Application of derivatives Questions and Answers

in which of the relations represented by the tables below is the output a function of the input Select all correct answers Select all that apply Input 3 4 5 7 Output 12 13 13 9 Input Output 13 4 3 3 1 12 10 32 Input 9 5 6 5 Output 12 5 1 11 Input 4 6 17 Output 11 0 5 5 Input 0 2 3 5 Output 5 0 11 5

Aron of a sector of a circle The area of a sector of a circle with a central angle of 3 radians is 19yd Find the radius of the circle Do not round any intermediate computations Round your answer to the nearest tenth

A circle has a radius of 4ft A sector of the circle has a central angle of radians Find the area of the sec 7 T 6 Do not round any intermediate computations Round your answer to the nearest tenth S

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

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

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

Find the distance from the point to the plane 2 3 1 x 2y 3z 17 The distance is Type an exact answer using radicals as needed

Let u 2 3 and v 2 3 Find the component form and magnitude length of the vector 5u 3v The component form is 5u 3v Simplify your answers

9 2 What Did One Dog Say To The Other Dog Write the letter of each answer in the box containing the exercise number Find the hypotenuse c of the right triangle with the given side lengths a and b 1 a 15 b 20 3 a 13 b 84 5 a 6 b 17 5 Find the side length b of the right triangle with the given hypotenuse c and side length a 7 c 61 a 11 8 c 82 a 80 9 c 34 a 16 10 c 65 a 63 12 c 10 a 5 13 An access ramp to a building is 3 7 meters long The distance from the beginning of the ramp to the base of the building is 3 5 meters How tall is the ramp 11 c 13 a 6 6 14 A rectangular garden is 14 feet wide and 48 feet long If you stand in one corner of the garden how many feet away is the corner diagonally across from you 10 6 2 a 5 b 12 4 a 65 b 72 6 a 6 b 7 2 13 14 4 12 1 8 3 7 Answers T 93 3 P 1 2 9 E 18 5 D 18 N 25 U 9 0 97 H 50 N 60 G 30 O 13 M 11 2 1 85 S 16 11 5

1 Let z e y sin x y e cos x y Show that it satisfies the equation xz Y y 0 Answer

1 Let z e sin x y e cos x y Show that it satisfies the equation x2 y y 0

2 Integrate f x y z x 3y z z over the line segment C joinin the origin to the point 1 1 1

ind all solutions of the following system of linear equations 4x2 8x3 x2 3x3 202 5 02 x1 371 12 1 6

Deductible 2000 00 Event 1 Description Tree damage Foundation repairs Repair cost 2 500 00 25 000 00 If no insurance claim is submitted for Event 2 what is the owner s out of pocket cost for the repair A 500 B 2 000 C 25 000 Event 2 D 2 500

Find the period phase shift and amplitude of the function y 2 cos TX 2 Give the exact values not decimal approximations Period Phase shift 8 X B

Question You are told that h is a one to one function with values h 2 9 and h 4 10 Which of the following must be true Select all correct answers Select all that apply h 2 9 h 9 2 h 10 2 h 9 10 h 10 4 h 4 10 m

How many functions are there from a set with 4 elements to a set with 6 elements

How many subsets has a finite set with 4 elements

There are 32 computers in a data center in the cloud Each of these computers has 24 ports How many different computer ports are there in this dat center O24 O 768 56 32

Find all solutions to the equation sec 0 2 0 Write your answer in radians in terms of and use the or button as necessary T Example 8 2ka k Z or 0 ka k 9 7 ka k Z Z 5 0 Help with this notation 8 B JU kzkez

Jane and Deandre are standing on a riverbank 190 meters apart at points A and B respectively See the figure below They want to know the distance from Deandre to a house located across the river at point C Jane measures angle A angle BAC to be 41 and Deandre measures angle B angle ABC to be 65 What is the distance from Deandre to the house Round your answer to the nearest tenth of a meter 419 190 m meters X Esp

Given the following table of values for the function f x determine f 0 6 5 4 08 6 5 0 3 6 Provide your answer below X 12 f x 11

ph the hyperbola 25x 9y 250x 18y 391 0 12 10 8 6 o 14 12 10 B Ch 4 10 2 T 19 10 6 8 10 12 14

Graph the ellipse 25x 4 100x 24y 36 0 XO B n XE X

23 d 5 Simplify your answer as much as possible 0 Olo

Calculate the number of possibilities Selecting 2 orange tabbies from a litter of 9 kittens at an animal shelter

Calculate the number of possibilities Seating 8 students in 8 seats in the front row of the auditorium

Determine the global extreme values of the f x y 10x 2y if y x 3 y x 3 y 5 Use symbolic notation and fractions where needed fmax

Find the volume of the solid obtained by revolving the region R bounded by y J x 0 around x 2 6 x x 1 and

14 Find the domain and range of the function 3 a domain b c 0 d range domain 3 range domain range domain range e none of the above 0 3 0 3 g t t 3

8 A real estate office handles an apartment complex with 50 units When the rent is 860 per month all 50 units are occupied However when the rent is 905 the average number of occupied units drops to 47 Assume that the relationship between the monthly rent p and the demand x is linear Predict the number of units occupied if the rent is raised to 1010 a 37 units b 60 units c 63 units d 43 units e 40 units

3 A moving conveyor is built to rise 7 meters for every 10 meters of horizontal change Find the slope of the conveyor

2 Convert each of the following a T to radian b 2 radian to degree

3 If cos0 1 and 0 is an acute angle find the other five trigonometri function value

the linear inequality Express the so 2 3x 1 4x 14

a Find symmetric equations for the line that passes through the point 5 1 7 and is parallel to the vector 1 3 4 X 5 x 1 2 7 y 3 4 O x 5 3 y 1 4 z 7 0X 5 y 1 2 7 4 Ox 5 Y 7 3 O x 5 3 y 1 4 2 7 b Find the points in which the required line in part a intersects the coordinate planes point of intersection with xy plane point of intersection with yz plane point of intersection with xz plane

Suppose 450100 f t f 1 dx 31 74 What should we write inside the symbol and why Justify your answer completely Explain why 31 became t dt 3

A factory selling cell phones has a marginal cost function C x 0 01x 3x 229 where a represent the number of cell phones and a marginal revenue function given by R x 429 2x Find the area between the graphs of these curves and x 0 h

Find parametric equations for the line Use the parameter t x t y t z t Find the symmetric equations the line through 6 4 5 and parallel to the line y z 1 X y O 1 2 1 2 5 3 O X 6 2 X 6 Y 4 2 3 V y 4 z 5 3 02 2 2 2 5 2 z 5 O y 0 x 6 24 24 3 5

Find an equation of the largest sphere with center 4 2 7 that is contained in the first octant 2 8x 4y 12z 65 0 x