OPTIMIZATION+HANDOUT

OK, so i (tiana) can't seem to figure out some of the problems on the second handout for optimization problems... can anyone help with #3, the dog question? what is the equation for total time supposed to be and the derivative for that?

**Hayyyyyyyyyyy,** **#3/The Dog Question:** t_water + t_land = t_total

t_water = d_water/v_water t_land = d_land/v_land

Therefore d_land/v_land + d_water/v_water = t_total

the velocities are given: v_water = 1.2 and v_land = 6 You designate a variable, x, for distance. So let the horizontal component of d_water = x which means the hypotenuse is sqrt(12^2 + x^2) <-- Pythagorean and d_land = 20 - x

Subbing that back into the equation, you get: (20 - x)/6 + sqrt(12^2 + x^2)/1.2 = t_total

I didn't derive it yet.. because i made a boo boo :( and now i dont want to go back and find my boo boo :( -NAN :D

hi, this is qing Can u guys confirm with me?

i got square root of 80 for number 1 - I concur with this answer - M (+- root10/2,7/2) for number 2 i can't solve the derivative for number 3 i got r = cube root of one over pi for number 4 V ery close but theres an extra 2 in the calculations. r = cube root of 1 over (2 pi) - M 4 cm^2 for number 5 i got v=4mr^3root3/9