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4 years ago

10

(6^-2·6^5)^-3 can't figure out the answer

1 answer:

deff fn [24]4 years ago

6 0

The answer is 0.000000099.

Hope this helps! :D

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7(x^2 y^2)dx 5xydyUse the method for solving homogeneous equations to solve the following differential equation.

aivan3 [116]

I'm guessing the equation should read something like

$7(x^2+y^2) \,dx + 5xy \, dy = 0$

or possibly with minus signs in place of +.

Multiply both sides by $\frac1{x^2}$ to get

$7\left(1 + \dfrac{y^2}{x^2}\right) \, dx + \dfrac{5y}x \, dy = 0$

Now substitute

$v = \dfrac yx \implies y = xv \implies dy = x\,dv + v\,dx$

to transform the equation to

$7(1+v^2) \, dx + 5v (x\,dv + v\,dx) = 0$

which simplifies to

$(7 + 12v^2) \, dx + 5xv\,dv = 0$

The ODE is now separable.

$\dfrac{5v}{7+12v^2} \, dv = -\dfrac{dx}x$

Integrate both sides. On the left, substitute

$w = 7+12v^2 \implies dw = 24v\, dv$

$\displaystyle \int \frac{5v}{7+12v^2} \, dv = -\int \frac{dx}x$

$\displaystyle \dfrac5{24} \int \frac{dw}w = -\int \frac{dx}x$

$\dfrac5{24} \ln|w| = -\ln|x| + C$

Solve for $w$ .

$\ln\left|w^{5/24}\right| = \ln\left|\dfrac1x\right| + C$

$\exp\left(\ln\left|w^{5/24}\right|\right) = \exp\left(\ln\left|\dfrac1x\right| + C\right)$

$w^{5/24} = \dfrac Cx$

Put this back in terms of $v$ .

$(7+12v^2)^{5/24} = \dfrac Cx$

Put this back in terms of $y$ .

$\left(7+12\dfrac{y^2}{x^2}\right)^{5/24} = \dfrac Cx$

Solve for $y$ .

$7+12\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}}$

$\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}} - \dfrac7{12}$

$y^2= \dfrac C{x^{14/5}} - \dfrac{7x^2}{12}$

$y = \pm \sqrt{\dfrac C{x^{14/5}} - \dfrac{7x^2}{12}}$

8 0

2 years ago

Probability of a coin landing on heads

Viefleur [7K]

Answer:

The answer would be 50% or 1/2

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Please help with actual steps, and don’t reply w nonsense just for the points. Thank you !!!

Anton [14]

Answer:

1. 24x^6

3. -15^10

5. 90x^5y^6

7. 40x^12y^18

9. 72x^12y^18

add exponents since we're multiplying then multiply the numbers and put the letters in order

5 0

3 years ago

What multiplies to -182 and adds to 1

hodyreva [135]

The answer to your question is:

13 and -14

3 0

4 years ago

Rewrite 4/7 and 3/5 so they have common denominator

Vladimir [108]

20/35 and 21/35. The common denominator is 35.

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3 years ago