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Dovator [93]
3 years ago
15

How many are 9 raised to 3 ???​

Mathematics
1 answer:
Nutka1998 [239]3 years ago
5 0

Answer:

\huge \boxed{729}

Step-by-step explanation:

9 raised to 3 is the base 9 with an exponent of 3.

9^3

9 is being multiplied by itself 3 times.

9^3 =9 \times 9 \times 9 = 729

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Find thd <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D" id="TexFormula1" title="\frac{dy}{dx}" alt="\frac{dy}{dx}" a
NARA [144]

x^3y^2+\sin(x\ln y)+e^{xy}=0

Differentiate both sides, treating y as a function of x. Let's take it one term at a time.

Power, product and chain rules:

\dfrac{\mathrm d(x^3y^2)}{\mathrm dx}=\dfrac{\mathrm d(x^3)}{\mathrm dx}y^2+x^3\dfrac{\mathrm d(y^2)}{\mathrm dx}

=3x^2y^2+x^3(2y)\dfrac{\mathrm dy}{\mathrm dx}

=3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}

Product and chain rules:

\dfrac{\mathrm d(\sin(x\ln y)}{\mathrm dx}=\cos(x\ln y)\dfrac{\mathrm d(x\ln y)}{\mathrm dx}

=\cos(x\ln y)\left(\dfrac{\mathrm d(x)}{\mathrm dx}\ln y+x\dfrac{\mathrm d(\ln y)}{\mathrm dx}\right)

=\cos(x\ln y)\left(\ln y+\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}\right)

=\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}

Product and chain rules:

\dfrac{\mathrm d(e^{xy})}{\mathrm dx}=e^{xy}\dfrac{\mathrm d(xy)}{\mathrm dx}

=e^{xy}\left(\dfrac{\mathrm d(x)}{\mathrm dx}y+x\dfrac{\mathrm d(y)}{\mathrm dx}\right)

=e^{xy}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)

=ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}

The derivative of 0 is, of course, 0. So we have, upon differentiating everything,

3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}+\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}+ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}=0

Isolate the derivative, and solve for it:

\left(6x^3y+\dfrac{\cos(x\ln y)}y+xe^{xy}\right)\dfrac{\mathrm dy}{\mathrm dx}=-\left(3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}\right)

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}}{6x^3y+\frac{\cos(x\ln y)}y+xe^{xy}}

(See comment below; all the 6s should be 2s)

We can simplify this a bit by multiplying the numerator and denominator by y to get rid of that fraction in the denominator.

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^3+y\cos(x\ln y)\ln y-y^2e^{xy}}{6x^3y^2+\cos(x\ln y)+xye^{xy}}

3 0
3 years ago
When you flip a biased coin the probability of getting a tail is 0.42.
ddd [48]

Answer:

0.58 or 58%

Step-by-step explanation:

If the highest probability is 1, and you already have 0.42, you have to find what is left, so our equation is:

1 - 0.41 = 0.58

So the probability of getting a head is 0.58 or 58%

8 0
3 years ago
The perimeter of the square can be represented by the expression 36x+44 robin wants to write an equivalent expression for the pe
sukhopar [10]

Answer:

4  (9 x + 11) is an equivalent expression for the perimeter that shows the side length of the square is  (9 x + 11).

Step-by-step explanation:

Here, given The perimeter of the square  = (36 x+44)

Now,as we know :

PERIMETER OF SQUARE = 4 x ( SIDES)

Simplifying the perimeter expression.

Take 4 common out of the expression (36 x+44), we get:

(36 x+44) =  4 (9 x + 11)

⇒ Perimeter of the square  =  4 x  (9 x + 11)

⇒4 x ( SIDES) = 4 x (9 x + 11)

⇒ Each Side = (9 x + 11)

Hence, 4 x (9 x + 11) is an equivalent expression for the perimeter that shows the side length of the square is  (9 x + 11).

5 0
3 years ago
Is the first number divisible by the second 790 by 2
gogolik [260]
Yes, 790 is divisible by 2. The answer is 395
3 0
3 years ago
If 12 and 20 each divide K without a remainder, what is the value of K?
Juli2301 [7.4K]

Factors of 12 : 1, 2, 3, 4, 6, 12

Factors of 20: 1, 2, 4, 5, 10, 20

In both lists of factors, 4 is in common. Therefore, the value of K is 4 because it can divide into both 12 and 20 without a remainder. 2 is also another possible value of K.

4 0
3 years ago
Read 2 more answers
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