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3 years ago

Find the given Value w(t) = 12t - 1;t = 1/3

Mathematics

1 answer:

Zepler [3.9K]3 years ago

5 0

Answer:

$w(t) = 12t - 1 \\ when \: t \: = \frac{1}{3} \\ w( \frac{1}{3} ) = 12( \frac{1}{3} ) - 1 \\ w( \frac{1}{3} ) = 3$

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lina2011 [118]

Answer:

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3 years ago

write each of the following products in standard polynomial form. (a) (x+3)(x-2)(x-8) (b) (x+2)(x-2)(x+3)(x-3)

Annette [7]

Answer: A)x²+x-6 B) 2x²-13

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3 years ago

-10 + 20p + 6p = -16

pshichka [43]

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Step-by-step explanation:

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+10 +10

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26 26

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4 years ago

F(n) = 4n - 2 g(n) = 4n + 3 find f(n) + g(n)

OLga [1]

Answer:

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Step-by-step explanation:

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3 years ago

(x^2y+e^x)dx-x^2dy=0

klio [65]

It looks like the differential equation is

$\left(x^2y + e^x\right) \,\mathrm dx - x^2\,\mathrm dy = 0$

Check for exactness:

$\dfrac{\partial\left(x^2y+e^x\right)}{\partial y} = x^2 \\\\ \dfrac{\partial\left(-x^2\right)}{\partial x} = -2x$

As is, the DE is not exact, so let's try to find an integrating factor µ(x, y) such that

$\mu\left(x^2y + e^x\right) \,\mathrm dx - \mu x^2\,\mathrm dy = 0$

*is* exact. If this modified DE is exact, then

$\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \dfrac{\partial\left(-\mu x^2\right)}{\partial x}$

We have

$\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu \\\\ \dfrac{\partial\left(-\mu x^2\right)}{\partial x} = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu \\\\ \implies \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu$

Notice that if we let µ(x, y) = µ(x) be independent of y, then ∂µ/∂y = 0 and we can solve for µ :

$x^2\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} - 2x\mu \\\\ (x^2+2x)\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} \\\\ \dfrac{\mathrm d\mu}{\mu} = -\dfrac{x^2+2x}{x^2}\,\mathrm dx \\\\ \dfrac{\mathrm d\mu}{\mu} = \left(-1-\dfrac2x\right)\,\mathrm dx \\\\ \implies \ln|\mu| = -x - 2\ln|x| \\\\ \implies \mu = e^{-x-2\ln|x|} = \dfrac{e^{-x}}{x^2}$