Algebra Questions

Five years ago Cedric and Zoe purchased a home and got a 345 741 mortgage with a 20 year amortization at 3 interest compounded semi annually and biweekly payments The term of the mortgage is now over and they are renewing on the same amortization timeline for another five year term at 4 75 interest compounded semi annually and monthly payments For full marks your answer should be rounded to the nearest cent a What is the balance remaining after the first term Balance 0 00 b How much are the new payments for the second term Payment 0 00

Which of the following relations does the above Hasse diagram represent a Con 3 4 b 2 on 3 4 c Con 3 4 0 d 2 on 3 4 3 4

DIC You will be comparing 4 people who are throwing objects into the air Their throws are represented in different ways below You will identify the following for each Maximum height longest time in air type of object and age of sibling Person 1 Represented by the equation below y 16 x 1 x 3

Homework 1 4 To verify the linear inverse by composition State if the given functions are inverses 1 f x x 4 g x x 4 f gex x 4 4 X 4 4 X g f x x 4 4 X 4 4 X Yes they are inverses 3 f n 3n 9 4 h n 2n 2 F ha I 0 2 3 A 2 5 g n 4 3n 2 2n 4 3 f n 9 4 60 6 9 1 65 2429 4 64 H FONDI 1 4 7 8 x x 3 3 f x x 2 2 g n 5n 20 8 f n 20 8n 5 f g x 5 2013 20 4 g x x 1 4x 8 3 f x 6 f x 2x 1 g x x 2 1 1 Period 4 8 g x x f x x 8

Exercise 1 Some exercises on the Week 10 exercise sheet will give you all the tools you need for this roblem You should work through those exercises but you can use them without including proofs of them Let b 2 2 and b 4 4 1 Is Bo b b2 a basis of Z 2 Let B spanz Bo Prove that B is a free abelian group of rank 2 3 Find a basis B b b of B a basis y c c of Z and positive integers d d2 such that b d c and b d c 4 Express Z2 B as a direct product of cyclic groups

Consider the set of vectors S 1 k 1 k 3 3 2 1 k Determine the value s of k such that the set S forms a linearly independent set in R i ii 4 marks Suppose that k 1 and an additional vector 3 4 5 is added to the set S Using TWO different methods discuss whether the new set of vectors form a basis for R 6 marks

The 1st 5th and 13th terms of an arithmetic sequence with common difference d d 0 are the first three terms of a geometric sequence with common ratio r r 1 Given that the 1st term of both sequences is 12 find the value of d and the value of r

OA 108 sophomores 92 juniors OB 124 sophomores 92 juniors OC 46 sophomores 62 juniors OD 62 sophomores 46 juniors algebra class If there are 108 students in this class find the number of sophomores and the number of SKLED

0899 0251 82 19 1423 OA 9 OB 600 OC 72 O D 36

Find all values of x satisfying the given conditions x 6 3 9 x x 8 7 f x OA 4 OB 4 5 O C 4 5 OD 18 and f x g x

K Use Gaussian elimination to find the complete solution to the system of equations or state that none exists x y z 7 x y 2z 7 2x 3z 14 OA OB O C O D 3z 3z 32 7 22 2 3z 7 22 2 22 2 7

OA 4 200 OB 4 000 OC 3 800 D 3 400

5t 21 2 A drug is injected into a patient and the concentration of the drug is monitored The drug s concentration C t in milligrams after t hours is modeled by C t means in practical terms OA y 1 25 After 1 25 hours the concentration of the drug is at its greatest OB y 2 50 2 50 is the final amount in milligrams of the drug that will be left in the patient s bloodstream OC y 2 50 After 2 50 hours the concentration of the drug is at its greatest OD y 0 0 is the final amount in milligrams of the drug that will be left in the patient s bloodstream What is the horizontal asymptote for this function De

Find the zeros of the function f x 2x 3 x 1 1 OA none OB 3 OC 3 1 OD 3 1

plete the square and write the equation in standard form Then give the center and ra 16x 64 y 8y 16 64 A x 4 y 8 64 Center 4 8 radius 64 B x 8 2 y 4 64 Center 8 4 radius 64 C x 8 2 y 4 64 Center 8 4 radius 8 D x 4 2 y 8 64 Center 4 8 radius 8

K Graph the solution set of the system of inequalities or indicate that the system has no solution 2x y 2 2x y 1 A 10 10 Q OB Q C O C 44 O D

K The logistic growth function f t nearest whole number OA 437 butterflies OB 9 880 butterflies OC 237 butterflies OD 337 butterflies 520 1 6 4e 0 13t describes the population of a species of butterflies t months after they are introduced to a non threatening habitat How many butterflies are expected in the habitat COLL

olve the logarithmic equation Be sure to reject any value that is not in the domain of the original loga pg 3x 4 A 1 262 B 64 C 81 D 12 www

e dimensions 6 feet by 11 feet 6 feet by 13 feet 8 feet by 11 feet 7 feet by 12 feet

etermine whether the following relation repre 4 6 6 2 9 9 2 2

3 Evaluate Sc dz n 2 3 4 where z a is inside the simple closed curve C

Write an equation modeled by the envelopes and counters and then solve the equation Provide your answer below

4 Let C be the curve y x 3x 4x 1 joining points 1 1 and 2 3 Find the v Sc 12z 4iz dz

The system of equations is shown on the gra 3x y 8 x 2y 4

Find a unit vector in the direction of V 10i 4j O 10 i 116 j 116 None of these 10 u 7 i j 84 84 0 10i 4j O 10 i 4 j 6 O 106 i 110 U

Your oldest daughter is about to start kindergarten in a private school Tuition is 30 000 per year payable at the beginning of the school year You expect to keep your daughter in private school through high school You expect tuition to increase at a rate of 5 per year over the 13 years of her schooling What is the present value of your tuition payments if the interest rate is 5 per year How much would you need to have in the bank now to fund all 13 years of tuition PV C r a 1 9 9 r

Let f be a function satisfying f 0 0 f 0 8 f 0 5 and f x 12 for 0 x 1 a The second Taylor polynomial p x of f about x 0 has the form p x ao a a x with ao a1 a2 b We approximate the function f by the second Taylor polynomial p of f about x 0 in the interval 0 1 Usin Taylor s theorem with the Lagrange remainder find the biggest a and the smallest b such that a and write the values of a and b in the boxes below b 1 1 ABY a f b

2 a Find a reduced and full QR factorisation of the matrix 2 1 11 2 0 B b Let A be an m x m matrix and let a be its jth column Using the full QR factorisation of A prove Hadamard s inequality m det A aj 2

For items 1 through 3 show that there exists a projective transformation r A B C S A2 B2 C A A B N B A2 B P B3 C C3 C R S S r P

d the average rate of change of the function from x to X 3x x from x 5 to x 6 A OB 2 OC 34 D D 1 6

have 228 feet of fencing to enclose a rectangular region Find the dimensions of the rectangle that maximize the enclosed A 114 ft by 28 5 ft B 57 ft by 57 ft C 114 ft by 114 ft D 59 ft by 55 ft

K x 6 x OA 2 3 12 OC 0 2 U 3 00 10 OB 00 3 U 2 00 OD 3 2 12 12 8 0

system of linear equations in three variables and then use matrices to solve the system ble below shows the number of birds for three selected years after an endangered species protection program was started mber of years after 1980 1 2 3 y Number of birds 42 61 86 ne quadratic function y ax bx c to model the data Solve the system of linear equations involving a b and c using matrices Find the equation that model y 5x 10x 32 y 3x 10x 29 C y 6x 30x 25 D y 4x 20x 24

aluate the determinant 3 3 3 4 2 0 4 0 3 A 21 B 75 C 21 D 75

Write the partial fraction decomposition of the rational expression 7x 11x 36 x x 4 x 3 O A OB O C O D 3 X X 3 X 9 X 4 x 3 7 3 x 4 x 3 8 2 x 4 x 3 4 x 8 2 x 3

Begin by graphing the standard function f x x Then use transformations of this graph to graph the given function h x x 2 O A 5 O B Q G SCLES O C Q O D Ay

A standard train ticket in a certain city costs 2 50 per ride People who use the train also have the option of purchasing a frequent rider pass for 17 25 each month With the pass a ticket costs only 1 75 per ride How m month make the frequent rider pass a better deal than standard train tickets OA 25 or more rides OB 23 or more rides OC 24 or more rides OD 22 or more rides D

rational zero of the polynomial function and use it to find all the zeros of the 2x3 12x 10x 3 1 3 2 2 2 2 1 3 2 5 2 5 1 4 2 2 2 2 1 3 2 5 2 5

we the logarithmic equation Be sure to reject any value that is not in the domain of the original logarithmic expressions 3X 5 A 243 B 15 C 1 465 D 125

K For the given functions f and g find the indicated comp X 2 3 f x g x 3x 2 gof x OA X 4 2 O B X 3 O C X OD 3x 4

Solve the equation by the square root property x 2 6 OA 2 6i OB 2 6 OC 21i 6 OD 4 8

are 20 more sophomores than juniors in an 8 AM algebra class If there are 66 students in this class find the number of sophomo 23 sophomores 43 juniors 66 sophomores 46 juniors 86 sophomores 46 juniors 43 sophomores 23 juniors

Three shrimp boats supply the shrimp wholesalers on Hilton Head with fresh catch The Annabelle takes 50 catch to Hudson s 20 to Captain J s and 30 to Mainstreet The Curly Q takes 40 of its catch to Hudson o Captain J s and 20 to Mainstreet The SloJoe takes 30 of its catch to Hudson s 40 to Captain J s at o Mainstreet One week Hudson s received 236 5 pounds of shrimp Captain J s received 205 4 pounds and Mainstreet received 157 1 pounds How many pounds of shrimp did each boat catch OA Annabelle 202 lbs Curly Q 226 lbs SloJoe 171 lbs OB Annabelle 226 lbs Curly Q 202 lbs SloJoe 171 lbs OC Annabelle 171 lbs Curly Q 226 lbs SloJoe 202 lbs D Annabelle 202 lbs Curly Q 171 lbs SloJoe 226 lbs

Solve the equation by the square root property x 9 2 O A 7 11 OB 9 21 OC 9 2 OD 9 2

The nutritional content per ounce for three foods is given in the table below What combination of these provide exactly 14 grams of fat 27 grams of protein and 10 grams of fiber Food A Food B Food C Fat g oz Protein g oz Fiber g oz 2 1 8 4 2 16 1 1 5 A 4 oz of Food A 6 oz of Food B 2 oz of Food C OB No possible combination of these foods OC 3 oz of Food A 5 oz of Food B 1 oz of Food C OD 7 oz of Food A 7 oz of Food B 1 oz of Food C

Find a rational zero of the polynomial function and use it to find all the zeros of the f x x 3x 4x 10x 4 OA 1 2 2 2 2 2 OB 1 2 2 2 2 2 OC 1 3 2 3 2 3 OD 1 2 2 3 2 3

A drug is injected into a patient and the concentration of the drug is monitored The drug s concentration C t 7t What is the horizontal asymptote for this function Desc 31 4 milligrams after t hours is modeled by C t his means in practical terms OA y 2 33 After 2 33 hours the concentration of the drug is at its greatest OB y 1 00 After 1 00 hours the concentration of the drug is at its greatest Oc y 2 33 2 33 is the final amount in milligrams of the drug that will be left in the patient s bloodstream OD y 0 0 is the final amount in milligrams of the drug that will be left in the patient s bloodstream

Find the zeros of the function f x 2x 3 x 1 1 OA 3 1 OB 3 1 OC 3 OD none

2x y 6 2x y 1 O A 10 Q B 10 O C 2 D

A stick 1 meter long casts a shadow 1 3 meters long A building casts a shadow 18 meters long How tall is the building to 2 decimal places