All categories

2 years ago

Which of the following numbers has a prime factorization of 3 x 3 x 3?

Mathematics

2 answers:

tester [92]2 years ago

7 0

You multiply them and you will get the correct answer
3×3=9
9×3=27
Therefore, 3×3×3 is a factor of 27

iogann1982 [59]2 years ago

5 0

The answer is d 3x3 is 9...9x3 equal 27

You might be interested in

Need some help with this please!!

beks73 [17]

Answer:

B,C and B,A

Step-by-step explanation:

Line the cordients and go up right,Then left to find your answer.

4 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 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

Find the area of the geometric figure. Square 9.8 ft

tresset_1 [31]

Answer:

96.04 ft

Step-by-step explanation:

nutiply 9. 8 by 9.8

8 0

3 years ago

The question is Stephen read for 34 minutes on Monday and 45 minutes on Tuesday. Use breaking apart to find how many minutes Ste

user100 [1]

Breaking apart means that you just take the tens from each number, and the ones from each number, then add them up.

The tens from your numbers are:
30 from 34
40 from 45

The ones from your numbers are:
4 from 34
5 from 45

Now, you have to add up the tens and ones separately.
30 + 40 = 70
4 + 5 = 9

Finally, you add up those 2 numbers that you got- 70 and 9

The answer: Stephen read for 79 minutes total.

7 0

3 years ago

Luis wanted to buy a skateboard that usually sells for $79.99. All merchandise is discounted by 12%. What is the total cost of t

Oliga [24]

79.99/6.75%=5.399325 if you want the exact but 5.40 if you want rounded

8 0

3 years ago