Questions

Which of the following sets are bases for P2 Choose all correct answers Explain your answer and include any necessa work in your uploaded supporting work A 1 t2 t 2 2t2 2t 3 4t2 1 B t2 2t 1 2t2 3t 2 C t t 1

Simplify the following expression Write as a single logarithm or monomial 712 In 64 1

Using synthetic division what is the quotient for 3x 3 5x 2 2x 37 by x 3 If the remainder is non zero express the remainder term as a fraction using the divisor as the denominator Provide your answer below

Use graphical methods to find all the real solutions of the following equation 3 2 0 97x 5 24x 3 55x 20 0

Use logarithmic differentiation to differentiate the following function f x x 8 3 3x 2 4 f x 3 x 8 3 3x 2 3 x 8 4 3x 2

A set of vectors in an inner product space V is orthogonal when every pair of vectors in S is orthogonal O True False

Use the fact that A and B are row equivalent 1 4 1 27 1 2 1 1 A 0 0 0 12 1 1 1 0 0 2 2 1 6 1 1 0 2 0 0 120 B 0001 1 2 0000 0 0000 0 a The rank of matrix A is b The nullity is c The dimension of the column space of A is d In your work include a basis for the column space of A Jel In your work includ

Work required Apply the Gram Schmidt orthonormalization process to transform the given basis into an orthonormal basis Use the Euclidean inner product dot product and use the vectors in the order in which they are given If you have difficulties with formatting your answer you may represent a square root as sqrt 3 to represent the square root of three and a fraction as a ratio Also there is no need to rationalize denominators I will interpret your answer and make corrections for formatting issues if Canvas incorrectly marks it incorrect during the grading process B 1 2 1 0 The orthogonal basis W1 W2 is W1 and W2 The orthonormal basis u1 u2 is u1 and u2

y varies inversely as the square root of x and when x 16 y 9

Which of the following is the same as 2 In 9x a In 81x2 c In 18x List all expressions that are equivalent In 81x2 Type a b c or d Use a comma to separate answers as needed b 18 d In

Work required The transition matrix from B to B if B 1 1 3 1 B 1 2 1 0 Answer matrix a b a b C d C ar

Graph all vertical and horizontal asymptotes of the rational function f x 3 x 56 5

Work required Find the coordinate matrix of x relative to the basis B B 5 6 3 2 x 17 22 Provide the components a and b of the coordinate matrix X B a a b

Work required Let u 4 2 and v 2 2 be vectors in R with the inner product u v u v1 22 v2 The vectors Select orthogonal Are the vectors orthogonal in the Euclidean sense Select Select yes

Find a Cartesian equation of the surface that is defined in spherical coordinates by the equation 1 p sincpcos 0 1 to conclude that 7 3 it is a sphere centered at x y z lof radius R

Define the nullspace of a matrix A

An orthogonal set of nonzero vectors in an inner product space is not necessarily linearly independent O True O False

Use the definition of the logarithmic function to find x Simplify your answer completely a logs X x b log10 x 3 x

c 2 d y 2 dx 3 2 dy 2 X y 14xe Solve the dx differential equation

Evaluate the integral by changing the order of integration in an appropriate way 10x ZeZy2 dy dx dz 00x2 10xzeZy2 dy dx dz Type an exact answer

An outcome is Pareto efficient Pareto optimal only if everyone prefers it to every other feasible outcome or is indifferent True or False

Find the volume of the region in the first octant bounded by the coordinate planes the plane y z 8 and the cylinder x 64 y The volume is

Find the volume of the region in the first octant bounded by the coordinate planes the plane x y 5 and the 2 2 cylinder y 4z 25 The volume is Type an exact answer using as needed

The time married men with children spend on child care averages 6 3 hours per week Time March 12 2012 You belong to a professional group on family practices that would like to do its own study to determine if the time married men in your area spend on child care per week differs from the reported mean of 6 3 hours per week A sample of 40 married couples will be used with the data collected showing the hours per week the husband spends on child care The sample data is contained in the Excel Online file below Construct a spreadsheet to answer the following questions X Open spreadsheet a What are the hypotheses if your group would like to determine if the population mean number of hours married men are spending in child care differs from the mean reported by Time in your area 6 3 Ho P Ha H 6 3 b What is the sample mean and the p value What is the sample mean to 1 decimal hours Calculate the value of the test statistic to 2 decimals What is the p value to 4 decimals Do not round intermediate calculations c Select your own level of significance What is your conclusion the null We enough evidence to disprove the reported time

7 Kofi Haris and Sharon are in a disagreement about how to solve for QU shown in the figure Kofi suggests setting up the proportion cos 27 and solving for QU 18 QU Haris suggests using the Law of Sines but Sharon says there is not enough information to do so since no angle and its opposite side are given Who is correct Explain your reasoning 111 S 27 U 18

1 Describe the end behaviour of the graph of the polynomial function f x 2x2 7x 2 080 11

5 Let x 3x 5x 1 and g 2 32 7 Find 9 4

Kara wants to solve for m N using the Law of Sines What one additional measurement does Kara need in order t do this Explain H 65 11 M

In 13 18 Tell whether the statement is true or false If false explain why 13 A trapezoid is also a parallelogram 14 A square is also a rhombus 15 Diagonals of a rectangle are perpendicular 16 A parallelogram has exactly one pair of opposite angles congruent 17 A square has diagonals that are perpendicular and congruent 18 All quadrilaterals have supplementary consecutive angles

Geometry Worksheet 9 6 all of the quadrilaterals that have the given characteristic 1 all sides congruent 2 diagonals congruent 3 no parallel sides 4 diagonals bisect each other 5 two pairs of parallel sides 6 all angles congruent

3 To the nearest tenth find the perimeter of isosceles triangle IEF E 73 12

1 Dewribe the end behaviour of the graph of the polynomial function f x 2 27 2

9 10

In ANAP mZN 87 AP 15 and mZA 25 Find the length of AN to the nearest tenth or explain why it is not possible

1970 s hp David Accords

4 Which of the following statements is FALSE A sin S sin O x Y z X B sin H sin O C z sin O y sin H D X sin S 2 sin H 2 S X Y H

The table below shows the number of each type of cookie in dozens that Karin sold in one week to two coffee shops a Write the information in the table as a 3 x 2 matrix S Mugsy s Coffee Shop The Coffee Club Chocolate 2 15 Chip Oatmeal 7 11 Peanut 6 10 Butter Karin s cost to make one dozen cookies is 2 00 for chocolate chip 1 50 for oatmeal and 3 50 for peanut butter S

4 12 pts Let f x 2 If I shift the graph of the function f x n 3 units to the right followed by b 4 units down What will be the function corresponding to the resulting graph

Find the length of GO Round to the nearest tenth G T 50 27 61

8 Solve the triangle by finding all missing side lengths and angle measures Round to the nearest tenth 5 39 R 94

Which factor has motivated many countries to pursue free trade policies in the 21st century A To protect local businesses from competition with huge foreign corporations B To prevent companies from producing pollution that affects the entire world C To make it cheaper and easier for companies to buy and sell foreign products D To allow all people regardless of race or gender to participate in the global economy

Is the set appropriate props stage etc You can answer yes or no

Are the costumes accurate for the setting and time period of the play You can answer yes or no

18 3 An antihistamine shows sharp peaks at Raman shifts of A 488 725 875 925 and 1350 cm At what wavelengths in nanometers would the Stokes and anti Stokes lines for the antihistamine appear if the source were a a helium neon laser 632 8 nm b an argon ion laser 488 0 nm

1 Describe the end behaviour of the graph of the polynomial function f x 2 2x 7 2

In 7 12 Identify all of the terms from the following list that apply to each figure quadrilateral parallelogram rectangle square trapezoid rhombus kite 7 8 H

11 12

Which character s did you like Dislike

What was great about the play Not so great

On a scale of 1 to 5 with 1 being not at all and 5 being yes did the characters seem like real people Your response should be a number