Application of derivatives Questions and Answers

Correct Determine the implied domain of the following function Express your answer in interval notation f x x 6 9 Answer

Given the following function determine the difference quotient Answer 8 C X P V 2 2 f x h f x h f x 2x x 7

The function P x 4x 1850x2500 gives the profit when x units of a certain product are sold Find a the profit when 90 units are sold 131600 3 OF dollars b the average profit per unit when 90 units are sold 1462 2 OB dollars per unit c the rate that profit is changing when exactly 90 units are sold 1130 OF dollars per unit d the rate that profit changes on average when the number of units sold rises from 90 to 180 dollars per unit e The number of units sold when profit stops increasing and starts decreasing Round to the nearest whole number if necessary

Determine the domain and range for the relation Answer S x y x E N and y E N R Domain OR ON OZ Range ON OZ

Find the following using the table below X 1 f x 3 4 2 4 3 2 2 3 4 1 g x 3 1 g x 1 4 3 h 3 if h x 4 1 h 3 if h x f x g x 8 g x h 3 if h x f g x 22

BELY 3 m x 2 x 2 3 Vertex 2 3 od gadgene 1 25 161brup goingsig 4 Xatav alt selg

A spinner has five congruent sections one each of blue green red orange and yellow Yuri spins the spinner 10 times and records his results in the table Color blue green red orange yellow Number 1 2 0 4 3 Which statements are true about Yuri s experiment Select three options The theoretical probability of spinning any one of the five colors is 20 The experimental probability of spinning blue is The theoretical probability of spinning green is equal to the experimental probability of spinning green The experimental probability of spinning vellow is less than the theoretical probability of spinning vellow

1 point The table below gives the height f t in feet of a weight on a spring where t is time in seconds a What is the period of f t b What is the the midline of f t c What is the the amplitude of f t include units include units sec 0 24 6 8 10 12 14 16 18 20 22 24 26 28 30 h feet 4 6321 823 4 66 27 2747 26 24 6 3 2 1 8 include units

K Fill in the blank with The boiling point of The boiling point

rom the Metric K Convert the quantity 14 pounds to kil

se a double integral in polar coordinates to find the volume of the solid bounded by the graphs of the equations for the following questions 1 2 3 x y 3 z 0 x y 1 z ln x y z 0 x y 1 x y 4

ind the general solutions of the following differential equations using D operator methods D 6D 9 y 3x cosh3x e

In the following exercises use a suitable change of variables to determine the indefinite integral 271 1 x da 10 ft 1 1 0 dt 272 273 f 274 7x 11 dx 275 cos 0 sin ede 276 277 11x 7 dx cos nt sin nt dt 278 sin cos xdr Hint sin x cos x 1 ftsin 280 t cos t sin t3 dt 279 281 sin 76 sin 0 cos de tsin t cos t dt 2 73 3 da

The annual revenue and cost functions for a manufacturer of zip drives are approximately Rx 520 003 and where x denotes the number of drives made What is the maximum annual profic x 160x 100 000 O 1 720 000 1 520 000 1 620 000 0 1 820 000

261 x 1 dx u x 1 262 263 264 265 266 270 x 1 d u x 1 267 ercis S 2x 3 dx u 2x 3 S 3x 2 dx u 3x 2 the antid rivative using the indicated substitution X dx u x 1 x 1 X 1 x dx u 1 x2 3 x 1 x 2x dx u x 2x 268 2 2x x 32 dr u 2 32 269 cos 0d0 u sine Hint cos 0 1 sin 0 sin 0d0 u cos 0 Hint sin 0 1 cos 0 u

In the following exercises find the antiderivative using the indicated substitution 261 x 1 dx u x 1 262 x 1 d u x 1 5 7 263 2x 3 dx u 2x 3 264 265 11 3x 2 da u 3x 2 S x dx u x 1 Vx 1

Determine G 1 922 3023 for matrix A al 911 922 3023 A 297 85 11

641 cm mm 41 cm mm Simplify your answer Type

Room temperature is 2 F Simplify your answer

Briefly explain how you would differentiate y O In O where inside the and O symbols there are functions of x 1 Which rules will you use in each step 2 What will you get at the end of each step Please type your answer in the space provided Instead of the and O symbols you can just type their names square and circle For the toolbar press ALT F10 PC or ALT FN F10 Mac BIUS Paragraph Arial 10pt 9 F AV H x Al 16 26 I 1

Sketch the following logarithmic function Identify three points that lie on the graph and determine the domain and the equation of any vertical asymptotes f x log 4 x 3 Fill in the missing coordinates of the points that lie on the graph of y log 4x and the corresponding points that lie on the graph of f x log 4 x 3 Points that lie on the Corresponding points that lie graph of y log 4x on the graph of f x log 4 x 3 Type exact answers in simplified form 1 0 Type ordered pairs Type exact answers in simplified form

ickels dimes and quarters in his coin box The total value of the coins is 8 85 If the number of nickels and quarters is four mone number of dimes find how many of each coin Matthew has in his coin box Matthew has Matthew has Matthew has nickels dimes quarters

Evaluate the following derivative assuming that f 1 1 and f 1 16 Enter only a number as your answer Do not type any other symbol d t In f t dt 1 1

Evaluate the following integrals by interpreting them in terms of areas a f f x dx da b f x dx c f x dx C Show Transcribed Text Please highlight the structures that you

Suppose z is a solution to the equation e w for some w E C 0 Then which of the following statements must be true 0e w O el w O Arg z Im w Owl 1 Ws

whether each sentence below is true or false 1 The formula for calculating the sum of any finite geometric sequence is B Standard Fals

11 How many different 5 membe 53 12 Kyle has 6 favorite books If he wishes to take 4 books on a road trip how many different combination NT 4 books are possible 360

Answer each question below Write your answer as a fraction 13 A bag has 6 red marbles 2 blue marbles and 5 green marbles Without looking two marbles are drawn 2 out of the bag What is the probability of selecting 2 green marbles 2 13

Find the partial sum S5 for the geometric sequence with a 2 r 2 S5

QUESTION 27 Solve the problem A swimmer swims 1 5 mph in still water

L 26 20 27 0 31 40 50 28 29 30 QUESTION 30 Graph the polar equation 5x 4 61 31

Determine whether point A is inside or outs

Choose the partially colored map that could be completed color A N

A barrel of oil has a height of 3 m and a

A street light is at the top of a 20 ft tall pole A woman 6 ft tall walks away from the pole with a speed of 5 ft sec along a straight path How fast is the tip of her shadow moving when she is 50 ft from the base of the pole ft

rectangular fish tank is 70 cm long 50 cm w a How many cubic centimeters of water w b How many milliliters of water will the ta c How many liters of water will the tank h The tank will hold cubic centimeters of b The tank will hold c The tank will hold milliliters of water liters of water

In the figure AB is parallel to CD m 4 E B D

A spring is being stretched by a weight d t centimeters and it is in seconds cm sec 100t 2t 15 Find the average rate of change on the interval 21 26 Select cm sec where d is measured in Find the average rate of change on the interval 25 26 Select Find the average rate of change on the interval 25 9 26 Select cm sec

O O Lines and 2 are parallel lines Determine the measu 412

and radius r t inches is given by the formula V 4 dV Which is the correct expression for dt dV dt dV dt dV dt dv dt dv dt 8 r dt dr dh dt dt 8 r 0 8 r ocean The volume of oil in a spill in the shape of a cylinder of height 4 inches dt dr dt Suppose that the radius of the spill is expanding at a rate of 0 2 inches per second How fast is the volume changing when the radius of the spill is 2 6 inches Round your answer to the nearest hundreth cubic inch per second cubic inch

A street light is at the top of a 18 ft tall pole A woman 6 ft tall walks away from the pole with a speed of 4 ft sec along a straight path ft Ray sec Woman Shadow How fast is the tip of her shadow moving when she is 35 ft from the base of the pole C

Use implicit differentiation to find y given that Here f is a function of x Upload an image or PDF of your solution x tan f y y f tan x

Let y 4 and da dt Find dy 4 dt when x 2

Oil has spilled in the ocean The volume of oil in a spill in the shape of a cylinder of height 5 inches and radius r t inches is given by the formula V 5 Which is the correct expression for O O dV dt O dV dt dV dt dV dt 0 dV dt 11 10Tr dr dt 10 r dt 577 dr dt dr dh dt dt 10TT dV dt Suppose that the radius of the spill is expanding at a rate of 0 4 inches per second How fast is the volume changing when the radius of the spill is 2 1 inches Round your answer to the nearest hundreth cubic inch per second

A spherical balloon is being inflated at a constant rate of 17 cubic inches per second How fast is th radius of the balloon changing at the instant the balloon s diameter is 8 inches Is the radius changing more rapidly when d 8 or when d 12 Why equation V 4 Recall that the volume of a sphere of radius r is V Tr Note well that in the setting of this 3 problem both V and r are changing as time t changes and thus both V and r may be viewed as dV dr Differentiate both sides of the implicit functions of t with respective derivatives and dt dt 4 3 Tr with respect to t using the chain rule on the right to find a formula for dr dt dV dt Time 1 that depends on both r and dV dt Time 2 dr dt At this point in the problem by differentiating we have related the rates of change of V and r Recall that we are given in the problem that the balloon is being inflated at a constant rate of 17 cubic inches per second Is this rate the value of dr dv dt dt Time 3 or dV dt

Content Question Completion Status Z Launch Me In a public park a triangular region of grass is bounded vertices of the triangle as shown in the figure The dista from A to C is 90 ft and the distance from B to C is 13 of rotation For each sprinkler head how large should th dry and to conserve water Round to the nearest degree

QUESTION 13 Find z1z2 and write the pro 2 0 cos 7 0 00 3 06 6 5 COS 30 Cos 5T 12 5n 12 isin isin isin 5 3 22 2 5 0 5 12 5T 12 8

QUESTION 1 Write a polar equation that represents 4 LENDI

Pedro is hosting a game night There are 4 card games and 3 board games to choose from For the role playing game Pedro has 8 options If Pedro and his friends want to play one of each type of game in how many different ways can they choose the games game nights

A magnitude of 700 pounds of force is required to hold a boat and its trailer in place on a ramp whose incline is 10 to the horizontal What is the combined weight of the boat and its trailer