Find the GCF of each pair of numbers.

DJ Davon is making a playlist for work; he is trying to decide what 12 songs to play and in what order they should be played. If

Marta_Voda [28]

Answer:

3.63 * 10^19

Step-by-step explanation:

Given that :

Number of choices to select = 12

Category available :

Blues - 14

Country - 25

Disco - 21

To select an equal number of song for each category ; then 4 songs will be selected from each :

Using combination :

(14C4 * 25C4 * 21C4)

Since the order matters for the 12 selected songs ; it thus requires 12 permutation

Thus ;

(14C4 * 25C4 * 21C4) * 12!

nCr = n! / (n-r)!r!

Using calculator;

14C4 = 1001 ;

25C4 = 12650

21C4 = 5985

12! = 479001600

Hence,

(1001 * 12650 * 5985) * 479001600

= 36301596217286400000

=3.63 * 10^19

5 0

2 years ago

Show that (2xy3 + cos x)dx + (3x2 y2 − sin y)dy = 0 is exact, and find the solution. Find c if y(0) = π

Licemer1 [7]

We're looking for a solution of the form $F(x,y)=C$ . By the chain rule, this solution should have total differential

$\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0$

and the equation is exact if the mixed second-order partial derivatives of $F$ are equal, i.e. $\frac{\partial^2F}{\partial x\partial y}=\dfrac{\partial^2F}{\partial y\partial x}$ .

The given ODE is exact, since

$\dfrac{\partial(2xy^3+\cos x)}{\partial y}=6xy^2$

$\dfrac{\partial(3x^2y^2-\sin y)}{\partial x}=6xy^2$

Then

$\dfrac{\partial F}{\partial x}=2xy^3+\cos x\implies F(x,y)=x^2y^3+\sin x+f(y)$

$\dfrac{\partial F}{\partial y}=3x^2y^2-\sin y=3x^2y^2+\dfrac{\mathrm df}{\mathrm dy}$

$\dfrac{\mathrm df}{\mathrm dy}=-\sin y\implies f(y)=\cos y+C$

$\implies x^2y^3+\sin x+\cos y=C$

With $y(0)=\pi$ , we get

$\cos\pi=C\implies C=-1$

$\implies\boxed{x^2y^3+\sin x+\cos y=-1}$

6 0

2 years ago

Plz help! Determine whether the equation represents a direct variation. If it does, find the constant of variation.

Finger [1]

Answer:

It does not have a direct variation, because y doesnt vary directly with x

Step-by-step explanation:

Hope This Helps!!!

8 0

3 years ago

Read 2 more answers

(5/8 x - 10) - (1/8 x - 12)

nikklg [1K]

Answer: 16x-25 over 4(4x-5)(2x-3)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Identify the zeros of f(x) = 2x^6 +2x^5

elena-14-01-66 [18.8K]

Answer:

0, -1

Step-by-step explanation:

zeros occur when 2x^6+2x^5=0

the first way for this to happen would be to set x to 0. both terms would become zero.

the second way is x = -1

first term becomes 2

second becomes -2

these add to zero

6 0

2 years ago