Application of derivatives Questions and Answers

Find the complete solution of del 3 z delx 3 3 del 3 z delx 2 dely 4 del 3 z dely 3 e x 2y

Find an equivalent statement for the following absolute value equation x 7 8

If the area of a rectangle is 2x 2 11x 15 and the width is x 3 find the length

18 4sin2x 4cosx 5 0 for 0 x 2n 58

A person borrows 27000 and agrees to repay the loan in monthly installments over 5 years The agreement is to pay 2 of the unpaid balance each month for using the money and 450 each month to reduce the loan What is the total cost of this loan that is what is the sum of all the monthly interest payments Cost of loan

Find the sum of the first 39 terms of the arithmetic sequence 9 18 27 36 839

7 2 7 Z Over 4 4 18 x 20 lim x 2 x 2 18 lim z 0 22 lim r 0 1 x 8 X 1 8

There is a 10 chance of rain tomorrow A spinner with 10 sections is spun to simulate the probability of rain where spinning a 1 indicates rain If the results are 3 6 1 8 and 3 then what is the difference in the experimental probability from the simulation and the prediction or

The population of College and Career Preparation can be represented by the exponential function P 5 67 1 10 where n is the number of years since 1979 Estimate the population in 2020

h Simplify the following expression 120 860

Question Completion Status Answers that are fractions write them with a For example 2 3 Answers that have exponents write them with a A For example 2y 3 A B C D E F G Expression 7 2 7100 1 2 3 m X m 6 2 6 4 2 2 m 1 n 2 4 14 0 Simplified Expression Answer D

ou have inherited land that was purchased for 30 000 in 1960 The value of the land increased by approximately 5 per year What is the approximate value of the land in the year 2011 or pros ALT F10 PC ALT EN F10 Mac

Bacteria can grow 130 per day After 5 days how many bacteria will we have from 6 bacteria For the toolbar press ALT F10 PC or ALT FN F10 Mac

Question Completion Status QUESTION 5 Evaluate the following If your answer is a fraction write it using a For example 2 3 If you answer contains an exponent write it using a A For example 3x 2 Question 3x00 4 2x 43 x 4 3 5 3 4 Answer

se any convenient method to determine whether the following system of equations is consistent inconsistent or dependent 6x 8y 14 x 2y 1 swer Only One Solution Inconsistent System O Dependent System

A yeast culture is growing at a rate of W t 0 3e0 09t grams per hour Find the area between the graph of W and the t axis over the interval 0 10 and interpret your res The area under the curve rounded to three decimal places is square units

Is it possible to multiply the following matrices 2 A 0 L5 O Yes 1 5 3 5 B 0 8 3 4 1

A company manufactures mountain bikes The research department produced the marginal cost function C x 400 3 0 x 900 where C x is in dollars and x is the number of bikes produce per month Compute the increase in cost going from a production level of 300 bikes per month to 900 bikes per month Set up a definite integral and evaluate it The increase in cost is

A For the graph given a Give the interval s where the function is increasing b Give the interval s where the function is concave down 3 2 1 UN 5

A small plane flew 440 miles in 2 hours with the wind Then on the return trip flying against the wind it traveled only 312 miles in 2 hours What were the wind velocity and the speed of the plane Note The speed of the plane means how fast the plane would be flying with no wind Answer How to enter your answer opens in new window speed of the plane mph Keyboard S

Use the method of substitution to solve the following system of equations If the system is dependent express the solution set in terms of one of the variables Leave all fractional answers in fraction form Answer 5x 9y 1 4x 7y 1 Selecting an option will display any text boxes needed to complete your answer Only One Solution Inconsistent System Rependent System Keypad Keyboard Shortcuts

A ro 1 4 2 3 0 L4 2 1 A B B 1 2 3 0 4 2 1 1 LO 5

2 1 A 10 5 L5 3 53 B 0 4 8 1 Determine the dimensions of the matrix represented by A B

5 If a sequence has the following terms determine the equation of the general term 1 Point U 12 U5 324

Use the graph to determine the values of a for which lim f x does not exist Enter your answers as a comma separated list x a a dne

Entered 0 037371822 a10 The answer above is NOT correct mission Preview My Answers Your score was recorded Find the 10th term of the geometric sequence with a3 3 32 and as 3 32768 Answer Preview Submit Answers 0 037371822

6 6 points State the definition of the tangent line to the graph of a function y f x at a point P a f a Draw a picture showing the graph of y f x and the tangent line at P and illustrate the definition of the tangent line in your picture Then explain why the slope of the tangent line is equal to In your picture what does f x f a a lim x a f x f a x a represent Upload an image a PDF of your solution Save Answ

Graph of Sketch function 7 of its derivative f x is shown 1 3 2 2 O f o and find the folutis 2

Solve the initial value problem dx dt Ax with x 0 xo 4 2 0 A 3 i 1 x t

The form of the partial fraction decomposition of a rational function is given below A 9x Now evaluate the indefinite integral 20x 45 1 9 x 5 x 9 B dx 4 C 9x 20x 45 x 5 x 9 A x 5 Bz C z 9

Fill in the blank to make a true statement cos x help formulas 1

Find f if f x sin x cos x f 0 2 and f 0 8 Answer f x T

19 sin x 2 sin x cos x 0 for 0 x 2n 58

Determine where the given function is increasing and where it is decreasing f x x 12x 4 O Decreasing on 2 and 2 increasing on 2 2 Increasing on 4 and 4 decreasing on 4 4 Decreasing on 2 increasing on 2 Increasing on 2 and 2 decreasing on 2 2 OO

Find the limit lim X 01 30 O 00 5x 1 15x 7 130 1 72

Determine the vertical asymptote s of the given function If none exists state that fact h x x 6 x2 9 Ox 3 x 3 x 6 x 9 x 6 x 3 x 3 Ox 0 x 9

Determine the horizontal asymptote of the given function If none exists state that fact h x 9x 3 x 6 Oy 0 Oy 6 Oy 9 no horizontal asymptotes

Determine where the given function is concave up and where it is concave down f x x 16x 68 Concave up on 8 concave down on 8 Concave up on 8 concave down on 8 Concave up for all x Concave down for all x

e A rectangular shipping container measures 6 feet by 10 feet by 4 feet Find the surface area of the hipping container 10 ft 4 ft

Suppose that 4000 is invested at an interest rate of 5 7 per year compounded continuously What is the doubling time time to reach 24 000 O 2 yr 12 2 yr 13 2 yr 11 2 vr

what is the volume of the solid formed in the second quadrant bounded by the curves y 9 x 2 the x axis and the y axis when it is rotated about the Line x 1

10 The function f x 75 1 29x represents the value of an iTunes gift card after x songs have been purchased Based on this model which statement is true 1 The gift card s value is 129 and it costs 0 75 per song 2 The gift card s value is 75 and it costs 1 29 per song 3 The gift card s value is 76 29 and it costs 1 29 per song 4 The gift card s value is 75 and it costs 0 75 per song

1 Prove that sin x cos x 1 cos x csc x

1 Two construction workers are lifting a beam using ropes Worker A pulls with a force of 500 newtons at an angle of 40 with the positive x axis Worker B is on the opposite side pulling with a force of 380 newtons at an angle of 115 with the positive x axis Find the a magnitude and b direction angle of the resultant force

Find all the points x y for which both f and f equal zero where f x y x y xy 2y 6

Hattie has recently inherited 9900 which she wants to deposit into an IRA account She has determined that her two best bets are an account that compounds daily at an annual rate of 3 1 Account 1 and an account that compounds semi annually at an annual rate of 2 8 Account 2 Step 2 of 2 How much would Hattie s balance be from Account 1 over 5 2 years Round to two decimal places Yound

Which of the sources below would be the most credible one to use in an essay describing the experiences of immigrants who went through Ellis Island in the first half of the 1900s O A 1915 letter written by a nurse stationed on Ellis Island to her family telling of an immigrant family she helped O A fiction story that is set in the early 1900s and traces an immigrant s journey through Ellis Island O A book published in 1960 that contains transcripts of interviews with immigrants who went through Ellis Island OA 2014 article describing the experiences of the author s father an immigrant who went through Ellis Island

In an effort to control vegetation overgrowth 55 rabbits are released in an isolated area free of predators If the population after 1 year has increased to 165 rabbits what will the population be after another 9 months Round your answer to the neare rabbit Answer 2 Points Ke Keyboard Sh

Question 18 of 30 step Use the properties of logarithms to condense the following expression as much as possible writing the answer as a single term with a coefficient of 1 All exponents should be positive 2log Slog Answer 2 Points log Keypad Keyboard Shortcuts

Consider the following piecewise defined function Answer 2 Points 7 2 3 4 ifx 3 7 ifx 3 f x 40 x 7 Step 3 of 3 Evaluate this function at x 5 Write the exact answer Do not round If the answer is undefined write Und as your answer f 5 K Keyboard S