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3 years ago

Complete the statement below.

Mathematics

1 answer:

S_A_V [24]3 years ago

8 0

Answer:

I would say 3, since you would need to move the decimal point up 3 times to get .0264

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5. Find the general solution to y'''-y''+4y'-4y = 0

CaHeK987 [17]

For any equation,

$a_ny^(n)+\dots+a_1y'+a_0y=0$

assume solution of a form, $e^{yt}$

Which leads to,

$(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0$

Simplify to,

$e^{yt}(y^3-y^2+4y-4)=0$

Then find solutions,

$\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}$

For non repeated real root y, we have a form of,

$y_1=c_1e^t$

Following up,

For two non repeated complex roots $y_2\neq y_3$ where,

$y_2=a+bi$

and,

$y_3=a-bi$

the general solution has a form of,

$y=e^{at}(c_2\cos(bt)+c_3\sin(bt))$

Or in this case,

$y=e^0(c_2\cos(2t)+c_3\sin(2t))$

Now we just refine and get,

$\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}$

Hope this helps.

r3t40

5 0

4 years ago

Use the number line above to correctly compare the following numbers.

tatyana61 [14]

Answer:

Step-by-step explanation:

9/4= 2.25

PIE=3.14

The square root of 12.96= 3.6

so the only answer that could be correct is C because 9/4 is bigger than PIE

3 0

3 years ago

PLEASE HELP Write an equation with the smallest possible degree for the function graphed attached.

arlik [135]

Answer:

Below

Step-by-step explanation:

First we can go ahead and create a general equation for this polynomial

Here are our roots :

x1 = - 3

x2 = -1

x3 = 1

Now because this function extends from quadrant 4 to 3, we know that this has been reflected in the x-axis :

f(x) = - ( x + 3 ) ( x + 1 ) ( x - 1 )

However if we look closely you can see that the graph appears to "bounce" off certain roots. In this case it bounces off x = 1. This means that this root is an order of 2. It also has a weird looking curve on x = - 3 which means that this root is an order of 3.

Our general equation will look like this :

f(x) = - ( x + 3 )^3 ( x - 1 )^2 ( x + 1 )

Now we need to sub in any point on the graph to solve for the <em>a </em>value. I'm just going to arbitrarily pick the y-intercept at ( 0 , -3 )

- 3 = - a ( 0 + 3 )^3 ( 0 - 1 )^2 ( 0 + 1 )

- 3 = - a (3)^3 (-1)^2 (1)

- 3 = - a (27)(1)(1)

- 3 = - a27

1/9 = a

Here is our FINAL equation :

f(x) = - 1/9 ( x + 3 )^3 ( x - 1 )^2 ( x + 1 )

Hope this helps! Best of luck <3

I would really appreciate a brainliest if possible :)