Use the method of lagrange multipliers to minimize the function subject to the given constraint. (round your answers to three decimal places.) minimize the function f(x, y) = x2 + 3y2 subject to the constraint x + y ? 1 = 0.

We just started the introduction into circles and i have no idea how to do this.

Asource of laser light sends rays ab and ac toward two opposite walls of a hall. the light rays strike the walls at points b and c, as shown below: what is the distance between the walls?

Tyler went to the supermarket to buy food for a food pantry. he has $36, and can carry up to 20 pounds of food in his backpack. pasta costs $1 for a 1-pound package. pasta sauce costs $3 for a 1.5 pound jar. let x = the number of packages of pasta and y = the number of jars of pasta sauce. one package of pasta is the right amount to go with one jar of pasta sauce. what is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry? how many packages of pasta? how many jars of pasta sauce? explain your reasoning.