by differentiating implicitly. Express your answers in terms 5. (2 marks) Find of x and y....
1. Let A be the surface area of a cube with side s at time t. a) If the side changes at a rate of 3.0 cm/min, at what rate is the cube's surface area changing when the side is 25 cm? b) If the side changes at a rate of -5.0 cm/min, what is the side of the cube when the surface area is changing at a rate of -240 cm2 /min? 2. Find dy/dx by differentiating implicitly. Express...
1. (2 marks) If y = 3x and x changes from 1.2 to 2.5: a) What is the average change in y? b) What is the instantaneous rate of change in y when x = 2.0? 2. (2 marks) The value "V" (in dollars) of a new laptop t years after it is purchased is given by the function: V(t) = 899.95e -0.71 a) What is the average rate of change of the value during the first two years? Round...
dy/ 1. Find 7dx by differentiating 2x2y = x - 3y2 implicitly. (8 pt) 2. Find dx if y = 4x -3x (6 pt) 3. Find dx if y = cos(x2) (6 pt)
6. (2 marks) The position of an object "S" (in meters) at time t is given by the function: s(t) = (3) cos(t) + 41? a) What is the velocity when t = 27 seconds? Indicate the correct units and round your answer to one decimal place. b) What is the acceleration when 1 = 27 seconds? Indicate the correct units and round your answer to one decimal place. 7. (4 marks) Solve the following related rates problems: a) A...
Name: Show your work for full credit!!! 1. If the position function for a moving particle is s(t) = (9 sin (5).-3 cos (5) + 1, 66°/2 + 4), where distances are in meters and r is in seconds, find the speed of the particle when t = 6. Give the simplified exact result or round accurately to 4 decimal places, and include the units with your answer. 2. A small spacecraft is maneuvering near an orbital space station. At...
If a rock is thrown upward on the planet Mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H = 17t - 1.86t^2.(a) Find the velocity of the rock after two seconds.(b) Find the velocity of the rock when t = a.(c) When will the rock hit the surface? (Round your answer to one decimal place.)(d) With what velocity will the rock hit the surface?
Find all values of x satisfying the given conditions. y = 2(3x - 5) - 2, yz = 2(x - 4)+4, y1 = y2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The value(s) of x for which y, = y, is/are { }. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O B. y = y for all values of x....
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
The wave equation can be written as:∂^2 y/∂x^2 = 1/v^2 (∂^2 y /∂t^2) where y = y(x,t) has units of meters, x is also in meters, and t is in seconds. (a) Show explicitly that the function y(x,t) = ymsin(kx)cos(wt) satisfies the wave equation (6 points). (b) Is the function for y = y(x,t) describe a traveling wave? You must explain your answer to get full credit (2 points). 8. On a winter day with a temperature of Tc, the...
At least one of the answers above is NOT correct. (1 point) Suppose f(x, t) = e 3t sin(x + 2t). (a) At any point (x, t), the differential is df = e^(-3t)cos(x+2t)dx+(e^(-3t))(2cos(x+2t)-2sin(x+2t))dt (b) At the point (-1,0), the differential is df = cos(-1)dx+(2cos(-1))+3sin(-1)dt (c) At the point (-1,0) with dx = -0.5 and dt = 0.3, the differential is df = 0.97344 Note. You can earn partial credit on this nrohlem (1 point) Consider the surface xyz = 20....