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marishachu [46]
3 years ago
7

Which choice is equivalent to the expression below? (V= square root)

Mathematics
2 answers:
ki77a [65]3 years ago
7 0
The answer is exactly c
DENIUS [597]3 years ago
6 0

Answer:

C

Step-by-step explanation:

i = \sqrt{-1}

\sqrt{125} is equal to 5\sqrt{5}

Since it is \sqrt{-125}, then you must have i as well

5i\sqrt{5}

please give a heart to give thanks :)

a crown would be nice too :)

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Order the numbers from least to greatest.<br> 23% , 1/4 , 0.225 .
Alla [95]
0.225, 23%, 1/4


Step my step

23% = 0.23
1/4 = 0.25
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2 years ago
Gabriela walked to a toy store around noon and , after browsing for 2222 minutes, decided to buy a race car for $9.22. Gabriela
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No change. She gave the salesperson exactly the right amount to buy the racecar.
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There are 25 bananas that will be cut and divided evenly between 4 loaves of bread. How many bananas go into each loaf? Choose t
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Answer: 6 1/4

Step-by-step explanation: 25 divided by 4 = 6 1/4

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Points Q and P on the coordinate grid below show the positions of two midfield players of a soccer team:
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3 years ago
Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).
I am Lyosha [343]
Take the homogeneous part and find the roots to the characteristic equation:

y''+4y=0\implies r^2+4=0\implies r=\pm2i

This means the characteristic solution is y_c=C_1\cos2x+C_2\sin2x.

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form y_p=ax\cos2x+bx\sin2x. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With y_1=\cos2x and y_2=\sin2x, you're looking for a particular solution of the form y_p=u_1y_1+u_2y_2. The functions u_i satisfy

u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx

where W(y_1,y_2) is the Wronskian determinant of the two characteristic solutions.

W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2

So you have

u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx
u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x

u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx
u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x

So you end up with a solution

u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x

but since \cos2x is already accounted for in the characteristic solution, the particular solution is then

y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x

so that the general solution is

y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x
7 0
3 years ago
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