Math - Others Questions

The height h in meters above the ground of a football t seconds after its been thrown can be modelled by the function h t 4 9t 19 6t 2 a What is the height of the ball when it was thrown b How long was the ball in the air to the nearest tenth of a second

H Domain Range Function 5 5 5

20 pts An investor can design a risky portfolio based on two stocks A and B Stock A has an expected return of 18 and a standard deviation of return of 20 Stock B has an expected return of 14 and a standard deviation of return of 5 The correlation coefficient between the returns of A and B is 50 The risk free rate of return is 10 The expected return on the optimal risky portfolio is

4 Consider the IVP Jy t 1 y t y 1 2 1 t 2 a Write out the midpoint method and modified Euler s method for this IVP with a step size h b Using h 0 5 to 1 and wo 1 use one step of the midpoint method and modified Euler method to compute an approximation to y t 2 The exact solution is y t tln t 2t

1 Consider the IVP y t f t y write down the Taylor expansion of two variables up to order 2 for f t h 2 y h 2f t y at t y TIF

3 Consider the following Heun s method wo a w 1 w hf t w 3hf t 2 h w hf t 3 w hf t w a Write Heun s method in the general form of Runge Kutta method using updates k k2 k3 i e the format we use for RK4 in lecture 5 b Write down the Butcher Tableau for Heun s method c Show Heun s method is consistent and stable

2 Consider the midpoint method for IVP and assume that f is Lipschitz continuous in a b x R Show that a the midpoint method is stable b the local truncation error of midpoint method is O h

Bayside Apartments is a 900 unit apartment complex When the apartments are 90 occupied monthly operating costs total 229 840 When occupancy dips to 80 monthly operating costs fall to 224 080 The owner of the apartment complex is worried because many of the apartment residents work at a nearby manufacturing plant that has just announced it will close in three months The apartment owner fears that occupancy of her apartments will drop to 60 if residents lose their jobs and move away Assuming the same relevant range what can the owner expect her operating costs to be if occupancy falls to 60 Let s begin by determining the formula that is used to calculate the variable cost slope Change in cost Change in volume Variable cost slope Now determine the formula that is used to calculate the fixed cost component Total operating cost Total variable cost Use the high low method to determine Bayside s operating cost equation y 64 x 178 000 Assuming the same relevant range what should the owner expect her operating costs to be if occupancy falls to 60 Round your answer to the nearest whole dollar The owner should expect her operating costs to be if occupancy falls to 60 Fixed cost Save

Big time Floats makes and sells floats shaped like mythical beasts and their weekly cost function is given by C 3100 16 0 4z where is the cost in USD when a floats are made each week How many floats must be made each week in order to minimize the average cost per float floats per week NOTE Round to 3 decimal places if needed

The table lists numbers N of employees in millions of a supermarket x years after 1980 a Find a power function f that models the data in the table b Use f to predict the number of employees in the year 2013 Did your answer involve interpolation or extrapolation c When did the number of employees first reach 1 million Points 0 of 1 12 17 22 X 7 27 N 0 19 0 36 0 67 1 4 2 1

ic 6 3 Conduct a test of Ho p2 2 3 versus Ha 2 3 for the sample data summarized here Use a 01 in reaching your conclusions Sample size Sample mean Sample standard deviation Population 1 13 50 3 7 23 2 21 58 6 6 98

Use the fundamental counting principle A password for a computer consists of five different digits from 0 to 9 followed by three different letters of the alphabet How many different passwords are possible How many distinct passwords are possible OA 78 624 000 OB 655 200 OC 471 744 000 OD 3 931 200

6 2 asic Inferences About Independent Samples 6 2 For each of the situations set up the rejection region a Ho 2 versus Ha b Ho MM2 3 versus Ha c Ho M2 9 versus Ha 2 with n 12 n 15 and a 05 2 3 with n n 25 and a 01 2 9 with n 13 n 15 and a 0

1 12 4 K This question 1 point s possible A group of 10 musical notes is made into a 10 tone musical phrase consisting of 10 different notes How many different phrases are possible to construct There are Question 9 of 24 different phrases possible to construct CIB

List all the ways to select two different members from S with repetition The order in which members are selected is important For example AA is allowed and AB is not the same selection as BA S D E F G H Identify the list of all the ways to select two members from S Choose the correct answer below O A DD DE DF DG DH EF EG EH FG FH GH OB DF DG DH EF EG EH FG FH OC DD DE DF DG DH EE EF EG EH FF FG FH GG GH HH OD DD DE DF DG DH ED EE EF EG EH FD FE FF FG FH GD GE GF GG GH HD HE HF HG HH

K Specify the number of ways to perform the task described Give your answers using P n r or C n r notation On a biology quiz a student must match fifteen terms with their definitions Assume that the same term cannot be used twice The number of ways to perform the task is Do not evaluate

Suppose that the surface area S of a bird s wings in square feet can be modeled by S w 1 24w wings having a surface area of 4 square feet W 3 1 where w is the weight of the bird in pounds with 1 ws 10 Estimate the weight of a bird with

K Find the number of combinations 8 objects taken 3 at a time There are combinations

You are taking a multiple choice test that has 7 questions Each of the questions has 4 answer choices with one correct answer per question If you select one of these choices for each question a leave nothing blank in how many ways can you answer the questions You can answer the questions in ways C

Find the equation of the perpendicular bisector of each of the following line segments a the line segment joining A 2 2 and B 4 6 b CD if the equation of the line passing through C and D is x y 3 and the midpoint of CD is 2 1

A ski resort is building two parallel straight ski slopes for children One of them has a 1 gradient of The other ski slope will pass 3 through points 2 3 and s 5 Find the value of s

Find the gradient of a line which is parallel 10 cach line with the given equation a y x 6 b x 7 Find the gradient of a line which is perpendicular to each of the following lines a y 3x 11 b b 2y 0

2 The distance between two towns P and Q is 2 km On a coordinate system town P has coordinates x 7 and Q has coordinates 3 5 The values of the coordinates are given in kilometres Find the value of x

3 A tracking station lies at the origin of a coordinate system with the x axis due east the y axis due north and the z axis vertically upwards Two aircraft have coordinates 20 25 11 and 26 31 12 relative to the tracking station All coordinates are given in km a Find the distance between the two aircraft at this time

Kerri Jungemann owner of Flowers 4 You operates a local chain of floral shops Each shop has its own delivery van Instead of charging a flat delivery fee Jungemann wants to se the delivery fee based on the distance driven to deliver the flowers Jungemann wants to separate the fixed and variable portions of her van operating costs so that she has a better idea how delivery distance affects these costs She has the following data from the past seven months Click the icon to view the data Read the requirements Requirement 1 Determine the company s cost equation use the output from the Excel regression Round the amounts to two decimal places y X Data table Month January February 17 400 March 15 400 April 16 300 May 16 500 June 15 200 July 14 400 Miles Driven Van Operating Costs 15 500 5 390 5 280 4 960 5 340 5 450 5 230 4 680 I X

Match the function with its graph v 4 x 2 3 77 Question Help Video Submit Question Ray W

4 2 point In class we showed Vf x is the direction in which a differentiable f increases the most a What is the direction that f decreases the most Use similar analysis we did in class to justify your answer b Suppose you are walking on a surface with elevation modeled by 2 2 Find a direction a unit vector in R2 from the point 2 2 in which the rate of increase is half that of the maximum direction x y 20

Question 7 Let f z 4 2 If g z is the graph of f z shifted up 6 units and right 2 units write a formula for g z g x Enter z as sqrt x

5 2 points Let C be the set of all points on the unit sphere x y 1 where the tangent plane contains the point 1 1 1 C is a circle Find its center and radius

f a in the box

Question 1 If the formula y z is changed by adding six shown in bold below what effect would that change have on the function s values f x x 6 Select an answer What effect would it have on the graph Select an answer

2 2 points What is y r for a function defined by the equation x cos xy y 3e as it passes through x 0

Move the slider kt so that the graph of g gets shifted up 2 units Then type the new function f z in the answer bax 7 T B 9 HO 3 2 T 2 2 f x 1 3 Ok 0 00 Don t forget to shift the graph up Using function notation i e f x enter the function that results from the transformation

Please give complete well written solutions to the following exercises and submit via Grade scope 1 2 points Let f x y t represents the temperature at a position x miles east and y miles north of New York City and time t hours after noon Suppose that temperature increases by 02 for every mile south and decreases by 03 for every mile east But temperature everywhere also depends on time of day and thus contains a term of the form 12 cos 2 Suppose you drive southwest at 10 27 mph at 2pm Estimate d Is it getting hotter or cooler

Which situation demonstrates the law of large numbers If it snowed four days last month it will snow four days this month If you roll a six sided number cube 36 times you will roll a 4 six times If 800 people are randomly surveyed about the TV shows they watch about 400 of them will be women If you flip a coin 44 times you will get heads about 22 times

Exercise 8 5 1 For each matrix below compute the determinant using all three methods 2 3 1 4 4 4 5 6 7 1 2 3 b A 3 3 1 2 3 2 1 1 1 0 0 1 1 1 a A c A 1 0

3 2 points Let f x y 1 a Find a direction u such that Duf 0 1 0 b At which point s x y is the function s direction of greatest growth parallel the line y x

Exercise 8 5 3 Check that the well known formula for the determinant of a 2 x 2 matrix det satisfies the three properties of Definition 8 2 1 and thus is a correct formula for the determinant

Exercise 8 5 5 Use the following steps to prove that det AT det A 1 First write PA LU as I did in definition 8 3 1 Then take the transpose of both sides 2 Now take the determinant of your equation with four terms Analyze which determinants you know which are simpl and which remain to be thought about 3 At the end lots of things should cancel and you should get det A det U det AT

Exercise 7 3 3 Why is it true that if B is a basis for W and L VW is a linear map whose image includes B then L is urjective What can you further say about the rank of L if you knew about the length of the basis B

Exercise 8 5 2 Use the fact that AA I and Proposition 8 2 8 to solve for det A in terms of det A

Exercise 8 5 2 Use the fact that A A I and Proposition 8 2 8 to solve for det A in terms of det A

Question 11 Given the following functions find each of the values f z z z 30 g z 5 f g 2 f g 3 f g 5 Question Help Video Submit Question

Question 15 If f x z z 1 simplify each of the following f a h f x h f z

Question 14 f x z 3z 10 g x x 5 Find 4 x The domain of A 4 z is z 9

Question 13 Let f z 4x 3 and g z 2z 3z After simplifying fg z Question Helps Vidon

Question 9 The function h z defined as 1 8 Question Help Video can be expressed in the form f g z where g z z 8 and f z is U

Which of the following functions will correctly return the number of pie slices to be equally shared among friends def piel slices friends slices per friend slices friends return slices per friend def pie2 slices friends slices per friend slices friends return slices per friend def pie3 slices friends slices per friend slices friends return slices per friend def pie4 slices friends friend slices friends

If f z z 7 g z f g h z 1 4 and h z 2 then

Select all true statements for why we use functions A Positronic data B Modularization C Testing D Troubleshooting F Re Use