Consider the following word problem. define a variable, write a function to be optimized and use calculus to find the extrema an art lover is looking at a painting that is 6 feet high and hanging on a wall so that the bottom of the painting is 2 feet above her eye level. how far from the painting should she stand so that the angle subtended at her eye by painting is as large as possible

adding a(n) to an electric circuit would increase the magnetic field around a wire;

b. solenoid

a solenoid is a type of electromagnet whose purpose is to generate a controlled magnetic field.

if the purpose of the solenoid is instead to impede changes in the electric current, a solenoid can be more specifically classified as an inductor rather than an electromagnet.

vapour or gas assuming atmospheriv pressure

no. dot product   =0 when vecs at right angles