Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) x^2 + 2y^2 = 17k^2

y = Ax^2

Step-by-step explanation:

below is the detailed solution

To determine the orthogonal trajectories of the family of curves

X^2 + 2y^2 = 17k^2

we have to differentiateX^2 + 2y^2 = 17k^2  with respect to x

= 2x + 4y dy/dx = 0

Hence : dy/dx = - x/2y

we have to determine the negative reciprocal

dy/dx = 2y/x 1

integrate equation 1

∫dy/2y = ∫dx/x

= 1/2 log y = log x + log c

log y = 2logx + 2logc

log y = logx^2 + logC^2

therefore : y = Ax^2  ;   where C^2 = A

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !

i dont know sorry

step-by-step explanation: