Algebra Questions

8 1 point Square the binomial below x 4 0 0 0 0 x 16 3 2 8x 16 Previous 8x 16 16

1 point What is the degree of the monomial 8x y z4

4 1 point The degree of 5x y z is 9 True False Previous

3 1 point 62 can be classified as a natural number True False

Solve the following systems of equations using the A b construct as well as the Gauss Seidel method with a tolerance of 10 7 in some cases convergence may not occur a 2x x 3x3 8 4X1 2x2 5x3 9 6x 3x2 x3 12 b 10x1 x2 2x3 3 X1 10X2 X3 1 5 2X1 X2 10x3 9 5 5

Which value or values satisfy the absolute value inequality y 4 3 select all that apply

Let G be a group and let Z G be its centre Prove that if G Z G is cyclic then G is abelian Hint If G Z G is cyclic prove that a generator gives rise to an element outside Z G which commutes with all elements of G

Using Green s Theorem calculate the area of the indicated region 4 The area bounded above by y 3x and below by y 4x3

1 15 marks For each of the following three dimensional integrals re order the integral so that the x integration is first the y integration is second and the z integration third That is dx dy dz a b c 1 pln 2 fm f x y z dy o r2 3 0 da dz f x y z dy dz dz 1 dy de 2

Find the least squares line given the matrix products AT A ATb 1946 3 39353 8 y Ex 1 2 Ex 1 2 30 4 79 79 1617

nd the solution of each inequality in the interval 0 27 Enter your answers using interval notation a sin x 0 5 7 6 6 b cos x 0 5 2 4 3 3 c 2 tan x 2 sin x 5 4 4 X 3 4 4 X d 3 cos x 3 sin x

Find the eigenvalues and eigenvectors of the following matrices using both eig and power metho for the dominant eigenvalue and eigenvector If the power method fails discuss why For those matrices that are diagonalizable give the diagonalized matrix a b 2 781344 1 921334 0 493612 1 367198 1 014289 0 015050 0 205731 0 903377 1 780261 0 824057 0 087144 0 606003 2 977860 0 140473 0 750938 0 212440 2 477599 0 980236 4 233562 1 207581 0 136646 1 168924 0 453692 0 915245 1 712964 1 54575 3 47002 1 70112 2 58917 3 28104 2 07998 1 45597 2 75629 0 55497 0 94078 2 02863 0 46100 5

Find nonzero vector in Nul A and and Cc A Find a nonzero vector in Nul A and a nonzero vector in Col A 5 231 10 1 0 2 21 1 5721

Consider three vectors d 1 2 2 b 3 5 1 7 0 2 3 Part a 4 points Find the area of the triangle formed by the vectors a and 2 Prove that a and do not lie in the same plane Suppose a 1 0 4 y1 is perpendicular to both a and b Find a Part b 3 points Part c 5 points and y

Solve the initial condition value problem x E 2 4 512 2 X x 0 1 3 C Steckch and describe the nature of the phase portrait for this system

2 Use the key features to sketch the graph Use graph paper or a coordinate plane to earn credit a x intercept 5 0 y intercept 0 2 Linearity linear Continuity continuous Positive for values x 5 Decreasing for all values of x End Behavior As x o f x and as x f x b x intercept 1 0 and 1 0 y intercept 0 1 Linearity nonlinear Continuity continuous 810 Symmetry symmetric about the line x 0 Positive for values 1 x 1 Negative for values of x 1 and x 1 Increasing for all values of x 0 Decreasing for all values of x 0 Extrema maximum at 0 1

1 5 4 2 M 10 8 6 2 0 1 2 4 6 8 10 1 3 4 a State the domain in interval notation b State the range in interval notation c State the end behavior d State the local maxima e State the local minima f State the x intercepts g State the y intercepts h State the intervals where the graph is increasing

Compare the key features of the function represented below 234 2 3 fix 3 4 x g x x intercept 1 0 1 0 2 0 y intercept 0 4 relative maximum 1 37 0 35 relative minimum 0 37 4 85 2 0 end behavior as x g x and as x g x 00

Describe the end behavior of each function b C 10 2 4 ty AA 4 3 4 3 2 10 M 234x As x f x As x f x As x f x x As x f x As x f x As x f x Choose Choose Choose

MODEL The height of a fish t seconds after it is thrown to a dolphin from a 64 foot tall platform can be modeled by the equation h t 16t2 48t 64 where h t is the height of the fish in feet The graph of the function is shown th t 100 80 60 40 20 0 1 2 3 4t At about The maximum height of the fish is Check seconds the fish reaches its maximum height Select one True feet Temperature C 0 50 100 150 200 Density g cm 1 000 0 988 0 958 0 917 0 865 0 799 True False As temperature approaches infinity increases the density decreases 350 0 713 0 573 250 300

f 2 Check g x 2x 3 g 3 Check h x 3x 4

engineering students built a catapult for a class project They tested the catapult by launching a watermelon and modeled the height h of the watermelon in feet over time t in seconds 24 MO What is the appropriate domain in context of the problem O 0 2 5 0 25 0 2 5 Check 2010 ENGINEERING Several engineering students built a catapult for a project They tested the catapult by launching a watermelon and modeled the height h of the watermelon in feet over time t in sec It takes the watermelon less than 2 seconds to reach its maximum height Select one

CONSTRUCT ARGUMENTS Sheena says that in the graph of f x shown below the graph has relative maxima at B and G and a relative minimum at A Is she correct Explain B A S 43 50 40 30 20 10 O NOVE F D E 20 30 40 50 2 Sheena is correct 9 Sheena is not correct because she has the relative maxima incorrect Sheena is not correct because A is not a relative minimum Sheena is not correct because there are relative minima at D and 1 Choose Choose Choose Choose

Identify the coordinates of the extrema Input minimum on the left first ty O Relative Max Relative Min and

Identify the vertex the axis of symmetry the maximum or minimum value and the range of the parabola y x 2 8x 15 The vertex is

The graph of W x 6 4 6 5 4 3 24 1 4 2 3 4 5 6 7 8 9 12 13 10 is shown below Use the graph to solve the equation W x 4 6 a Enter the solution s in the box below If there is more than 1 solution separate the values with a comma example 3 2 If there are no solutions enter DNE for Does Not Exist 6

Multiple Choice Question A car travels 30 miles on one gallon of gasoline Gasoline costs 4 00 per gallon Calculate the cost of driving the car 300 miles

The conversion between Celsius x and Fahrenheit y can be expressed as a linear equation When it is O degrees Celsius it is 32 degrees Fahrenheit When it is 100 degrees Celsius it is 212 degrees Fahrenheit Which of the following equations represents the relationship between degrees Celsius and Fahrenheit

Sketch 3 Cycles of the function represented by f t 12 2 1 1 t if Cos 3Mt if 0 2 12 t 1 100 t 1 if 17 1 2

Answer Attempt 1 out of 5 1 6 7x 9x x The expression represents a quadratic is the leading term is polynomial with 4 terms The constar and the leading coefficient is V

9 a Find the state table for the finite state machine in Fig 6 8 where I 0 0 1 Start 1 0 So 0 0 51 1 1 0 1 SA 1 0 0 0 52 0 0 1 0 S5 0 0 1 0 0 0 1 0 Figure 6 8 b Let x J with x 4 If 1 is a suffix of w so x what are the possibilities for the string x c Let A 0 1 be the language where w so x has 1 as a suffix for all x in A Determine A d Find the language A 0 1 where w so x has 111 as a suffix for all r in 4

1 1 Explain how to complete each diagram so that it shows a 1 2 A student shows a as What is wrong with the diagram b Question 2 Vraag 2 2 1 Match each application with a fraction model Fraction Model 1 Part of a whole 2 Point on a number line Application a Your height in inches b Fraction of those surveyed who jog c The fraction of the day for which you are asleep d Evenly sharing 3 pizzas among 5 people 3 Division 4 Part of a group 2 1 4

With T defined by T x Ax find a vector x whose image under T is b and determine whethe is unique 63 0 1 6 b 2 2 1 A 1

Note The vector a b C in Maple syntax should be entered as a b c b Geometrically U is a plane through the origin in R4 and v is the position vector of a point A in R4 Find the exact value of the shortest distance of A from the plane U Enter your answer in Maple syntax in the box below

does anyone know how to make this in autocad the design is also included in the project FIGURE 5 10 10

Find the nth term an of a sequence whose first four terms are give 8 22 119 9 33 10 44

Identify whether graph represents a polynomial function that has a degree that is even or odd and whether the leading term is positive or negative 244 18 15 12 9 6 3 6 9 12 15 18 21 even and leading term is positive odd and leading term is positive even and leading term is negative

Find the area of the shaded portion of the flag below Show or explain how you got your answer 8 in 6 in

Determine whether the data show a linear relationship If so write an equation of a line of fit Months x Hair length in y y 9 3 13 18 22 23 5 7 10 11 The data do not show a linear relationship O The data show a linear relationship The equation is y 1 75x 4 25 O The data show a linear relationship The equation is y 0 55x 2 25 O The data show a linear relationship The equation is y 2 25x 0 55 If there is a linear relationship use the selected equation to estimate y when x 15 and interpret its meaning in the context c the situation which means after months the hair will be inches in length

Find the following sum and write it in lowest terms 6 3 11 11 6 3 11 11 Type an integer or a simplified fraction

Find the difference and write in lowest terms 7 5 4

Evaluate and write in lowest terms 64 7 16

Replace the with the correct symbol 2 3 2 3 318 318 V

List all elements of the set Select all that apply A 3 73773777 C 7 E 7 6 7 8 0 7 3 73773777 that are also elements of the set of irrational numbers 6 B D O F No elements in the set are in the set of irrational numbers 8

Find the least common multiple LCM of the following numbers 117 and 72 The LCM of 117 and 72 is

Write as a fraction 0 2

The number 0 351 rounded to the nearest hundredth is

Write as a decimal 9 8

Rewrite the fraction 1 with 35 as the denominator 7

Replace the question mark by or whichever is correct 667 0 9 0 9