1. [-/2 Points] DETAILS SCALCET9 14.7.046. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the points on the surface y? = 64 + xz that are closest to the origin. smaller y-value (x, y, z) = larger y-value (x, y, z) = Need Help? Read It Submit Answer 2. [-/1 Points] DETAILS SCALCET9 14.7.049. MY NOTES ASK YOUR TEACHER Find the maximum volume (in cubic units) of a rectangular box that is inscribed in a sphere of radius / units cubic units Need Help? Read it Watch it Submit Answer 3. [-/1 Points] DETAILS SCALCET9 14.7.054. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs nine times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials. (Let x, y, and z be the dimensions of the aquarium. Enter your answers in terms of V.) (x, y, z) - Need Help? Read It Submit Answer 4. [-/2 Points] DETAILS SCALCET9 14.8.007. MY NOTES ASK YOUR TEACHER This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. ((x, y) = 2x2+ 62, x4+ 34 = 1 maximum value minimum value Need Help? Read it Submit Answer 5. [-/2 Points] DETAILS SCALCET9 14.8.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A package to be mailed using a certain postal service may not measure more than 90 inches in length plus girth. (Length is the longest dimension and girth is the largest distance around the package, perpendicular to the length.) length girth Use Lagrange multipliers to find the exact dimensions (in inches) of the cylindrical mailing tube of greatest volume that may be mailed using the postal service. radius length 6. [-/2 Points] DETAILS SCALCET9 14.8.029. MY NOTES ASK YOUR TEACHER Find the extreme values of f on the region described by the inequality. (If an answer does not exist, enter DNE.) f(x, y) = e-xy, x2 + 4y2 s 1 maximum minimum Need Help? Read It Watch It Submit Answer 7. [-/1 Points] DETAILS SCALCET9 14.8.053. MY NOTES ASK YOUR TEACHER If the length of the diagonal of a rectangular box must be L, use Lagrange multipliers to find the largest possible volume