Compute the double integral ∫∫d3xy2dxdy ∫∫d3xy2dxdy over the region dd bounded by xy=1, xy=16, xy2=1, xy2=25 xy=1, xy=16, xy2=1, xy2=25 in the first quadrant of the xyxy-plane. hint: make a change of variables t: ℝ2→ℝ2t: r2→r2 that converts a rectangular region d∗d∗ in the uvuv-plane into the region of integration d=t(d∗)d=t(d∗) in the xyxy-plane.

Prove that the sum of two consecutive exponents of the number 5 is divisible by 30.if two consecutive exponents are 5n and 5n + 1, then their sum can be written as 30.

Atemperature of 1.64◦f corresponds to answer in units of ◦c.

Acoffee shop orders at most $3,500 worth of coffee and tea. the shop needs to make a profit of at least $1,900 on the order. the possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea: 6c + 13t ≤ 3,500 3.50c + 4t ≥ 1,900 which graph's shaded region represents the possible combinations of coffee and tea for this order?