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3 years ago

Solve the given equation. z - 42 = 7

Mathematics

2 answers:

Westkost [7]3 years ago

8 0

7 + 42 = 49 so it’s 49

Pani-rosa [81]3 years ago

5 0

Answer:

z = 49

Step-by-step explanation:

z - 42 = 7

+42 +42

z = 49

1. add 42 to both sides (adding because its - 42)

2. that leaves us with 7+42 = 49 so z=49

to check your answer u can always plug in 49.

49 - 42 = 7

yup. 49-42 does equal 7.

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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 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 :

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

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 F(x, y) = C. 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 x :

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

Differentiate both sides of this with respect to y :

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

Then the general solution to the DE is

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

5 0

3 years ago

Simplify: 3x^2-8x+4 and show work please

Bad White [126]

believe what you're asking is to turn the trinomial into two binomials

So you first have to get 3x²; the only way to get this is

(3x )(x ) when multiplying that, you would get 3x²

when dealing with the -8x and the 4, you must find numbers that are factors of four (when multiplied together they will equal 4) and will multiply with the x's to get -8

(3x-2)(x-2)

you can tell that this is the answer because when you multiply though you will get:

3x-2x²-6x+4

or: 3x²-8x_4

Hope this helped

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3 years ago

What is the value of 7r

lara31 [8.8K]

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2 years ago

amy has 72 Suites in a bag she keeps one fourth of them for herself and share the rest with their friends how many sweets will h

yKpoI14uk [10]

So,

If she keeps one-fourth for herself, she will keep:
72 * 0.25 = 18

That leaves the rest for her friends.
72 - 18 = 54

Her friends will get 54 "Suites."

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2 years ago

Find the mean and median for this set. 6, 7, 7, 8, 8, 8, 8, 8, 8.5, 9, 9, 9, 9, 9.5, 10, 10.

julsineya [31]

Mean: 8.375

Median: 8.25

To find mean you must add up the numbers. Then divide the total and the total numbers there are.

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3 years ago

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