Calculus Answers

Two friends part company at 11pm. The first walks north at 1.2 m/sec, while the second walks east at 1.8 m/sec. How fast is the distance between them increasing 45 seconds later? Round your answer to the nearest tenth of a m/sec.

A rocket blasts off from rest at time t = 0 and accelerates upward at a constant rate for 20 seconds. The engines then cut off. At time t = 50, the rocket attains its maximum height and begins to fall. It crashes to the ground at t = 90. Use the axes below to sketch the velocity of the the rocket as a function of time. Be sure to label the t-axis appropriately.

Newton’s laws of cooling proposes that the rate of change of temperature is proportional to the temperature difference to the ambient (room) temperature. And can be modelled using the equation: 𝑑𝑇𝑑𝑡=−𝑘(𝑇−𝑇𝑎) This can also be written as: 𝑑𝑇𝑇−𝑇𝑎=−𝑘 𝑑𝑡

Where: 𝑇=𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑜𝑓 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑇𝑎=𝐴𝑚𝑏𝑖𝑒𝑛𝑡 (𝑟𝑜𝑜𝑚) 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑘=𝐴 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 a) Integrate both sides of the equation and show that the temperature difference is given by: (𝑇−𝑇𝑎)=𝐶𝑜𝑒−𝑘𝑡

supply price = 50+q/2 demand price = 150-q/5 find producer and consumer surplus

∫ √(1 + cos θ) dθ

∫ Sec^6 t dt from (-π/4) to (π/4)

∫ (sec θ - tan θ)² dθ

∫ tan⁴ (½)z dz

∫ cot³ 2x dx

∫ csc⁴ θ dθ