Math - Others Questions

sider the following matrices 1 0 0 Z 1 a Find scalars a and b such that Z ax by a b X 1 Y 2 W a b c 1 1 b Do there exist scalars a and b such that W ax bY Yes O No c If ax bY CW 0 is it true that a b c 0 Yes O No d Find scalars a b and c not all equal to zero such that aX bY cZ C

Show that AB and BA are not equal for the given matrices 1 A 4 6 3 B 03 1 6 AB DA 20

0 2 1 A 213 8 1 and c B C Perform the indicated operations given A B C A

6 Give the equation of the function described below and then sketch its graph The graph of y x is shifted 4 units to the left Then the graph is shifted 3 units downward Equation 7 y f x 1 f x x W

6 Give the equation of the function described below and then sketch its graph The graph of y x is shifted 4 units to the left Then the graph is shifted 3 units downward Equation y axis

Express the column matrix b as a linear combination of the columns of A Use A A2 and A3 respectively for the columns of A 1 1 2 43 b 1 3 3 b A

Factor each completely 9 2p 3p 5 11 2n 9n 18 13 4n 5n 6 15 6a a 2 10 3x 14x 8 12 3k 17k 20 14 10x 9x 2 16 4r r 18

5 Complete the other half of the graph of s t below if s is odd t 3 2 1 3 21 2 1 2 2 3 4 5 3 3

se Exhibit to answer question Bacon 50 40 30 20 10 A 10 B E C D 20 30 40 50 60 70 Eggs he economy is operating at point C the opportunity cost of producing an additional 15 units of bacon is a 20 units of eggs Ob 40 units of eggs c 50 units of eggs d 30 units of eggs e 10 units of eggs

Exhibit to answer question Bacon 50 40 30 20 A 10 B E F C D 10 20 30 40 50 60 70 Eggs he economy were operating at point E a the opportunity cost of 20 additional units of eggs is 10 units of bacon b the opportunity cost of 20 additional units of eggs is 20 units of bacon c the opportunity cost of 20 additional units of eggs is 30 units of bacon O d 20 additional units of eggs can be produced with no impact on bacon production

Find if possible AB and BA If not possible enter IMPOSSIBLE in any single cell 12 5 23 2 1 3 2 1 2 0 4 1 1 3 4 2 A a AB b BA 7 B 53

Find if possible AB and BA If not possible enter IMPOSSIBLE in any single cell 0 B 3 A 3 1 2 a AB b BA 32

Find if possible A B A B 2A 2A B and B A If not possible enter IMPOSSIBLE in any single cell A 6 5 1 4 a A B 8 5 It b A B c 24 d 24 B B e B A 1 5 1 10 11 11 11 K

Express the column matrix b as a linear combination of the columns of A Use A A2 and A3 respectively for the columns of A 11 b A 1 1 2 3 3 b

x y 19 4 9 4 3 13 11 12 02 4 0 1 19 3 0 4 13 2x 1 4 11 3x 2 3y 14 0

Solve for x y and z in the matrix equation 4 STEP 1 Simplify the right side of the equation 4 3 4x STEP 2 Set corresponding entries equal to each other to obtain four equations 4y 4z 4 X 41 z 1 STEP 3 Solve for x y and z x y z

nd if possible A B A B 24 2A B and B A If not possible enter IMPOSSIBLE in any single cell 38 0 A 3 6 1 30 1 a A B E 8 11 b A B c 24 E d 2A B E e B A B 8 11 11 K

5 12 points Solve the homogeneous linear system corresponding to the coefficient matrix A 27 1 0 2 2 1 2 4 02 4 1 2

Write the system of linear equations in the form Ax b and solve this matrix equation for x 3x 3 X2 31 2x1 x 6x X1 30 CHO X2 31

Find C11 and 22 where C 2A 3B A a C11 4 1 1 1 and 3 7 B 5 3 2 0 5 b C22

Let A be a matrix with the following size A 4 x 3 If defined determine the size of the matrix 3A If an answer is undefined enter UNDEFINED X If not defined explain why O 3A is defined O 3A is not defined because the number of columns of A does not equal the number of rows of A O 3A is not defined because the number of columns of A equals 3 O 3A is not defined because the number of rows of A does not equal 3 O 3A is not defined because 3 is not a matrix

1 In 2004 the restaurant industry in the United States employed about 11 9 million people In 2014 this number increased to 13 5 million employees a Find a linear function E that models these data where x is the year I b Interpret the slope of the function E x Attach the units c If this trend continues use your equation to predict the year that the number of restaurant industry employees might reach 14 5 million

3 Let 4 A 3 0 3 0 3 a 3 points Determine a21 for matrix B b 3 points Find BT w and B c 6 points Determine the product AB if possible 9 3 6 4

4 6 points A 4 0 and B 1 2 2 Find X if 2X 2A B I

Question Find the area in square units bounded above by f x 6x 2x 19 and below by g x 7x 12x 21

Use the Venn diagram to write the elements of B Enter your answer as a set using the listing method 5 A ak 1 n h a f d B C i bo g b m U

Use the Venn diagram to write the elements of B Enter your answer as a set using the listing method 1 A kg d E h n B i j a b U

Use the Venn diagram to write the elements of BC Enter your answer as a set using the listing method a A mf h C n DO g j B k b 1 d U

Which of the following statements are true More than one answer may be possible Select all that appl o a c 0 O o a s o o a a H 0 O o a 2 o

Use the Venn diagram to write the elements of A n B Enter your answer as a set using the listing method 408 1 n A m h f g ro B a i j k C U

e the Venn diagram to write the elements of B Enter your answer as a set using the listing method U h a n A b 3 2 m g B j i d 1 k

Which of the following statements are true More than one answer may be possible Select all that app 6 7 8 c 7 8 6 7 8 7 8 6 7 8 7 8 6 7 8 2 7 8

7 State all the asymptotes vertical horizontal or oblique of the following functions a y b y 4x 7x 6 3x 27 4x 2x 6 x 4 C 3 C 3

6 A piece of wire 10 m long is cut into two pieces One piece is bent into a square and the other is bent into an equilateral triangle How should the wire be cut so that the total area enclosed is a a maximum b a minimum Hint 1 Use the first derivative test to figure out if your answer is a min or max Hint 2 Think about whether you even need to cut the wire A 2 T 3

8 Sketch a graph of the following function Be sure to include all asymptotes increasing and decreasing intervals and max and min You do not have to find any concavity or points of inflection y x 1 3 KU 2 A 2 C 2T 2

10 Differentiate the following functions You do not have to simplify a y 5x x4 b y tan ex KU 2 KU 3

1 Determine the following limits If the limit does not exist write DNE x 8x 12 x 4 a limx 27 b lim xo 2 x 2 x 2x 3x 2x 3 d Limx x 3x 1 x c limx 1 57 KU 2 KU 2 T 3 T 4

17 The line L x y z 3 1 2 t 1 2 1 intersects the sphere with equation x y z 6 at two points What are the two points T 4

16 Find the vector parametric and symmetric equations of the line which contains the point 5 3 8 and is perpendicular to the plane 3x 6y 7z 3 0 A 3 T 2

18 Find the intersection if any and provide a geometric interpretation of the A 3 following three plane systems x y 2z 2 0 3x y 147 6 0

11 For what values of x does the function y xe x have maximum or min values A 2 T 2

12 Show that the vectors 1 2 6 3 2 1 and 7 10 9 lie on the same

9 Prove that a third degree polynomial function always has exactly one Point of Inflection T2

5 A box with a square base and open top must have a volume of 32 000 cm Find the dimensions of the box that minimizes the amount of material ucod 102T 21

PART A 1 2 3 4 5 6 7 9 10 11 12 MULTIPLE CHOICE What is the radius of a circle with the equation of x2 y 64 a 8 b 16 c 25 d 64 What is the length of the line segment joining A 4 7 and B 16 9 a 13 4 b 180 c 656 d 25 6 What is the optimal value of this quadratic function a 2 b 1 C 2 d 1 What is the greatest common factor for 24m n4 4m n 16m n a 4 b 4m n c 48m n4 d 4mn What is the expression 2x 5 in expanded simplified form a 4x 10x 25 b 4x 20x 25 c 4x 5 What is the vertex of the quadratic relation y 5 x 1 8 a 1 8 b 1 8 c 1 8 d 1 8 e x 1 What are the roots of the quadratic relation y x 5x 14 a x 0 x 24 b x 2 x 7 d x 2 x 7 e x 2 x 7 For the quadratic relation y x 3x 2 what is the y intercept a 1 b 3 c 2 d 0 e 1 and 2 Use the following triangle to answer questions 9 12 D 12cm Sin F is 5 13 a E 5 cm F Cos F is 5 13 a Tan D is a 13 cm 13 b 1 2 5 12 5 12 The degree of LF is a 0 385 b 0 923 12 13 12 c 13 c 12 13 c 2 4 d 2 2 d 1 3 d 1 3 5 d 22 6 e 1322 e c x 5 x 14 13 12 13 e 122 e 67 4 e 128W e 12 e 4m n d 4x 25 1

Suppose a company makes surgical screws To pass inspection the screws must be 63 millimeters long and can vary by no mo than 0 03 millimeter a Write the possible screw lengths in mm using plus minus notation mm mm b Write the possible screw lengths in mm using interval notation Simplify your answer completely mm c All screw lengths must be between which two values in mm All screw lengths must be between a lower value of mm mm and an upper value of

In a poll the pollsters found that only 35 of 5th through 12th graders strongly agreed that they could find many ways ard problems that arise in their lives The survey had a margin of error of 0 092 percentage point a Write the results of the poll using plus minus notation Enter your answers in decimal form b Rewrite using interval notation Enter your answers in decimal form Simplify your answer completely c Let p be a percentage and write the interval as a compound inequality

Solve the compound inequality and write the answer using interval notation Simplify your answer completely x 1 9 or x 1 9

Solve the compound inequality and write the answer using interval notation Simplify your answer completely 12 x 14 12

Consider the following compound inequality x 1 or x 2 a Graph the compound inequality Use the tools to enter your answer 10 8 WebAssign NumberLine 4 2 0 2 0 0 0 0 6 8 10 Rewrite the compound inequality using interval notation for a real number x Simplify your answer complet