Math - Others Questions

2 Convert the following to decimal degrees 52 12 07

ind all values of 0 if 0 is in the interval 0 360 and has the given function alue 3 sin 8

Find the measure of each marked angle 3 7x 19 2x 1 3x 5 8v 30 4x 30 15 TY

2 AABC is an equilateral triangle Find the angle of rotation that maps A to B O 120 360

pts Matrix A and its reduced row echelon form R are given A 1 1 0 1 1 21 32 4 1 1 2 3 1 22 1 0 1 0 2 R 0 0 1 00 00 a Find bases for the subspaces Col A Row A Null A 1 3 1 0 00 2 1 0 00 0000

2 Complete the proof of the sine sum identity in the space below sin cos 90 B Letting B A B Q C sin A B cos 90 A B b d 06 8 proved previously along with cos sin 90 cos 90 A B cos 90 A cos B sin 90 A sin B

her W below is a mine the dimension of the subspace W A I2 13 subspace of R If it is a subsp o R 3x 2x2 13

9 Find the exact value of the indicated trigonometric function of 0 given that sec 8 8 Find tan 0 17 8 Question Viewer and 0 is in quadrant IV

2 True or false The Set of complex vector of the Z form 2 for ZEC is Subspace of c

1 15 pts Let 3 b b a Show that B is a basis for R L 1 2

On the Unit Circle List the angles whose measure is a non reducible increment of one twelfth pi To get started in the circular direction the first is The others are 1 12 The U 1 414 0 707 1 414 0 707 0 707 0 707 T 12 and 1 414

0 1 with characteristic polynomial 6 20 pts Consider the matrix A x 1 a Find the eigenvalues of matrix A with their multiplicities b Find a basis for each eigenspace 1 2

1 15 pts Let 6 b b 2 3 2 2 a Show that B is a basis for R2

0 b Find a basis for each eigenspace 0 6 20 pts Consider the matrix A x 1 a Find the eigenvalues of matrix A with their multiplicities 0 1 1 2 with characteristic polynomial

A family of polynomials has equation y k x 2 x 4 x 1 x 5 What is the value of k for the family member represented by this graph YA 32 4 2 0 32 3 96 a k 8 Ob k 1 5 Ook 1 1 20 d k 8

A family of polynomials has equation y k x 2 x 2 What is the value of k for the family member represented by this graph 80 16 A

A quintic polynomial function degree of 5 with zeros x 4 order 2 x2 2 ord 3 and y intercept at 52 as shown Find the value of the leading coefficient of the polynomial rounded to two decimal places Show your work by attaching a file X1 This graph is not to be scaled Your Answer y intercept X2

What is the equation for the family of quartic functions with zeros 2 and 1 3 Check all that apply Oy k x 2 x 2 x 2x 2 k0 Oy k x 4 x 2x 2 k 0 y k x 4 x 2x 2 k 0 y k x 2 x 2 x 2x 2 k 0

1 Determine the whether the incated set of linearly independent complex vectors are 8 dependent 1 2i 96 2 1 1

If tan 0 1 32 0 then Sin 0 coslo sec 0

7 0 8 5 3 0 5 15 pts Find the characteristic polynomial of the matrix A 9 5 use it to find eigenvalues of A Determine the multiplicities of the eigenvalues and

Compute the sine and cosine of 117 by using the reference angle to 1 what is reference angle 2 In what quadrant is this angle radians Sin 11 Cos 112T to

convert 340 to radians to degrees Convert 23 to 18 Crive a exact answer

Use a double angle formula to rewrite the expression 4 sin x cos x 5

Find x correct to 2 decimal places 185 55 17 X 42

If 0 12 then find exact 4 values for these Sec 0 sc 0 tan 0 cot 0

B C 1 Ad b Suppose a 7 b 11 Find exact value or give at least two decimal places Sin A Cos A tan A a 7 sec A csc A cot A

LAT If 0 47 then 3 sin 0 Cos o Give exact values

Branch and Bound algorithm Knapsack Problem Item 1 Knapsack Capacity 10 lkg 1 1 Branch and Bound algorithm 1 2 Backtracking algorithm Guess and Check 7 6 E Weight kg 5 5 5 1 5 4 75 6 D Price 50 000 25 000 15 000 60 000 75 000

Evaluate the determinant 14 21

In an electric instrument called a Wheatstone bridge electric resistances are related by Find R if R 3 02 R 87 50 02 and R 21 00 2 R 0 Simplify your answer Type an integer or decimal R R R R4 L Ri E

Convert the angle in radians to degrees 3x 3x 4 radians radians

Plot the given points and then join these points in the order given by straight line segments Name the geometric figure formed A 4 3 B 3 3 C 3 2 D 4 2 Plot the given points and then join these points in the order given by straight line segments Name the geometric figure formed Choose the correct answer below 0 0 0 0 cube O rectangle GILD O triangle square Choose the correct graph below OA O C Q Q 2 OB O D Q Q

Draw the given angles in standard position 280 210 Which graph below shows the angle 280 in standard position OA O B Q G 1 Which graph below shows the angle 210 in standard position OA Q Q Q Q O C Next question 4 O C Q 2 OD Q O S

Let F ez ez z e y Use Stokes Theorem to evaluate 11 CurlF S curlFdS where 2 S is the hemisphere x y z 36 z 0 oriented upward

Let F 42 y 8y z 3z x F Use Stokes Theorem to evaluate F dr where C is the triangle with vertices 2 0 0 0 2 0 and 0 0 2 oriented counterclockwise as viewed f above

emet To earn full This is an evaluation that must be completed on your own with no help from tutors friends marks you must justify your solution Include the following as needed Show diagram Define variables State formula theorem equation or function used Show substitutions and or steps in solving an equation State restrictions State concluding statement Use correct notation No marks are given if your solution includes e or In differentiation integration This is an evaluation make sure you are completing the work on your own 1 Given the polynomial function f x 2 x x 4 x 3 answer the following questions 7 marks a Fill in a different number for each in the equation b Value of leading coefficient c Degree d Maximum number of turning points for a polynomial with same degree e Maximum number of zeros for a polynomial with same degree f End behaviour As x 00 y As x y g Sketch a possible graph of the function f x Label the x and y intercepts

Use the spinner below Write your answer as a reduced fraction 1 4 2 1 P odd number 80 2 3 2 3 X

Match the following equations with their fully factored form x 1 3x 2 x 1 x 1 x 3 x 1 x 2 x 3 x 4 x 1 x 3 1 x3 3x2 x 3 2 x42x2 3 3 x410x3 35x2 50x 24 4 3x3 4x2 x 2

Use the spinner below 10 9 11 8 12 1 7 6 2 5 3 4 P greater than 2 Enter the probability as a reduced fraction

If 0 5TT 2 6 sin 0 cos 0 then Give exact values No decimals allowed 2 Example Enter sqrt 2 2 for 2 sqrt 2 2 will work but sqrt2 2 will not With functions like sqrt be sure to use function notation pare

Find the exact value tan 2190 cot 2190

If sin 0 cos 0 1 and is in the 2nd quadrant find cos 0 6

A group of 2418 students were surveyed about the courses they were taking at their college with the following results 1034 students said they were taking History 1281 students said they were taking Dance 1064 students said they were taking English 581 students said they were taking Dance and English 575 students said they were taking Dance and History 462 students said they were taking English and History 262 students said they were taking all three courses Fill in the following Venn Diagram with the cardinality of each region Dance I 1281 IV 575 II 581 V 262 VII 1034 History English VI 462 III 1064 VIII

3 Rewrite each expression as a power of x a x b x3 c 1 724 d x x

College classes Math 18 14 5 3 Science 8 History 19 13 How many students are taking math 20 D How many students are taking science and history How many students are taking math and science but not history

2 Suppose that consumers demand for each of the differentiated goods is Qd 10 p p where Qa is the quantity of demand n is the number of differentiated goods p is the price of the differentiated good and p is the average price of differentiated goods The cost function to produce each of the differentiated good is C 10 Qs where C is the total cost and Q is the quantity of supply Answer the following questions a 8 points Calculate the equilibrium level of n and p b 8 points Suppoe the cost function is C 5 Q Should n increase or decrease Explain

Let a 5 5 and b 1 0 Find the projection of b onto a proj b Question Help Video Submit Question V

The spinner below is spun P even shaded 9 8 5 7 2 A 6

Find the magnitude of the projection of 4 5 onto the vector 2 4 Round your answer to at least one decimal place if needed Submit Question