Water is being pumped into a spherical tank of radius 60 feet at a constant rate of 10 ft^3 per second. Find the rate at which the radius of the top level of water in the tank changes when the tank is half full.

Use implicit differentiation to find an equation of the tangent line to the ellipse defined by 2x^2−xy+3y^2=71 at the point (−4,3).

3) A researcher has collected population data along with time. Afler comparing the populations from consecutive times, he finds out the population is increasıng and also that in the early slages, the rate of change of the population (derivative with respect to time) is proportional to the population itself aj Find an equation describing this situation. What can you say regarding the coefficient of proportionality (positive or negative)? Explain. b) The rescarcher decides to make a corroction to this cquation by subtracting a constant (the rate of change of the population with respect to time becomes proportional to the population itself minus a constant). Give an expression for the general solution of this equalion.

Chris pulls a slinky a distance of 14 inches from its equilibrium position and then releases it. The time for one oscillation is 3 seconds. Step 2 of 2: Find the function in terms of t for the displacement of the slinky. Assume that the slinky is at its maximum displacement at t = 0. Also assume that the function includes no horizontal or vertical shifts. } = X y = Keypad Keyboard Shortcuts