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3 years ago

Brainliest, could you help me with the scientific notation

Mathematics

1 answer:

Minchanka [31]3 years ago

3 0

Answer:

1. 2.13 x 10^-1

2. 8.9 x 10^-2

3. 5.7 x 10^-5

4. 2.84 x 10^4

5. 8.1 x 10^-5

6. 2.65 x 10-5

Step-by-step explanation:

Good luck! Brainliest is always appreciated!

Sincerely,

Philip

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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

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

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3 years ago

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Answer:

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Step-by-step explanation:

A significant figure is the most important (largest) number you can round it to.

As it wants 1 significant figure, you count 1 to the left and round the 4 down.

Hope this helps :)

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3 years ago

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Answer:

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Step-by-step explanation:

they are parallel once graphed

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3 years ago

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