Application of derivatives Questions and Answers

A circle has a radius of 4 5m A sector of the circle has a central angle of 1 5 radians Find the area of the sector Do not round any intermediate computations Round your answer to the nearest tenth 2 X 3

A fish is reeled in at a rate of 2 7 feet per second from a point 10 feet above the water see figure At what rate is the angle between the line and the water changing when there is a total of 25 feet of line out Round your answer to three decim de dt rad sec MY NOTES 10 ft

Convert 21 96 to degree minute second form If necessary round your answer to the nearest second ww

An airplane flying at an altitude of 6 miles passes directly over a radar antenna When the airplane is 10 miles away s 10 the radar detects that the distance s is changing at a rate of 210 miles per hour What is the speed of the ai mph

At a sand and gravel plant sand is falling off a conveyor and onto a conical pile at a rate of 16 cubic feet per minute The diameter of the base of the cone is approximately three times the altitude At what rate is the height of the pile changing when h is 12 feet high Hint The formula for the volume of a cone is V h ft min MY NOTES ASK YOUR TEA

The radius r of a circle is increasing at a rate of 5 centimeters per minute Find the rate of change of the area when r 38 centimeters cm min

Answer the following Round your answers to the nearest hundredth a Convert 7 11 14 radians to degree measure b Convert 248 to radian measure radians X

A point is moving along the graph of the given function at the rate dx dt Find dy dt for the given values of x y 4x 7 dx dt a b c x 1 X 0 x 1 5 centimeters per second cm sec cm sec cm sec

Rina wishes to use a canoe to cross to the other side of a river which is 20 m wide The river is flowing at 7 m min and Rina can paddle at 12 m min Round your answers to the nearest tenth where possible a In what direction should she aim the canoe in order to land at a point directly opposite her starting point How long will it take to make this crossing b Her goal is a dock which is 5 m downstream from a point directly opposite her starting point In what direction should she aim her canoe

An object is falling towards the ground according to the equation h t 245 5t 2 where t is measured in seconds and h t is measured in meters The height that the object is above the ground at t 3 seconds is meters 200 0 290 245

Evaluate the following limit 2 25 lim H 2 x 5 Does not exist 0 7 7 0 5

Use the graph to determine the limit If an answer does not exist enter DNE 8 7 6 a lim f x x ct b lim f x x c c lim f x x c 4 7 C 4 4 4 a 5 Is the function continuous at x 4 Yes 4 3 2 1 y 8 7 6 5 4 3 2 1 1 X

A ladder 25 feet long is leaning against the wall of a house The base of the ladder is pulled away from the wall at a rate of 2 feet per second 25 ft a What is the velocity of the top of the ladder when the base is given below 7 feet away from the wall ft sec 15 feet away from the wall ft sec 20 feet away from the wall ft sec b Consider the triangle formed by the side of the house ladder and the ground Find the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the ft sec c Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall

Assume that x and y are both differentiable functions of t and find the required values of dy dt and dx de y x a Find dy dt given x 1 and dx dt 7 dy dt b Find dx dt given x 64 and dy dt 2 dx dt

Consider the given function and point f x 9x 11x 2 1 0 a Find an equation of the tangent line to the graph of the function at the given point yw b Use a graphing utility to graph the function and its tangent line at the point Use the tangent feature of the graphing utility to confirm your results y O

2 You are constructing a cardboard box with the dimensions 2 m by 4 m You then cut equal sized squares from each corner so you may fold the edges What are the dimensions of the box with the largest volume