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3 years ago

15

Write (p^2)^3 without exponents

1 answer:

Rasek [7]3 years ago

4 0

Answer:

$p*p*p*p*p*p*p*p*p$

Step-by-step explanation:

$(p^2)^3$

$2^3=8$

$=p^8$

$p^8$ = $p*p*p*p*p*p*p*p$

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Solve the Differential equation 2(y-4x^2) dx + x dy = 0

padilas [110]

Assume a solution of the form $\Psi(x,y)=C$ . Taking the differential of both sides would give the ODE

$\Psi_x\,\mathrm dx+\Psi_y\,\mathrm dy=0$

where $\Psi_x=2y-8x^2$ and $\Psi_y=x$ . The ODE is exact if $\Psi_{xy}=\Psi_{yx}$ . We have

$\Psi_{xy}=(2y-8x^2)_y=2$

$\Psi_{yx}=(x)_x=1$

so the ODE is not exact. However, multiplying both sides by $x$ gives

$(2xy-8x^3)\,\mathrm dx+x^2\,\mathrm dy=0$

and now

$(x\Psi_x)_y=(2xy-8x^3)_y=2x$

$(x\Psi_y)_x=(x^2)_x=2x$

so the ODE is now exact.

Now,

$\Psi_x=2xy-8x^3\implies \Psi(x,y)=x^2y-2x^4+f(y)$

$\Psi_y=x^2=x^2+f_y\implies f_y=0\implies f(y)=C$

So the ODE has solution

$\Psi(x,y)=x^2y-2x^4+C=C$

or simply

$\boxed{x^2y-2x^4=C}$

3 0

4 years ago

Abbey is stacking boxes of candles for a store display. The volume of each cube-shaped box is 125 cubic inches. If the display h

OLEGan [10]

The display after stacking of 6 layers of cube is 30 inches high.

Step-by-step explanation:

The volume of cubic box used by Abbey= 125 inch³

Total no of layer he has in display= 6

Height of the display-

We know that the volume of the cube is a³

Where a is the side of the cube

Hence to find the side of the cubic box we need to find the cube root of the volume i.e. ∛125

Hence the side of each cube is 5 inch. Since all the sides for cube are equal hence the height would also be 5 inch

The total height of the display would be 6*5= 30 inches

4 0

3 years ago

Can a prime number be a multiple of any other number except itself why or why not

Crank

Nope. Because Thats The Opposite Of What A Prime Even Is!

8 0

3 years ago

What is the midpoint between the following two points

qwelly [4]

Answer:

B, (6,0)

Take the average of the x values and the average of the y values:

(3+9)/2 = 6

(-2+2)/2 = 0

This means the answer (the average (midpoint) of the two points) is (6,0)

5 0

4 years ago

Solve the equation by completing the square if necessary round to the nearest hundredth x^2-18x=19

Gennadij [26K]

See the photo attached. The answer is x = 19, x = -1, so B.

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3 years ago