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3 years ago

Given : 2x+8=5x-13; prove x=7

Mathematics

2 answers:

spayn [35]3 years ago

8 0

Step-by-step explanation:

If we want to prove that x is equal to seven, we should first solve the equation for x so:

2x + 8 = 5x - 13

We should first add 13 on both sides and subtract 2x from both sides:

2x + 8 + 13 - 2x = 5x - 13 + 13 - 2x

21 = 3x

We can then divide both sides by 3 to get:

x = 7

solmaris [256]3 years ago

7 0

Answer:

True

Step-by-step explanation:

The left side 22 is equal to the right side 22 , which means that the given statement is always true.

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sergij07 [2.7K]

10% of 65
Of means multiply
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Or you can use another way which is (part/whole) *(percent/100)

Whole=65
Percent=10
And part(part of 65)=unknown

(X/65)* (10/100)
Cross multiply
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Step-by-step explanation:

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3 years ago

Solve these linear equations in the form y=yn+yp with yn=y(0)e^at.

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Answer:

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Step-by-step explanation:

a) $y' -4y = -8$

The first step is finding $y_{n}(t)$ . So:

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$r - 4 = 0$

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So:

$y_{n}(t) = y_{0}e^{4t}$

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' -4(y_{p}) = -8$

$(C)' - 4C = -8$

C is a constant, so (C)' = 0.

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$4C = 8$

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The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{4t} + 2$

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The first step is finding $y_{n}(t)$ . So:

$y' + 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r + 4 =$

$r = -4$

So:

$y_{n}(t) = y_{0}e^{-4t}$

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' +4(y_{p}) = 8$

$(C)' + 4C = 8$

C is a constant, so (C)' = 0.

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{-4t} + 2$

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Answer:

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