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steposvetlana [31]
2 years ago
15

What is x^2=7x number 9

Mathematics
1 answer:
ipn [44]2 years ago
8 0

Let's do this in steps, show your work!

<u>#1. We need to move all terms to one side.</u>

<u>x^2 - 7x = 0</u>

<u>#2. Then factor out the common term x.</u>

<u>x(x - 7) = 0.</u>

<u>#3. Simplify to get..</u>

<u>x = 0, 7.</u>

<u />

If you need help with any other question let me know.

<u />

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HOW CAN YOU WRITE 10/3 AS A DIVISION EXPRESSION AND AS A MIXED NUMBER?
Anni [7]

Answer: 10.3 would be a mixed number

Step-by-step explanation:

Divide 12 into 46. You get 3 with a remainder of 10. 3 is the whole number of the mixed number, 10 is the numerator of the fraction, and 12 is the denominator. The fraction can be reduced to 5/6.

5 0
2 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
A person walks 1 mile every day for exercise, leaving her front porch at 9:00 am and returning to her front porch at 9:25 am. wh
shusha [124]
The answer would be 0
4 0
3 years ago
University theater sold 529 tickets for a play. Tickets cost $25 per adult and $15 per senior citizen. If total receipts were $9
astra-53 [7]

Adults = x

Senior Citizens = y

x + y = 529......1

25x + 15y = 9745...2

Multiply (1) by 15

15x + 15y = 7935....3

25x + 15y = 9745....2

Subtract 3 from 2

10x = 1810

 

x = 181

Substitute x = 181 in

Eq (1)

x + y = 529

181 + y = 529

y = 529 - 181

y = 348

181 adults and 348 Senior Citizens

Hope this helps.

3 0
2 years ago
8. A dolphin is traveling 5.5 meters
navik [9.2K]
Distance = final height - depthOFdolphin
Distance = 2.4 - (-5.5)
Distance = 2.4 + 5.5
Distance = 7.9 meters
8 0
2 years ago
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