Questions

A matrix is give 18 9 01 a Determine whether the matrix is in row echelon form Yes No b Determine whether the matrix is in reduced row echelon form Yes No c Write the system of equations for which the given matrix is the augmented matrix Enter each answer in terms of x ar 9 7

Solve the system of linear equations If the system is dependent express your answer in terms of t where x x t y y t and z t If the system is inconsistent enter INCONSISTENT x 2y 3z 8 2x 4y6z 16 3x 7y 2z 31 x y z

Solve the system of linear equations If the system is dependent express your answer in terms of t where x x t y y t and z t If the system is inconsistent enter INCONSIS 2x y 3z x y z x 17 7z 18 3x 2y z 20

The system of linear equations has a unique solution Find the solution using Gaussian elimination or Gauss Jordan elimination y z 8 x 2x 3y 2z 16 3z 4 x y z 4x y

Find the volume of a pyramid with height 23 and rectangular base with dimensions 3 and 9 using integration

Find the volume of the solid obtained by rotating the region bounded by y x y 0 and x 3 about the y axis V

State the dimension of the matrix 21 18

State the dimension of the matrix 612

A matrix is given in row echelon form 1 0 2 4 1 2 5 14 0 0 1 4 a Write the system of equations for which the given matrix is the augmented matrix Enter each answer in terms of x y and z 5 14 b Use back substitution to solve the system x y z

The graphs of x 8 y f x solid and y g x dashed are shown the graph is not drawn to scale Region One B A a The intersection points are A 8 4 B 8 7 and C 1 5 Suppose Region One is revolved around the x axis Using the method of washers the volume can be computed by evaluating the integral

Let R be the region bounded by 5 y 2x 10 y 3x 25 To find the volume of the solid when R is revolved around the x axis evaluate the integral dx The volume of the solid formed when R is revolved around the x axis is Type pi to enter

Find the volume of the solid obtained by rotating the region bounded by the g curves about the specified axis 2 y x y 1 about y 3

Find the volume of the solid obtained by rotating the region above the x axis bounded by y x and 5about the y axis y

As a hardworking student plagued by too much homework you spend all night doing math homework By 6am you imagine yourself to be a region bounded by y 722 x 0 x 2 y 0 As you grow more and more tired the world begins to spin around you However according to Newton there is no difference between the world spinning around you and you spinning around the world Unfortunately you are so tired that you think the world is the x axis What is the volume of the solid you the region create by spinning about the x axis

In ELISA the enzyme horseradish peroxidase HRP is bound to the region of the secondary antibody well of microtiter plate SARS CoV 2 antigen the tested sample

Why is it necessary to wash the samples repeatedly in ELISA To enhance the interaction between antibody and antigen To remove any proteins or antibodies which are unbound To increase samples concentration To make the sample clean Question 6 1 point Listen An antibody is Are also called immunoglobulins or lgs Made up of variable domains and a constant domain Composed of glycoproteins All of the above Y shaped in antigens

bodies are unique and respond to a specific antigen Where does the antigen attach to the antibody structure The variable domains Fab The binding site the variable domains and the Fab The binding site Fc Question 8 1 point Listen Microneutralization is the gold standard but it is labor intensive and time consuming and requires at least 5 days to get results True

How many types of controls do you need to have in the Microneutralization Assay One Virus Control Two Sample Control and Virus Control Two Virus Control and Cell Control No controls are need

What is the purpose of the ELISA test for this lab To detect COVID 19 virus from serum in people who might have been infected To produce COVID 19 antibody from serum in people who have been infected To detect COVID 19 antibody from serum in people who might have been infected To isolate COVID 19 virus from serum in people who have been infected

Use a graphing utility to graph the function include two full periods Graph the corresponding reciprocal function in the same viewing window y csc 4x 4 y y UU UU 2 2 2 2 y 2 2 2 2 2 y 4 2 X

Use the graph of the function to answer each question 2 x 2 f x csc x 2 3 2 a Find all x intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE x b Find all y intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE y c Find the intervals on which the graph of y f x is increasing and the intervals on which the graph of y f x is decreasing Enter your answers using interval notation If an answer does not exist enter DNE increasing decreasing d Find all relative extrema if any of the graph of y f x Enter your answers as a comma separated list of ordered pairs If an answer does not exist enter DNE relative minima relative maxima e Find all vertical asymptotes if any of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE

Match each of the Maclaurin series with right function 1 2 n 0 n 0 1 22n2n 2n 1 2x2n 1 2n 1 3 2 n 0 4 n 0 n 1 2x2n 1 2n 1 A 2 arctan r B e2 G Cos 2x

The function f x sin 4x has a Maclaurin series Find the first 4 nonzero terms in the series that is write down the Taylor polynomial with 4 nonzero terms

Write the improper integral L as a limit or limits of proper integrals 0 2 x 1 da lim lim I S x 1 de lim L 20 dx x 1 2 da lim 8110 I da Jo 2 1 2 lim 2 1 2 da lim 8 100 da x 1 0 lim a10 dx lim da 2 1 2 22 1 2

15 a 0 048 yards b 0 063 yards c 0 075 yards

y csc 2x x 2 111 111 111 111 2 020 14 12 337588 U 111 111 111 III

21 The area of a triangle is 40 centimeters Find the length of the side included between the angles A 30 and B 50

Use the graph of the function to answer each question 2x x 2 f x cot x 2 3 2 a Find all x intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE x b Find all y intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE y c Find the intervals on which the graph of y f x is increasing and the intervals on which the graph of y f x is decreasing Enter your answers using interval notation If an answer does not exist enter DNE increasing decreasing d Find all relative extrema if any of the graph of y f x Enter your answers as a comma separated list of ordered pairs If an answer does not exist enter DNE relative minima relative maxima e Find all vertical asymptotes if any of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE

Each problem below refers to triangle ABC In each case find the area of the tri angle Round to three significant digits 1 a 50 centimeters b 70 centimeters C 60 2 a 10 centimeters b 12 centimeters C 120 3 a 41 meters c 34 meters B 151 5 4 a 76 3 meters c 42 8 meters B 16 3 5 b 0 923 kilometers c 0 387 kilometers A 43 20 6 b 63 4 kilometers c 75 2 kilometers A 124 40 7 A 46 B 95 c 6 8 meters 8 B 57 C 31 a 7 3 meters 9 A42 5 B 71 4 a 210 inches 10 A 110 4 C 21 8 c 240 inches 11 A 43 30 C 120 30 a 3 48 feet 12 B 14 20 C 75 40 b 2 72 feet 13 a 4 inches b 6 inches c 8 inches 14 a 5 inches b 10 inches c 12 inches 15 a 4 8 yards b 6 3 yards c 7 5 yards 16 a 48 yards b 75 yards c 63 yards c 17 a 4 38 feet b 3 79 feet c 5 22 feet

Each problem below refers to triangle ABC In each case find the area of the tri angle Round to three significant digits 1 a 50 centimeters b 70 centimeters C 60 2 a 10 centimeters b 12 centimeters C 120 3 a 41 meters c 34 meters B 151 5 4 a 76 3 meters c 42 8 meters B 16 3 5 b 0 923 kilometers c 0 387 kilometers A 43 20

Sketch the graph of the function Include two full periods Use a graphing utility to verify your result y 2 sec 2x 1 I 4 U 4 3 4 2 y

Verify that the function satisfies the three hypotheses of Rolle s Theorem on the given interval Then find all numbers that satisfy the conclusion of Belle s Theorem Enter your answers as a comma separated 1 12 22 12x 1 0 4

Determine the remaining sides and angles of the triangle ABC a 100 m A 39 42 C 25 46 What is the measure of angle B B

Describe the relationship between the graphs of f and g Consider amplitude period and shifts 4 y 3 2 3 2x J 8 0 g 1 1 k X 2 3 B O The graph of g is a horizontal shift 3 units to the right of the graph of f O The graph of g is a reflection of f in the x axis O The amplitude of g is twice that of the amplitude of f O The graph of g is a vertical shift 3 units upward from the graph of f The period of a is 3 times that of f

Find the indicated roots Sketch the roots in the complex plane The fifth roots of 32 b The cube roots of i c The cube roots of 1

Sketch the graph of the y 2 cos x 1 2 37 k k K12 2 k12 3 3 2x 2 3 KIN KIN KIN 2 k KIN 13 X 2 k2 KIN k

Which has a trigonal pyramid structure O SO32 O CO2 OSO3 ONO3 OCH4

Determine the percentage composition by mass of lead in PbCl2 O 74 5 85 4 42 7 57 3 12 7 1 pts Question 4

Which has a tetrahedral structure O SO32 O CO32 OSO3 O NH3 OCH4

Which has a bent structure O H O NH3 O CaCl2 O CO2

EXAMPLE 5 Suppose that f 0 3 and f x 9 for all values of x How large can f 5 possibly be SOLUTION We are given that fis differentiable and therefore continuous everywhere In particular we can apply the Mean Value Theorem on the interval 0 5 There exists a number c such that f 5 f 0 f c 0 SO f 5 f 0 f c 3 f c We are given that f x s 9 for all x so in particular we know that f c s have 5f c s SO 7 f 5 3 f c 3 The largest possible value for f 5 is 29 Multiplying both sides of this inequality by 5 we

Which of the following elements are arranged in an increasing order for both atomic radius and ionization energy OS OF and F O S OFSO and O S F OS F O and S F O OFOS and S O F Onone of these

For the reaction C H4 g 302 g 2CO2 g 2H2O g if 5 0 mol of CO2 are produced how many moles of O2 were reacted 3 3 mol O 6 2 mol 7 5 mol O 12 5 mol O none of these

The molar mass of barium cyanide Ba CN 2 is O 189 4 g mol 300 7 g mol 326 7 g mol 177 4 g mol 163 4 g mol

A supervisor records the repair cost for 17 randomly selected TVs A sample mean of 94 57 and standard deviation of 20 65 are subsequently computed Determine the 80 confidence interval for the mean repair cost for the TVs Assume the population is approximately normal Step 1 of 2 Find the critical value that should be used in constructing the confidence interval Round your answer to three decimal places

Consider the series The interval of convergence goes from x to x The radius of converge is R 8 If needed enter INF for co and INF for 0 n 1 n x 8 8T n 1

Solve the linear programming problem Maximize P 10x 70y Subject to x 6y 18 x y 0 What is the maximum value of P Select the correct choice below and if necessary fill in the answer box to complete you OA P Simplify your answer Type an integer or a fraction

Let A x represent the area bounded by the graph the horizontal axis and the vertical lines at t 0 and x for the graph below Evaluate A x for x 1 2 3 and 4 5 3 M 2 1 A 1 A 2 1 A 3 A 4 2 3 50

13 a 410 meters c 340 meters B 151 5

Each problem below refers to a triangle ABC Any answers that involve angles should be rounded to the nearest tenth of a degree 1 If a 100 inches b 60 inches and C 60 find c 2 If a 100 inches b 60 inches and C 120 find c 3 If a 5 yards b 6 yards and c 8 yards find the largest angle 4 If a 10 yards b 14 yards and c 8 yards find the largest angle 5 If b 4 2 meters c 6 8 meters and A 116 find a