h(t) be the radius of the circle at time t. (1 point) Let A- f(r) be...
(1 point) Let C be a semicircle of radius r> 0 centered at the origin. Let P be a point on the x-axis whose coordinates are P= (r + rt, 0) where t> 0. Let L be a line through P which is tangent to the semicircle. Let A denote the triangular region between the circle and the line and above the x-axis (see figure.) (Click on image for a larger view) MON Find the exact area of A in...
5. Let f a, b R be a 4 times continuously differentiable function. For n even, consider < tn = b, a to < t< an uniform partition of [a, b] with b- a , i = 0,1,.. , n - 1 h t Let T denote the composite Trapezoidal rule associated with the above partition which approx imates eliminate the term containing h2 in the asymptotic expansion. Interprete the result which you obtain as an appropriate numerical quadrature rule...
Let P = f(t) = 850(1.057)* be the population of a community in year t. (a) Evaluate f(0) = (b) Evaluate f(10) = (retain at least 3 decimal places) (c) Which of these statements correctly explains the practical meaning of the value you found for f(10) in part (b)? (select all that apply if more than one is correct) A. What the population will be in 10 years. B. The growth rate per decade of the population. C. How long...
(1 point) Let P = f( = 1150(1.059)' be the population of a community in year 1. (a) Evaluate f(0) = (b) Evaluate f(10) = (retain at least 3 decimal places) (c) Which of these statements correctly explains the practical meaning of the value you found for f(10) in part (b)? (select all that apply if more the is correct) A. How many years it takes for the population to reach 10,000 people. B. The growth rate per decade of...
Let K be a cone with a circular bottom, that has a radius r, and the apex is directly above the center of the bottom. Let h represent the height of the cone. Show that the surface area of the cone K without the bottom is equal to pi * r * sqrt(r^2 + h^2) . (Use that a sector that is given with angle θ in a circle with radius R has the area (θ * R^2)/2.
h gr f j b k a Time t Select the point(s) on graph from options that has negative acceleration (Select all that apply). ( take the reference of above t vs v graph) k b f h Velocity h gr f j b k a Time t Select the point(s) on graph from options that has negative acceleration (Select all that apply). ( take the reference of above t vs v graph) k b f h Velocity
Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does the line with equation y = 2.52 + 3 intersect the circle with radius 4 and center (0, 3)? Enter your answer correct to 3 decimal places.
A particle of mass m moves in a circle of radius R at a constant speed v, as shown below. The motion begins at point Q at time t = 0. Determine the angular momentum of the particle about the axis perpendicular to the page through point P as a function of time. (Use any variable or symbol stated above along with the following as necessary: t.)
The curvature of vector-valued functions theoretical Someone, please help! 2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos t, a sin t), show that the curvature is n(t) = (b) Recall that the tangent line to a curve at a point can be thought of as the best approx- imation of the curve by a line at that point. Similarly, we can...
O in the t of time. In a circle of radius r=1.50 m at a certain (b) At this instant, find the speed of the partidle.