Find a solution to dydx=xy+6x+4y+24dydx=xy+6x+4y+24. If necessary, use kk to denote an arbitrary constant

f(x, y) = yx²/2 + 3x² + 4yx + 24x + K

Step-by-step explanation:

Given the expression dy/dx=xy+6x+4y+24

To find the solution, we are to make y the subject of the formula as shown

dy = (xy+6x+4y+24)dx

∫dy =∫(xy+6x+4y+24)dx

y = ∫(xy+6x+4y+24)dx

We are to integrate the function with respect to x keeping y constant. Since all constant are brought out if integral sign we will have;

y = ∫(xy)dx + ∫(6x)dx + ∫(4y)dx + ∫24dx

y = y∫xdx + 6∫xdx + 4y∫dx + 24∫dx

Integrate;

y = yx²/2 + 6x²/2 + 4yx + 24x + K

y = yx²/2 + 3x² + 4yx + 24x + K

Hence the solution to the differential expression is;

f(x, y) = yx²/2 + 3x² + 4yx + 24x + K

Where K is the constant of integration.

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.