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2 years ago

Describe the relationship between religion and government in the Byzantine Empire

Mathematics

1 answer:

Serhud [2]2 years ago

8 0

Answer:

so lots of romans were christians, but the gov. was like "Naaahhh" and persecuted them

Step-by-step explanation:

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Which of the following best describes the solutions to the inequality shown below?

Digiron [165]

3z < 30 - 6
3z < 24
z< 24/3
z< 8
answer is z < 8

4 0

3 years ago

Find the distance between each pair of points J(-3,4)k(2,-4)

raketka [301]

$J(-3,4)\ \ \ and\ \ \ K(2,-4)\\\\|JK|= \sqrt{(-3-2)^2+(4-(-4))^2} = \sqrt{(-5)^2+8^2} = \sqrt{25+64} = \sqrt{89}$

7 0

3 years ago

Find the form of the general solution of y^(4)(x) - n^2y''(x)=g(x)

Dennis_Churaev [7]

The differential equation

$y^{(4)}-n^2y'' = g(x)$

has characteristic equation

r ⁴ - n ² r ² = r ² (r ² - n ²) = r ² (r - n) (r + n) = 0

with roots r = 0 (multiplicity 2), r = -1, and r = 1, so the characteristic solution is

$y_c=C_1+C_2x+C_3e^{-nx}+C_4e^{nx}$

For the non-homogeneous equation, reduce the order by substituting u(x) = y''(x), so that u''(x) is the 4th derivative of y, and

$u''-n^2u = g(x)$

Solve for u by using the method of variation of parameters. Note that the characteristic equation now only admits the two exponential solutions found earlier; I denote them by u₁ and u₂. Now we look for a particular solution of the form

$u_p = u_1z_1 + u_2z_2$

where

$\displaystyle z_1(x) = -\int\frac{u_2(x)g(x)}{W(u_1(x),u_2(x))}\,\mathrm dx$

$\displaystyle z_2(x) = \int\frac{u_1(x)g(x)}{W(u_1(x),u_2(x))}\,\mathrm dx$

where W (u₁, u₂) is the Wronskian of u₁ and u₂. We have

$W(u_1(x),u_2(x)) = \begin{vmatrix}e^{-nx}&e^{nx}\\-ne^{-nx}&ne^{nx}\end{vmatrix} = 2n$

and so

$\displaystyle z_1(x) = -\frac1{2n}\int e^{nx}g(x)\,\mathrm dx$

$\displaystyle z_2(x) = \frac1{2n}\int e^{-nx}g(x)\,\mathrm dx$

So we have

$\displaystyle u_p = -\frac1{2n}e^{-nx}\int_0^x e^{n\xi}g(\xi)\,\mathrm d\xi + \frac1{2n}e^{nx}\int_0^xe^{-n\xi}g(\xi)\,\mathrm d\xi$

and hence

$u(x)=C_1e^{-nx}+C_2e^{nx}+u_p(x)$

Finally, integrate both sides twice to solve for y :

$\displaystyle y(x)=C_1+C_2x+C_3e^{-nx}+C_4e^{nx}+\int_0^x\int_0^\omega u_p(\xi)\,\mathrm d\xi\,\mathrm d\omega$

7 0

2 years ago

Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount. How much did Lydia pay

mestny [16]

Retail Price= $40

Price after 20% discount

20/100 x 40 = $8

40-8= $32 after discount

tax paid on $32 shirt = 5/100 x32 = $1.6

she paid $32+$1.6= $33.6

4 0

2 years ago

Find the area of the shaded part of the figure. Will mark brainliest! 15 pts

Leona [35]

Answer:25sqrt3-25pi/3

Step-by-step explanation:

Assuming the triangle is equilateral, we clearly need to find the radius of the circle, and subtract from the entire area of the triangle.

First, the area of an equilaterail triangle is given by the formula s^2 *sqrt3/4.

Next, the connect the center of the radius to points of tangency. Note this bisects the angle of the equilateral triangle into a 30 degree angle, and connecting radii to points of tangency forms a 90 degree angle, so this is a 30-60-90 triangle. This bisects the side length of the triangle, and the ratio of sides of a 30-60-90. Set this length as x. Thus, we have 4x^2=x^2+25, so 3x^2 =25. Dividing both sides by 3, we get x^2=25/3. Note that we only need x^2, as the formula is x^2 * pi. Hence, the area of the shaded region is 25sqrt3-25pi/3.

8 0

2 years ago

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