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11111nata11111 [884]

3 years ago

10

If in a parallelogram, its diagonals bisect each other right angle and are

1 answer:

Vladimir [108]3 years ago

3 0

Answer:

(c)Rhombus

Step-by-step explanation:

A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.

A rhombus is a parallelogram (that is opposites sides and angles are equal to each other and parallel) with all sides of equal length. The diagonals of a rhombus bisect each other at 90° to form four equal right angled triangles with the sides of the rhombus as the hypotenuse.

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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

1 year ago

Write an expression equivalent to

Crazy boy [7]

Answer:

Step-by-step explanation:

2x6²( = 2x36 ) = 72

8 0

3 years ago

(x,2) and (6,3); m = -1/2

ExtremeBDS [4]

Y=mx+b
3= -1/2(6) + b
3= -3+b
3+3= b
b= 6

y= mx+b
2= -1/2x+ 6
2-6 = -1/2x
-4 = -1/2x
-4•-2 = -1/2x •-2
x = 8
(8,2)

8 0

3 years ago

Please i need help with this

masha68 [24]

Answer:

1.) Smith

2.) Johnson

4 0

3 years ago

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If Dwayne drinks 48 bottles of water in 12 days, how many bottles of water will he drink in 4 days?

ikadub [295]

Answer:

16

Step-by-step explanation:

48/12=4 bottles per day

4x4=16

7 0

2 years ago

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