Sequences & Series Questions and Answers

Construct a truth table for the following statement Identify if it is a tautology contradiction or neith sr v p s Fill in the truth table for sr v ps line by line S rp s r v p s TTT TTF TFT TFF FTT FTF FFT FFF

Using the convergence theorems show that the sequence Xn 1 3n 5 1 n 5 is convergent and find its limit

roblem 6 ind the amplitude period frequency and vertical shift of the function whose graph is given below If a 1 b 3 c 1 d 3 e 2 and f 0 Note With a few assumptions made about what the points c d and e f represent as far as the period of tangent or cotangent is concerned we don t actually need to know the locations of the asymptotes They are included here to make things more explicit C 0 Y x c d e f Amplitude Period Frequency Vertical Shift

423 3 A 11012 3 B 21001 3 D 20011 3 C 10122 E 10012 3 HARRAN N VERS TES Y S 2019

Chun and Mali Tung bought a house for 135 980 They made a 30 000 down payment Their annual expenses were mortgage interest of 7 540 depreciation of 2 5 of the purchase price of the house and taxes repairs and insurance of 10 380 They rented the house for 1 850 per month Determine a the annual net income and b the annual yield

1 May Kawasaki is 72 and has an IRA with a fair market value of 98 000 a Use the Uniform Life Table on p 47 to determine her required minimum distribution b What penalty would she incur if she failed to take the distribution c What penalty would she have paid if she had made an early withdrawal of 10 000 to take a vacation 2 Amir Bahoud is 70 and has a Roth IRA with a fair market value of 156 800 a Use the Uniform Life Table or p 46 to determine her required minimum distribution b What penalty would he incur if he failed to take the distribution c What penalty would he have paid if he had made an early withdrawal of 20 000 to help pay E his grandchildren s college education

Complete the table 1 IRA Fair Market Value 260 000 546 000 186 400 418 680 328 840 284 348 Amount Withdrawn at Age 55 50 000 35 000 10 000 35 000 0 23 780 a a a a you are finished check the solutions with your teacher Penalty for Early Withdrawal 5 000 3 500 Age 73 72 74 80 77 71 b a a b b b ent practice Required Minimum Distribution b b C C C C Penalty If Not Withdrawn

problem 2 Nora Beck is 80 and has an IRA with a fair market value of 350 000 a Use the Uniform Life Table on p 4 to determine her required minimum distribution b What penalty would she incur if she failed to take the distribution c What penalty would she incur if she had made an early withdrawal of 20 000 to pay for grandchild s college education

Complete the table 1 Purchase Price Cash Invested 89 700 10 000 235 700 40 000 515 250 1 750 000 75 000 350 000 Monthly Rent 450 4 000 6 000 15 000 Annual Expenses Annual Rental Income 5 400 4 500 43 800 a 67 500 a 145 000 a b b b Annual Net Income 900 a C C C Annual Yield

The following is an initial value second order differential equation where d x dt 5x dx dt dx dt x 7 sin wt 0 and x 0 6 Note that w 1 Decompose the equation into two first order differential equations Afte the decomposition solve the system from t 0 to 1 with a step size of 0 5 Use Heun method 0 1 5

9 Let P3 be the vector space of polynomials of degree 3 and let T P3 R 1 0 1 be the linear transformation defined by T f x Find a basis

Find the time of the loan Use a banker s year of 360 days Time Principal 39 200 00 days Rate 6 5 The time of the loan was days Interest 980 00

Evaluate logarithmic expressions without using a calculator it possible log N 2 log N

KE log 1587 5 log 1587 5 Do not round until the final answer Then round to four dec

Determine the solution y x for each of the following initial value problems 1 1 1 2 y yx cos x 0 with y a 1 2y 0 with y 1 y X

3 6 pts A hydraulic arm has the dimensions shown below Through what angle 8 must the arm rotate upward for the arm to reach a height of 3 meters Round to 2 decimal places Give your answer in both degrees and radians 2 5 m 0 11 0 degrees radians 2 m 10 3 m

function Use the red point as a slider to select the number of zeros that your graph will show You may click on a point verify its coordinates Sorry that s incorrect Try again 10 5 100 80 60 40 20 O 20 40 60 O f x 2 x 7 x 5 x 1 0 O zeros 4 10

Determine the exact value of each of the following a sin b cos c tan 37 37 8 500 d sin FF e cos 1 tan 500 500 500 g sin h cos 1 tan 117 12 117

Complete the table for the radioactive isotope Round your answer to two Half life Initial Amount After Isotope years Quantity 1000 Years 226Ra 1599 69 9

If there exists a surjection f N A then A countable

The graph shows stopping distances for trucks at various speeds on wet roads Use this information to complete parts a and b below Stopping Distance feet Stopping Distances at Selected Speeds 700 600 500 400 300 220 200 100 0 340 30 40 Speed miles per hour a Use the statistical menu of your graphing utility and the quadratic regression program to obtain the quadratic function that models a truck s stopping distance f x in feet on wet pavement traveling at x miles per hour f x x x 480 50 655 60

4x 2x 1 8 7x 31 8 4x 2x 1 1 7x 31

a Write a linear cost function representing the cost C x in S to the vendor to produce x products b Write a linear revenue function representing the revenue R x in S for selling x products c Determine the number of products to be produced and sold for the vendor to break even d If 90 products are sold will the vendor make money or lose money Part 1 of 4 a The linear cost function representing the cost is C x 260 0 75x Part 2 of 4 b The linear revenue function representing the revenue is R x 4x Part 2 4 Part 3 of 4

graph to determine the following a Find the numbers at which f has a relative maximum What are these relative maxima b Find the numbers at which f has a relative minimum What are these relative minima a The number s at which f has a relative maximum is are Type an integer or a decimal Use a comma to separate answers as needed The relative maximum maxima is are Type an integer or a decimal Use a comma to separate answers as needed b The number s at which f has a relative minimum is are Type an integer or a decimal Use a comma to separate answers as needed The relative minimum minima is are Type an integer or a decimal Use a comma to separate answers as needed

Consider the set of integers Z under the operation defined by a b a b 1 Show that f Z Z where f x 1 2 is an isomorphis

Shawn Rebecca and Karen went to an office supply store Shawn bought 6 pencils 6 markers and 7 erasers Her total was 28 50 Rebecca spent 22 25 buying 5 pencils 4 markers and 6 erasers Karen bought 4 pencils 5 markers and 5 erasers for 21 25 What is the cost of each item Provide your answer below

Draw the graphs of the equations x y 1 0 and 3x 2y 12 0 Determine the coordinates of the vertices of the triangle formed by these lines and the x axis and shade the triangular region

An arch is in the shape of a parabola It has a span of 48 meters and a maximum height of 8 meters Find the equation of the parabola assuming the origin is halfway between the arch s feet Determine the height of the arch 12 meters from the center meters

The half life of carbon 14 is 5600 years If a piece of charcoal made from the wood of a tree shows only 77 of the carbon 14 expected in living matter when did t tree die The tree died about years ago

b c a Xx 2 cm 62 degrees 10 m 7 in 30 degrees

For f x x and g x x 3 find a fog x b the domain of fog a fog x Simplify your answer

5 Ramon Benoit deposited a total of 40 000 in two simple interest accounts The annual simple interest rate on one account is 8 The annual simple interest rate on the second account is 12 How much was invested in each account if the total annual interest earned is 11 of the total investment

sin 2x sin 8x cos2x cos 8x Note that each Statement must be based on a Rule chosen from the Rule menu To see a detailed description of a Rule select the More Information Button to the right of the Rule Statement cot 3x sin 2 sin 8x cos2 cos 8x Rule Select Rule 0 0 cos cot F

Which of the following pairs of linear equations are consistent inconsistent If consistent obtain the solution graphically i x y 5 ii x y 8 2x 2y 10 3x 3y 16 iii 2x y 6 0 4x 2y 4 0 iv 2x 2y 2 0 4x 4y 5 0

Rohit Kunal and Sarthak are partners in a firm They decided to dissolve their firm Pass necessary Jou entries for the following after various assets other than Cash and Bank and the third party liability been transferred to Realisation Account a Kunal agreed to pay off his wife s loan of Rs 6 000 b Total Creditors of the firm were Rs 40 000 Creditors worth Rs 10 000 were given a piece of furniture costing Rs 8 000 in full and final settlement Remaining Creditors allowed a discount of 10 c Rohit had given a loan of Rs 70 000 to the firm which was duly paid d A machine which was not recorded in the books was taken over by Rs Kunal at Rs 3 000 whereas expected value was Rs 5 000 e The firm had a debit balance of Rs 15 000 in the Profit and Loss Account on the date of dissolution f Sarthak paid the realisation expenses of Rs 16 000 out of his private funds who was to get remuneration of Rs 15 000 for completing dissolution process and was responsible to bear all the realisation expenses

Form the pair of linear equations in the following problems and find their solutions graphically i 10 students of Class X took part in a Mathematics quiz If the number of girls is 4 more than the number of boys find the number of boys and girls who took part in the quiz ii 5 pencils and 7 pens together cost Rs 50 whereas 7 pencils and 5 pens together cost Rs 46 Find the cost of one pencil and that of one pen

A child enters a carousel that takes one minute to revolve once around The child enters at the point 1 0 Assume the carousel revolves counter clockwise When will the child have coordinates 0 309 0 951 if the ride lasts 6 minutes Round to the nearest second There are multiple answers enter just one seconds

The letters x y and z represent the number of cars passing three given points between these three intersections Find values for x y and z that would realize this desired traffic flow If conditions on Berry limit the value of z to 750 then what values for x and y would keep the traffic flowing Choose the correct set of values A 600 y 900 Z Z B 700 z 900 Z Z OC z 300 900 Z Z OD z 1500 900 z z The values for x and y when z is 750 are x and y TID The diagram shows the number of cars that desire to enter and leave each of the three intersections on three one way streets in a 30 minute period 350 cars hr Rich 500 cars hr 250 cars hr X 200 cars hr Berry Presley Z 500 cars hr 400 cars hr

Part 1 of 2 a Write the component form of v 2 2 Part 1 2 Part 2 of 2 b Sketch v in standard position P vectorgrid

Show that the relation R in the set 1 2 3 given by R 1 2 2 1 is symmetric but neither reflexive nor transitive

Using the property of determinants and without expanding prove that b c q r c a r p a b q r y z z x 2b p q x y P 9 y

Use the Comparison Test to determine whether the series is convergent or divergen 8 n 1 n 6n 1 O conver Odiverg n 6n 1

1xbxhx3 49x33x24 3 7 4x 4 22 r 7x7 x 7 3 3 3 1 r 21 cm Hence right option is 21 cm i e option a 11 A mason construction a wall of dimensions 270 cm x 300 cm x 350 cm with the b each of size 22 5 cm x 11 25 cm 8 75 cm and it is assumed that space is covered 8 the mortar Then the number of bricks used to construct the wall is

1 Find the mean marks of the students for the following distribution Marks Number of Students 0 and above 80 80 10 and above 77 20 and above 72 30 and above 65 40 and above 55 50 and above 43 Marks Number of Students 60 and above 28 70 and above e 16 16 80 and above 10 90 and above 8 100 and above 0

Determine the number of triangles with the given parts and solve the triangle Y 60 b 26 c 134 3 A Inere is only one possible solution for the triangle The measurements for the remaining angles a and B and side a are as follows B a Type exact answers using radicals as needed Use integers or fractions for an the expression B There are 2 possible solutions for the triangle

Rewrite the polar equation r 5 sin 0 as a Cartesian equation Preview

D 16 If D 15 2 2 area of AABC E 7 3 and F D Sol In AABC D is mid point BC E is mid point of AC and F is mid point of AB ADEF AAFE AFBD AEDC So area of AABC 4 area of ADEF The mid points of sides of AABC are 1 5 given by D are the mid points of sides of AABC find the E 7 3 and F 3 3

6 In the given figure ABCD is a trapezium with AB CD AB 18 cm DC 32 cm and distance between AB and DC is 14 cm If arcs of equal radii 7 cm with centres A B C and D have been drawn then find the area of the shaded region of the figure a 18 cm SORDIST b 32 cm 0 B Sol In the given figure there 4 sectors and one trapezium

3 Draw a AABC in which BC 6 cm CA 5 cm and AB 4 cm Construct a triangle similar to it and of scale factor Sol Here scale factor is 4 B M 5cm 6 cm C B B B Steps of construction B 3 5 1 so the resulting figure will be larger 3

18 The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window At certain instant the angles of elevation of a balloon from these windows are observed to be 60 and 30 respectively Find the height of the balloon above the ground Sol Let B be a balloon at a height GB x m 4m 2 m 60 H x 6 4 m 2m x 2 C Let W be the window which is 2 m above the ground H