Application of derivatives Questions and Answers

Solve the given initial value problem x t 6 8 8 6 x t x 0 4 6 Question content area bottom Part 1

The following chart shows living wage jobs in Rochester per 1000 working age adults over a 5 year period Year 1997 1998 1999 2000 2001 Jobs 625 680 725 760 780 What is the average rate of change in the number of living wage jobs from 1997 to 1999 Jobs Year What is the average rate of change in the number of living wage jobs from 1999 to 2001 Jobs Year

The U S Energy Information Administration projected that imports of petroleum products in 2005 would be 4 81 quadrillion Btu and would increase by 5 47 each year through 2020

2 The two tangent lines from the point P 0 3 to the parabola y 1 touch the parabola at the points A and B The distance AB a 2 2 b 2 c 3 d 3 2 e 2 3 correct

Find and T N B for the given space curve begin aligned r t In cos t 10 mathbf i 1 mathbf j 9 t mathbf k pi 2

Solve the word problem below 24 A flag that is 5 feet tall is raised on a flagpole so that the bottom of the flag is 15 feet above the ground 50 An observer standing 24 feet from the pole measures the angle from the bottom to the top of the flag as shown in the figure below What is the measurement of angle in degrees Round your answer to two decimal places 5 ft 15 ft 2 C 24 ft 15 24 725 576 C 90 c 28 3 C 801 C 28 3

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Textbook Let s t 4t 6t 72t be the equation of motion for a particle Find a function for the velocity v t Where does the velocity equal zero Hint factor out the GCF t and t Find a function for the acceleration of the particle a t

H z 4 Give exact answers not decimal approximations Let f x Find the values of z where f z 3 The greater solution is z The lesser solution is

The slope of the tangent line to the curve y 3 3 at the point 7 is

Let F x f 1 and G x f x You also know that a 11 f a 2 f a 3 f a Then F a and G a

Find inverse laplace function f t for F s F s s 1 s s 1 s 2

b 8 points Find the sum of the following series if it exists 3 en n n 3 3n 1 M8

b Find all intervals on which is increasing decreasing extremum points

recursive an is bounded above by 17 using mathematical i an is an increasing sequence using 4 8 an and ai 0

an 1 4 8 an and a a Show that an is bounded above by 17 using math er the sequence defined recursivel 0

25 Identify the conic by writing the equation x y 2x 4y 4 0 a Circle x 1 y 2 9 b Circle x 1 y 2 9 c Ellipse 9 x 1 y 2 9 d Hyperbola x 1 9 y 2 9 C O He 2 d G C E

20 Evaluate tan a 1 b 1 2 C 3 d 3 TT 14 ASI

12 Find the exact value of cos U v given that sin u and cos v quadrant II a b C d 335 25 72 125 125 11 24 25 Both u and v are

14 Find the component form of the vector when given the magnitude and direction u 20 a 5 13 2 b 17 3 10 c 5 14 2 d 17 3 10 0 150 48 VII S x Snoiloupe nevio erit ai noitbezoinoo to eq

1 What type of conic section is the given equation x 2 y 1 25 a circle b parabola c ellipse d hyperbola 16

11 What type of conic section is the given equation x 2 25 a circle b parabola c ellipse d hyperbola y 16

6 Convert the point from rectangular form to polar for 3 8 a 73 111 b 5 69 c 73 69 d 13 120

7 Write the standard form equation of the hyperbola Vertices 10 3 10 11 Foci 10 2 10 12

Using the MACRS rates from the following table what is the book value of a 3 000 computer after 2 years Year MACRS Rate 1 2345 20 0 32 0 19 2 11 52 11 52 book value Round to the nearest hundredth

Solve the following inequality x 4 x 9 5 x 0 Write your answer as an interval or union of intervals If there is no real solution click on No solution 0 2 0 0 0 0 0 0 0 0 DVO E No

The functions f g and h are defined as follows x 10 3 f x Find 2 8 1 and h 4 g 4 Simplify your answers as much as possible ba g x 13 16x h x 1 3x 2 0 h 4 0 2 0 0 X 3

Find the derivative of z In 9 e dz

4 points Given a power function of the form u s as with u 1 24 and u 3 648 find n and a n Ves Problem 2 a

Let A x f p u du The figure below illustrates the graph of p F 1 118 A I 1 T 1 1 4 1 1 1 1 4 1 3 4 1 1 1 1 1 1 1 1 1 1 T 1 4 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 T 1 1 1 1 On the interval 0 x 6 A x has a local mimimum at x A x has a local maximum at x 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8

2 Let X X2 X be iid N o random variables Let X X n and S a 2pts What is the distribution of X b 2pts What is the covariance of X and S c 2pts What is the distribution of n 1 S o d 2pts What is the distribution of T X H in S 1 n 1 x x X X

Let g 1 4 g 5 3 and Evaluate the integral 5 2 zg z dz 1 S 1 g z dz 5

Verify the following identities 1 tan x tan sin x sin x

The thickness of the ice on a lake for one week is modeled by the T d 0 1d 1 2d 4 4d 14 8 where T is the thickness in cm and d is the number of days after December 31st a Graph this function using graphing technology Ensure your axes are properly set up and state the domain and range that are appropriate for the situation When do you think the warmest day occurred during the week Justify your answer then determine the average rate of change on a short interval near the point you chose b Determine the instantaneous rate of change at this point c Are the rates you calculated in a and b the same or different Why do you think this is 3 D C

y 10x 12y 12 0 The standard form of the equation is Type an equation Graph the hyperbola Choose the correct graph below O A B 11 y 10 The foci is are Type an ordered pair Type an exact answer using radicals as needed Use a con The equation of the asymptote with the positive slope is The equation of the asymptote with the negative slope is Simplify your answers Use integers or fractions for any numbers in the equation

two triangles or no triangle at all Solve the triangle that results A 99 a 14 b 22 Select the correct choice below and if necessary fill in the answer boxes to complete yo Round side lengths to the nearest tenth and angle measurements to the nearest degree OA There is only one possible solution for the triangle The measurements for the re side c are as follows B C C OB There are two possible solutions for the triangle The measurements for the solution with the smaller side length c are as follow B C C 3 The measurements for the solution with the larger side length c are as follows B C C OC There are no possible solutions for the triangle

What value of x in the interval 0 x 360 satisfies the equation 3tan2x 1 0 a 75 165 b 105 15 c 60 120 d 90 180

8 Find the cos 2x if cos x 4 7 a b C 2 16 49 32 49 71 17 49

Given the function f x x 3 24x 2 determine all intervals on which f is both increasing and concave up

Region II First quadrant bounded by y x and y 1 x and y x 1 or each region A Provide a sketch B Compute the a C Compute the volume of the solid when rotated about the x axis about the y axis about y 2 about x 1

12 For z 3 1 and w 1 2i find a z w ww b z C

You want to estimate the mean cost for repairing microwave ovens A random sample of 87 microwave ovens gave a mean repair cost was 54 70 and a standard deviation of 10 50 Find the margin of error for a 99 5 confidence interval for estimating the mean repair cost for all microwave ovens Report your answer accurate to one decimal place E Answer should be obtained without any preliminary rounding However the critical value may be rounded to 3 decimal places

Which of the following would result in the widest confidence interval A sample size of 30 with 99 confidence A sample size of 100 with 95 confidence A sample size of 100 with 99 confidence A sample size of 30 with 95 confidence

The solution s to the following equation is are 8 sin x 10 sin x 7 for 0 x 2 a 7 6 Ob 0 7 6 and 2 7 c and 6 7 d and 11T 6 1

Convert the following measure to radians 120 radians O a T 6 O b O c 2 3 5T 3 O d T

For the curve f x tan 2x 6 tan x find the equation of the tangent line at x 0 O a y 1 y 4 b y 4x Oc y 4x O d 1 4 X X

ate the given binomial coefficient 33 9 A 10 B 20 C 120 D 40 33

Find the horizontal asymptote s if any of the graph of the rational function x2 3x 2 X 2 17 g x A y 3 C y 2 B y 5 D no horizontal asymptote