Aregion r in the xy-plane is given. find equations for a transformation t that maps a rectangular region s in the uv-plane onto r, where the sides of s are parallel to the u- and v- axes. (let u play the role of r and v the role of θ. enter your answers as a comma-separated list of equations.) r lies between the circles x2 + y2 = 1 and x2 + y2 = 5 in the first quadrant

cheater

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

answer: 0.1,0.85

step-by-step explanation: