Math - Others Questions

ferentiatle woth respect to x y x 7x 4 2 3

3 a Solve x 2 b Solve 1 xy xy 1 xy ydx 0 UNIT II OR 7M 8M

15 2 Determine the reactions at the supports El is constant 3 6 kN m 2m 2 1 m Prob 15 2 12 kN 2 1 m 3

4 Solve the given IVPS a yv 5y 4y 10 b x y xy y x e x y 0 1 y 0 0 y 0 0 y 0 C y 1 1 y 1 3 y 1 14

5 There are 200 ants in a nest the ant population double every month a Write an expression to represent the number of ants after n months b What will the population of the ants be after 6 months Round to 1 decimal place c What will the population of the ants be after 1 year Round to 1 decimal place 6 A new car is purchased at a cost of 25000 The value of the car depreciates at a rate of 30 per year a Write an equation to represent the value of the car after years b What is the value of the car after 3 years c What is the value of the car after 6 years 7 A loaf a bread costs 2 but the rate of inflation is 3 per year a Write an expression to represent the cost of a loaf of bread after years b How much would the loaf of bread cost in 2 years c How much would the loaf of bread cost in 10 years

A long year end status report for work is 465 pages long You need to print 203 copies for a meeting next week How much is the paper going to cost for those reports Paper is sold in reams 500 pages for 14 each Answer Give your answer to the nearest cent only for the paper you use partial reams are OK

1 Solve the following IVPs Show the details a y sinh x cosy y 0 4 b c d xy y 3x cos y x xy 4y 8x4 y y y y 1 n 3 y 1 2 y 0 1 3

1 Use the graph of y f x to graph the function g x f x 4 2 B 6 y f x Ay 6 8 ob 6 44 a 2 4 6 2 X

in 2N cos 2N sin 2N 4 sin N cos N GLITR To verify the identity rewrite the more complicated side of the equation so that it is identical to the simpler side Choose the correct transformations and transform the expression at each sin 2N 4 sin Ncos N Use a double angle identity Use a reciprocal identity Combine like terms

1 Evaluate the following expressions Leave your answers in fraction form where applicable a 3 b 9 d 2 2 Solve for x in the following exponential equations a 3 36 c 8 32 20 7 49 2 32 5 11 e 5 125 978 2 32x 8 b d c 3 3 Complete the chart by first by first writing the powers with the same base Then solve the equation Equation Rewrite with Common Base 62x 5 1 6 f 343 9 3 2 Solve for x

se the number line model to illustrate the following operation 2 1 3 2 1 2

Subtract Illustrate using fraction strips 31 25 3

Multiply using the rectangular area model 3 4 1 7 1 1 20

4 Consider this image below Use ex 5 5 5 8 25 525 5 Consider this image below Use exponent laws to evaluate them 3 3 5 9 9 6 Consider this image below Use exponent laws to evaluate them 2 2 2 2 16 16 1 16 7 Write in radical form and then evaluate the following

1 Match the picture to the Exponent Law a amn Product Law Quotient Law Power of a Power Power of a Product Zero Exponenet Law Negative Exponent Law 2 Match the picture to the Exponent Law a d am n Product law Quotient law Power of a Power Power of a Product Zero Exponent Law Negative Exponent Law 3 Match the picture to the Exponent Law axa amen

1 Match the picture to the Exponent Law a Product Law Quotient Law Power of a Power Power of a Product Zero Exponent Law Negative Exponent Law 2 Match the picture to the Exponent Law a 1 Product Law Quotient Law Power of Power Power of a Product Zero Exponent Law Negative Exponent Law 3 Match the picture to the Exponent Law ab arb Product law Quotient Law Power of a Power Power of a Product

1 Simplify the following Express final answer with POSITIVE EXPONENTS ONLY 9x y 4x y 12x y 8 2 Simplify the following Express final answer with POSITIVE EXPONENTS ONLY 6x y 5 2x y 3ry 4 3 Solve for x in each of the following equations by obtaining a common base on both sides of the equation 4 64 Question 3 options 21 3 4 Solve for x in each of the following equations by obtaining a common base on both sides of the equation 1 32 Question 4 options 0 In The tab bre doe

1 Solve for x in each of the following equations by obtaining a common base on both sides of the equation 3x www Question 5 options 3 1 3 3 27 2 Solve for x in each of the following equations by obtaining a common base on both sides of the equation Upload your solutions 2 marks 625 3 Solve for x in each of the following equations by obtaining a common base on both sides of the equation Upload your solutions 2 marks C 21 8 4 Solve for x in each of the following equations by obtaining a common base on both sides of the equation Upload your solutions 2 marks 32 4 27 2 5 Consider this image for the following questions Joel has two investment options Option 1 Option 2 500 invested at 5 per year compounded annually The amount A after a years is given by the equation A 500 1 05 400 invested at 7 25 per year compounded annually The amount A after years is given by the equation U

7 Evaluate the following expression exactly no decimals Draw a diagram for full credit arccos csc arccos

OR a Find the real root of the equation tanx x using Bisection method

25 Kamini is constructing the kite shown below The kite includes 2 perpendicular supports one of length 40 inches and the other of length 28 inches The ends of the supports are connected with string to form a 4 sided figure that is symmetric with respect to the longer support A layer of paper will cover the interio of the 4 sided figure Which of the following is closes to the area in square inches that Kamini will cove with paper A 101 B 280 560 D 840 E 980 string 28 in 40 in

The sum of 2 and 200 of 1 has the same value as which of the following calculations 2 2004 100 of 2 B 150 of 2 300 of 2 C D 300 of 1 E 400 of 1

UNIT IV 7 a Fit a polynomial for the following data x0 1 2 3 4 5 y 10 12 19 25 30 42 b Find the y 4 for the following data X 1 2 V 7 8 5 9 12 30 8M 7M

A city would like to know how many vehicles it could move through its streets in an emergency The most likely situation is an evacuation starting at the school and ending at the park The connections between these two locations plus their capacity and direction is shown below Path A B C Capacity 30 10 20 DE F G 15 30 15 15

an A bank found that in recent years the average monthly charge on its credit card was 1 350 With an improving economy they suspect that this amount has increased A sample of 40 customers resulted in average monthly charge of 1 376 11 with a standard deviation of 182 57 Do these data provide statistical evidence that the average monthly charge has increased Formulate the appropriate hypothesis test and draw a conclusion Use a level of significance of 0 05 Is there sufficient evidence at the 0 05 level of significance that the average monthly charge has increased Determine the null hypothesis Ho and the alternative hypothesis H Ho H 1350 H H 1350 Type whole numbers Compute the test statistic 0 90 Round to two decimal places as needed Using a level of significance of 0 05 what is the critical value 1 68 Round to two decimal places as needed Find the p value for the test 0 184 Round to three decimal places as needed What is your conclusion The p value is the chosen value of a so greater than the null hypothesis There is evidence to conclude that mean is greater than 1 350

A bank found that in recent years the average monthly charge on its credit card was 1 350 With an improving economy they suspect that this amount has increased A sample of 40 customers resulted in an average monthly charge of 1 376 11 with a standard deviation of 182 57 Do these data provide statistical evidence that the average monthly charge has increased Formulate the appropriate hypothesis fest and draw a conclusion Use a level of significance of 0 05 Is there sufficient evidence at the 0 05 level of significance that the average monthly charge has increased Determine the null hypothesis Ho and the alternative hypothesis H Ho H 1350 H 14 1350 Type whole numbers Compute the test statistic 0 90 Round to two decimal places as needed Using a level of significance of 0 05 what is the critical value 1 68 Round to two decimal places as needed Find the p value for the test Round to three decimal places as needed

State the hypotheses for the simple linear regression tests Ho H K Using the accompanying Concert Sales data on sales dollars and the number of radio TV and newspaper ads promoting the concerts for a group of cities Develop simple linear regression models for predicting sales as a function of the number of each type of ad Compare these results to a multiple linear regression model using both independent variables State the model and explain R square Significance F and p values with an alpha of 0 05 Click the icon to view the Concert Sales data at least one B is not 0 B B Bk 0 B 0 O Points 0 of 5 B 0 Save 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Sales 1000 Thousands of radio and TV ads 1064 997 919 626 869 950 946 1199 881 1011 1614 1562 1067 934 1395 1336 1401 1496 1561 1715 1774 1786 0 0 25 25 32 30 34 33 38 41 47 43 48 48 53 54 62 62 68 64 70 68 Thousands of newspaper ads 39 41 26 25 29 30 34 33 25 24 45 47 48 52 20 21 32 32 33 33 39 42

4 Andy bought an airplane and wanted to determine the most efficient power setting She kept records on the range of the aircraft in kilometers starting with a full tank of fuel for a number of power settings in revolutions per minute rpm The results are T 15 shown below Power Setting rpm Range km 1500 1600 1700 1800 1900 649 695 733 763 785 a Does the Power Setting show equal intervals b Calculate the first differences What does it imply about the rate of change constant increasing decreasing c Calculate the second difference What does it imply

1 Given that sin 0 7818 use equivalent trigonometric expressions to evaluate the following 3 14 cos

Standard Product Cost Atlas Furniture Company manufactures designer home furniture Atlas uses a standard cost system The direc labor direct materials and factory overhead standards for an unfinished dining room table are as follows Direct labor 28 00 per hr 5 0 hrs 12 00 per bd ft 18 bd ft standard rate standard time per unit standard price standard Variable factory overhead standard rate Fixed factory overhead standard rate a Determine the standard cost ner dining room table X P Incorrect Direct materials oak quantity Feedback 2 00 per direct labor hr 3 80 per direct labor hr b A standard cost system provides Atlas Furniture Company s management a cost control tool using the principle of management by exception Using this principle major cost deviations from standards can be investigated and corrected Check My Work Remember the process discussed in chapter for calculating standard cost

Learning Goal from Lesson 6 1 I can compute the sales tax Find the sales tax and total purchase price 2 points Clarissa Byrne purchased a 399 99 electronic organizer 78 94 in office supplies and a 98 95 office chair for work Clarissa lives in New Orleans Louisiana where the state tax is 4 and the city tax is 4 What is the a total sales tax and b total price 1 Learning Goal from Lesson 6 2 How I Did Circle one I can calculate the total purchase price I got it I m still learning it How I Did Circle one I got it I m still learning it

Trish invests 6 000 in her IRA in a bond trust that pays 10 interest compounded semiannually Sean invests 6 000 in his IRA in a certificate of deposit that pays 9 7 compounded continuously Who has more money afte years Trish or Sean After 20 years Trish will have Round to the nearest cent as needed

What rate of interest compounded annually is required to double an investment in 8 years The rate of interest required is Round to two decimal places as needed

What will a 160 000 house cost 4 years from now if the price appreciation for homes over that period averages 6 compounded annually The future cost of the house will be Do not round until the final answer Then round to the nearest cent as needed

Find y as a function of tif 5y 300 0 9 1 0 4 6 Note This particular webWork problem can t handle complex numbers so write your answer in terms of sines and cosines rather than using e to a complex pow

The sodium potassium pump is called an electrogenic pump because it decreases the voltage difference across the membrane is used to drive the transport of glucose against a concentration gradient pumps equal quantities of Na and K across the membrane in opposite directions generates voltage across the membrane

4 How can double angle and compound angle identities help us solve trigonometric equations and simplify trigonometric expressions

1 Given that sin cos 3 14 0 7818 use equivalent trigonometric expressions to evaluate the following

1 Given that sin 3 14 cos 0 7818 use equivalent trigonometric expressions to evaluate the following

2 Use an appropriate compound angle formula to express as a single trig function and then determine an exact value T sin cos TE TL cos sin T

In the diagram below angle A is in standard position Find the coordinates of point B and then find sin A cos A and tan A XB YB sin A COS A tan A

expectation when you throw the dart 9 a The probability that the dart lands on 5 is 16 Type a fraction Simplify your answer The probability that the dart lands on 10 is Type a fraction Simplify your answer The probability that the dart lands on 70 is Type a fraction Simplify your answer The probability that the dart lands on 100 is 100 1 16 W

Coca Cola Enterprises CCE is the largest bottler of Coca Cola in Western Europe The company purchases Coke and Sprite concentrate from The Coca Cola Company KO dilutes and mixes the concentrate with carbonated water and then fills the blended beverage into cans or plastic two liter bottles Assume that the estimated production for Coke and Sprite two liter bottles at the Wakefield UK bottling plant is as follows for the month of May Coke Sprite In addition assume that the concentrate costs 75 per pound for both Coke and Sprite and is used at a rate of 0 15 pound per 100 liters of carbonated water in blending Coke and 0 10 pound per 100 liters of carbonated water in blending Sprite Assume that two liters of carbonated water are used for each two liter bottle of finished product Assume further that two liter bottles cost 0 08 per bottle and carbonated water costs 0 06 per liter Prepare a direct materials purchases budget for May assuming inventories are ignored because there are no changes between beginning and ending inventories for concentrate bottles and carbonated water 153 000 two liter bottles 86 500 two liter bottles Materials required for production Coke Sprite Feedback Coca Cola Enterprises Wakefield Plant Direct Materials Purchases Budget For the Month Ending May 31 assumed data Concentrate 2 Liter Bottles Total materials Direct materials unit price Total direct materials to be purchased Check My Work x s 459 lbs 173 632 lbs 75 153 000 btls 86 500 239 500 btls 0 08 Carbonated Water x 5 306 000 Itrs 173 000 479 000 Itrs 0 06 19 140 X

Situation II Water flows through a pipe at 130 L s that changes gradually in diameter from 154 mm at point A to 429 mm at point B Point B is 4 6 m higher than point A The pressures at point A and point B are 70 kPa and 48 3 kPa respectively Assume that the datum line passes through point A 8 Which of the following most nearly gives the specific energy at point A a 9 565 m c 6 979 m d 6 894 m b 9 618 m 9 Which of the following most nearly gives the specific energy at point B a 9 565 m c 6 979 m b 9 618 m d 6 894 m 10 Which of the following most nearly gives the head loss in the pipe a 0 053 m c 2 586 m b 0 085 m d 2 724 m

Solve x In x y y 2 In x using integrating factors

Solve homogeneous equation x 2 y xy y 2

8 a Find the missing values in the following data X 1 2 3 4 y 11 22 40 b Find the polynomial f x interpolating the following data 0 1 4 5 X f x www 5 140 2 2 6 7M

6 The determinant of a 2x2 matrix a b C Question Find the determinant of is ad bc 6 39 1 4 For more information on this topic look in your textbook at section 8 3 You might also want to look at the Matrix Operations presentation

O 30 O 12 O 15 27 auct The dot product of two vectors u a i b j and v a i b j is defined as u v a a2 b b For more information on this topic look in your textbook at section 6 7 You might also want to look at the Dot Product presentation Question How much is 3i 2j 7i 3j NOTE Two vectors are orthogonal perpendicular if and only if their dot product is zero

Assume that you are 28 years old today and that you are planning on retirement at age 65 Your current salary is 54 000 and you expect your salary to increase at a rate of 4 per year as long as you work To save for your retirement you plan on making annual contributions to a retirement account Your first contribution will be made on your 29th birthday and will be 8 of this year s salary Likewise you expect to deposit 8 of your salary each year until you reach age 65 Assume that the rate of interest is 9 The present value PV at age 28 of your retirement savings is closest to 71 196 60 133