The particle moves in such a way that the distance between the particle and the origin increases at a constant rate of 3 units per second. (c) A particle moves along the portion of the curve r = 3 + 2cosθ for 0 < θ < π/2. (b) Find the slope of the line tangent to the graph of r = 3 + 2cosθ at θ = π/2. Write an expression involving an integral for the area of R. (a) Let R be the shaded region that is inside the graph of r = 4 and also outside the graph of r = 3 + 2cosθ, as shown in the figure above. The curves intersect at θ = π/3 and θ = 5π/3. The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above.Related rates–which are almost always on polar questions. Finding the slope of the tangent line (convert to parametric and find dy/dx).
#Calculus memes plankton free#
According to this model, what is the rate ofĬhange of the height of the tree with respect to time, in meters per year, at the time when the tree isĪP Calculus BC 2018 Free Response Question 5Ī polar question! Finding polar area between two curves.
When the tree is 50 meters tall, the diameter of theīase of the tree is increasing at a rate of 0.03 meter per year. X is the diameter of the base of the tree, in meters. (d) The height of the tree, in meters, can also be modeled by the function G, given by, where (c) Use a trapezoidal sum with the four subintervals indicated by the data in the table to approximate theĪverage height of the tree over the time interval 2 ≤ t ≤ 10. (b) Explain why there must be at least one time t, for 2 < t < 10, such that H'(t) = 2. Using correct units, interpret the meaning of H'(6) in the (a) Use the data in the table to estimate H'(6). Selected values of H(t) are given in the table above. The height of a tree at time t is given by a twice-differentiable function H, where H(t)) is measured in meters and t is measured in years.Related rates problem using a new function. Trapezoidal Rule to approximate average value.
Find the total distance traveled by the boat over the time interval 0 ≤ t ≤ 1.ĪP Calculus BC 2018 Free Response Question 4 Time t is measured in hours, and x(t) and y(t) are At time t ≥' 0, the position of the boat is (x(t),y(t)), where (d) The boat is moving on the surface of the sea. Plankton cells in the column is less than or equal to 2000 million. That gives the number of plankton cells, in millions, in the entire column. Write an expression involving one or more integrals Water in part (b) is K meters deep, where K > 30. (c) There is a function u such that 0 ≤ f(h) ≤ u(h) for all h > 30 and. To the nearest million, how many plankton cells are in this column of water between h = 0 and (b) Consider a vertical column of water in this sea with horizontal cross sections of constant area 3 square Using correct units, interpret the meaning of p'(25) in the context of the problem. The continuous function f is not explicitly given. Plankton cells, in millions of cells per cubic meter, is modeled by
There are 20 people in line at time t = 0. They exit the line at a constant rate of 0.7 person per second. Where r(t) is measured in people per second and t is measured in seconds.
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