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enot [183]
3 years ago
11

Factor 24j-16 to identify the equivalent expressions. Its multiple choice. A=8(3j−2) B=6(4j−2j) C=4(6j−4) D2(12−8)​

Mathematics
1 answer:
Ivan3 years ago
6 0

Answer:

I would say either A or C

Step-by-step explanation:

because when you distribute both they both come out to be 24j - 16

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(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
A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a
levacccp [35]

Answer:

P(x>12) = 0

Step-by-step explanation:

Given

x = \{1,2,3,4,5,6,7,8,9,10,11,12\} --- outcomes

n(x) = 12 -- sample size

Required

P(x > 12)

This is calculated as:

P(x > 12) = \frac{n(x > 12)}{n(x)}

n(x>12) = 0 because none of the outcomes is greater than 12:

So:

P(x > 12) =\frac{0}{12}

P(x>12) = 0

6 0
2 years ago
Given the graphs of f(x) =x -7 and g(x) =-5x-1, what is the solution to the equation f() = g(x)?
lions [1.4K]

Answer:

1

Step-by-step explanation:

x-7=-5x-1

x-(-5x)-7=-1

x+5x-7=-1

6x-7=-1

6x=-1+7

6x=6

x=6/6

x=1

8 0
2 years ago
Roy has 5 pounds of dried fruit to make snack bags. He separates each pound of dried fruit into thirds and wants to use 1 third
Dahasolnce [82]

Answer:

15

Step-by-step explanation:

1 turns in to 3 and you multiply that by 5

5 0
3 years ago
Which expression is equivalent to 8a + 12b?
Jet001 [13]

Answer:

4 (2 a + 3 b)

Step-by-step explanation:

Simplify the following:

8 a + 12 b

Factor 4 out of 8 a + 12 b:

Answer: 4 (2 a + 3 b)

4 0
2 years ago
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