Final answer:
The values of y that satisfy the given condition are y = 3 and y = 7.
Step-by-step explanation:
To find the values of y such that the distance between (3,y) and (-2,3) is 14, we can use the distance formula. The distance formula is given by:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the given coordinates and the distance:
14 = sqrt((-2 - 3)^2 + (3 - y)^2)
Simplifying the equation:
196 = 25 - 10y + y^2
Rearranging and solving for y:
y^2 - 10y + 171 = 0
Using the quadratic formula, we find two values of y: y = 3 or y = 7. Therefore, the values of y that satisfy the given condition are y = 3 and y = 7.