6 if the temperature was-5.4 at midnight what was it at noon

Mathematics

1 answer:

Deffense [45]2 years ago

3 0

Answer:

24.2

Step-by-step explanation:

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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

Water freezes at 0 degrees Celsius. A student discovered that adding half a cup of salt to a gallon of water lowers its freezing

Artemon [7]

Answer:

-7°C

Step-by-step explanation:

Freezing point of water = 0°C

By adding salt, freezing point lowers by 7°C ;

The freezing point of salt water can be expressed as ;

Since temperature lowers :

Freezing point of salt water :

Freezing point of water - 7°C

0°C - 7°C

= - 7°C

4 0

3 years ago

I don’t know this question? Can you pls answer it...

vladimir2022 [97]

Answer:

12i

Step-by-step explanation:

be careful with your screenshots and make sure it doesnt show your name

3 0

3 years ago

How many committes of 3 people can be formed from 7 people order does not matter?

Phoenix [80]

You can form 2 and then you have the odd one out.

5 0

3 years ago

Solve 2 + 1/6y = 3x + 4 for y.

ruslelena [56]

The answer is y=18x+12

5 0

3 years ago