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3 years ago

41 + 2y = 0 - 4x – 9y= - 28 Solve each system by elimination

Mathematics

1 answer:

Iteru [2.4K]3 years ago

4 0

Question:

4x + 2y = 0

- 4x – 9y= - 28

Solve each system by elimination

Answer:

The solution is x = -2 and y = 4

Solution:

Given system of equations are:

4x + 2y = 0 ------ eqn 1

-4x – 9y = - 28 ------- eqn 2

We have to solve the system of equations by elimination method

Add eqn 1 and eqn 2

4x + 2y -4x -9y = 0 - 28

0 + 2y - 9y = -28

-7y = -28

Divide both sides by -7

y = 4

Substitute y = 4 in eqn 1

4x + 2(4) = 0

4x + 8 = 0

4x = -8

Divide both sides by 4

x = -2

Thus the solution is x = -2 and y = 4

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move -20 to the other side

sign changes from -20 to +20

40+20= x-20+20

40+20=x

60=x

Answer:

b 60

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3 years ago

A) Work out the value of 213 + (29)2

Alina [70]

a) 2^13 / 2^18

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2 years ago

Find the volume of the solid generated by revolving the region bounded by

Rama09 [41]

Answer:

$V =\dfrac{25\pi}{\sqrt{2}}$

Step-by-step explanation:

given,

y=5√sinx

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$V = \int_a^b(\pi y^2)dx$

a and b are the limits of the integrals

now,

$V = \int_a^b(\pi (5\sqrt{sinx})^2)dx$

$V =25\pi \int_{\pi/4}^{\pi/2}sinxdx$

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$V =25\pi [-cos x]_{\pi/4}^{\pi/2}$

$V =25\pi [-cos (\pi/2)+cos(\pi/4)]$

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$V =\dfrac{25\pi}{\sqrt{2}}$

volume of the solid generated is equal to $V =\dfrac{25\pi}{\sqrt{2}}$

4 0

3 years ago

D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

3 years ago

Question in the image

Komok [63]

Answer:

0.4

Step-by-step explanation:

consider this like some lines overlapping each other.

one line (A) is 0.5 long, the other (B) 0.4 long.

together they are 0.8 long.

that means that they overlap at a length of 0.1 (they share a segment 0.1 long).

of the combined line of 0.8 that has 0.1 of a joined segment, the complimentary part of B is therefore 0.4 (0.8 minus the original length of B).

8 0

3 years ago