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2 years ago

The absolute value of a number is

Mathematics

2 answers:

makvit [3.9K]2 years ago

7 0

Answer: the magnitude of a real number without regard to its sign.

Step-by-step explanation:

Meaning whether it is 5 or -5 the absolute value is 5 for both because that is their distance from zero.

agasfer [191]2 years ago

6 0

Answer:

A numbers distance from zero. *always positive*

Step-by-step explanation:

The absolute value of 5 is 5.

The absolute value of -3 is 3

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Put the equation in standard linear form.

$x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}$

Find the integrating factor.

$\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5$

Multiply both sides by $\mu$ .

$(t+5) x'(t) + x(t) = 5(t+5)e^{5t}$

Now the left side the derivative of a product,

$\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}$

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$(t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt$

On the right side, integrate by parts.

$(t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C$

Solve for $x(t)$ .

$\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}$

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