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Mariana [72]
2 years ago
8

Translate and solve the following the difference of 5C and 4C Is 602

Mathematics
1 answer:
poizon [28]2 years ago
8 0

Answer:

c=602 is the answer i will explain later

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On the number line below, the letters a and b are the same distance from 0. What is a + b?
jolli1 [7]

Answer:

The answer here would be 0.

Step-by-step explanation:

If a and b are both equal distances from 0, then adding the together would equal 0. Since a is the inverse of b,  using any number and its inverse will show you why the answer is 0. For example, if b is 9 then a would be -9. Adding these together equals 0.

5 0
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 <em>µ(x, y)</em> 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 <em>µ(x, y)</em> = <em>µ(x)</em> be independent of <em>y</em>, then <em>∂µ/∂y</em> = 0 and we can solve for <em>µ</em> :

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}

The modified DE,

\left(e^{-x}y + \dfrac1{x^2}\right) \,\mathrm dx - e^{-x}\,\mathrm dy = 0

is now exact:

\dfrac{\partial\left(e^{-x}y+\frac1{x^2}\right)}{\partial y} = e^{-x} \\\\ \dfrac{\partial\left(-e^{-x}\right)}{\partial x} = e^{-x}

So we look for a solution of the form <em>F(x, y)</em> = <em>C</em>. This solution is such that

\dfrac{\partial F}{\partial x} = e^{-x}y + \dfrac1{x^2} \\\\ \dfrac{\partial F}{\partial y} = e^{-x}

Integrate both sides of the first condition with respect to <em>x</em> :

F(x,y) = -e^{-x}y - \dfrac1x + g(y)

Differentiate both sides of this with respect to <em>y</em> :

\dfrac{\partial F}{\partial y} = -e^{-x}+\dfrac{\mathrm dg}{\mathrm dy} = e^{-x} \\\\ \implies \dfrac{\mathrm dg}{\mathrm dy} = 0 \implies g(y) = C

Then the general solution to the DE is

F(x,y) = \boxed{-e^{-x}y-\dfrac1x = C}

5 0
3 years ago
Determine the following<br>quadratic equations have real<br>roots<br><br>1) 3x² - √2x-√3​
IceJOKER [234]

Step-by-step explanation:

√3 x² - 2x - √3 = 0

√3 x² - 3x + x - √3 = 0

√3 x(x - √3) + 1(x - √3) = 0

(x - √3 ) (√3 x + 1) = 0

x - √3 = 0 , √3 x +1 = 0

x = √3 , x = -1/√3

3 0
3 years ago
If John has an apple, an orange, a pear, a banana, and a kiwi at home and he wants to bring two fruits for lunch, how many diffe
SVEN [57.7K]

Answer:

10

Step-by-step explanation:

5 choose 2 is 5x4/2, which is 20/2, which is 10.

5 0
3 years ago
A train travelled 275 km in 2.5 hours how fast will the train go in an hour?
mylen [45]

Answer: 110 mph

Step-by-step explanation: 275 / 2.5 = 110 mph

5 0
3 years ago
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