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nikdorinn [45]
3 years ago
9

2^1/2 x 3^2/3 in simplest form hurry help im on my test!!!!!!! Will mark as brainliest!

Mathematics
2 answers:
Kisachek [45]3 years ago
8 0

Answer:

3

Step-by-step explanation:

Good luck

zloy xaker [14]3 years ago
8 0

Answer: Your answer is 3. Good luck.

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Y''+y'+y=0, y(0)=1, y'(0)=0
mars1129 [50]

Answer:

y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form ay''+by'+cy=0.

Given: y''+y'+y=0

Let y=e^{rt} be it's solution.

We get,

\left ( r^2+r+1 \right )e^{rt}=0

Since e^{rt}\neq 0, r^2+r+1=0

{ we know that for equation ax^2+bx+c=0, roots are of form x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} }

We get,

y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}

For two complex roots r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta, the general solution is of form y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )

i.e y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )

Applying conditions y(0)=1 on e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right ), c_1=1

So, equation becomes y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )

On differentiating with respect to t, we get

y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )

Applying condition: y'(0)=0, we get 0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}

Therefore,

y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )

3 0
3 years ago
The graph shows a scuba diver's ascent over time. Use the graph to find the slope of the line. Complete the description of what
Burka [1]

Answer:

The slope of the line is <u>.25</u> This indicates that the diver <u>ascends</u> at a rate of <u>.25 </u>m/s.

Step-by-step explanation:

0 - (-10)

------------  == 10/40 == .25

40 - 0

6 0
3 years ago
What's the area of the square?​
mart [117]
Your answer is D. 25.25
8 0
3 years ago
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What is the square root of 30? round to the nearest tenth
Feliz [49]

Answer:

5.5

Step-by-step explanation:

5.477

Rounded to the nearest tenth it will be

5.5

5 0
3 years ago
Read 2 more answers
What is the value of the expression shown below?
faltersainse [42]

Answer:

It should be

Step-by-step explanation:

<h2><u><em>B.</em></u></h2><h2>23    1/4</h2>
5 0
2 years ago
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