Quadratic equations Questions and Answers

If f x In x g x x and h x x find the following a fog x What is the domain of f o g b gof x What is the domain of g o f c fog 7 d f o h x What is the domain of f o h e foh e

Milan is saving up money for a down payment on a condominium She currently has 2525 but knows she can get a loan at a lower interest rate if she can put down 3258 If she invests the 2525 in an account that earns 5 3 annually compounded quarterly how long will it take Milan to accumulate the 3258 Round your answer to two decimal places if necessary

Does prison really deter violent crime Let x represent the percent change in the rate of violent crime and y represent the percent change in the rate of imprisonment in the general U S population In 7 recent years the following data have been obtained Use your graphing calculator to find the line of best fit for the given data Round to 3 decimal places as needed B y 5 8 6 1 6 4 6 7 7 7 3 7 6 7 9 0 42 0 42 0 38 0 25 0 21 0 23 0 4 0 42 Linear Regression Equation Use your regression equation to predict the percent change in the rate of imprisonment when the percent change in the rate of violent crime 8 11

Consider the Sturm Liouville system x y xy 2y 0 220 and y e 0 y 1 0 a 10 marks Find all eigenvalues and eigenfunctions b 2 marks Are the eigenfunctions obtained in part a orthogonal Justify your answer

Solve the system by graphing If the system does not have one unique solution also state the number of solutions and whether the system is inconsistent or t equations are dependent 3 y x 1 3x 4y 4 Part 0 2 Part 1 of 2 Graph the lines 16 14 12 10 8 6 4 y X

A borrower obtains a 76 000 mortgage loan at 11 2 interest If the monthly payments of 785 are credited first on interest and then on principal what will the balance of the principal be after the borrower makes the first payment

during a wheel alignment the camber on a certain car is measured to be 3 degrees and 54 inches If the maximum acceptable camber for this car is 3 850 degrees is the camber within this limit

x 3y 0 Use the graphing tool to graph the equation Use the intercepts when drawing the line If only one intercept exists use it and another point to draw the line Click to enlarge graph Use intercepts to graph the linear function 5x 2y 10 Use the graphing tool to graph the linear equation Use the intercepts when drawing the line If only one intercept exists use it and another point to draw the line Click to enlarge graph SIDD Plot the intercepts to graph the equation x y 7 Use the graphing tool to graph the equation Use the intercepts when drawing the line If only one intercept exists use it and another point to draw the line 10 10 4 2 10 2 Ay AY 10 2

Each of the following polynomial functions has x intercepts at 6 0 and 5 Determ appropriate equation for each and then sketch the function a A cubic function with a positive leading coefficient b A quartic function that extends from quadrant 3 to quadrant 4 c A degree 6 function with a negative leading coefficient quadrant to quadrant 4

A doll sold for 200 in 1975 and was sold again in 1989 for 479 Assume that the growth in the value V of the collector s item was exponential a Find the value k of the exponential growth rate Assume V 200 k 0 062 Round to the nearest thousandth b Find the exponential growth function in terms of t where t is the number of years since 1975 V t

Will takes out a loan of 13 000 with a 4 3 interest rate that is compounded semi annually if he pays off the loan in 6 years how much will he end up paying Round your answer to the nearest cent Do NOT round until you have calculated the final answer

Use Cramer s rule to solve the system 5x 2y 10 6x 2y 34 The solution set is Simplif answer Type an ordered pair using integers or fracti

Submit Answer 1 Points Submit Answer DETAILS 2 Points SPRECALC7 6 1 062 Find the radius r of the circle if an arc of length 50 cm on the circle subtends a central angle of 60 Round your answer to two decimal places r cm DETAILS MY NOTES SPRECALC7 6 1 060 ASK YOUR MY NOTES ASK YOUR

1 Determine the exact primary trigonometric ratios for 8 A B 3 4 1 2 Determine the length of DC to the nearest tenth of a centimetre A D 28 38 78 4 16

The motion of a racecar is described by the formula d t 35t 5t2 where d is the distance in meters that the car has traveled from its original position and t is the time in seconds since the car started moving How long in seconds will it take for the car to travel 220 meters

Verify the identity cos 3x cos2x cosx sin 3x sin 2x sinx Statement cos3x cos2x cosx cot 2x

Algebraically solve the following equations and state any restrictions on x a log x 4 1 b C log x 5 log 2x 8 3 2 2x 1 4

Given the graph of y f x shown below what is the graph of y f x 1 2 7 6 5 4 3 2 N 6 LO t 5 4 3 st N H T N 3 4 5 1 2 3 4 5 6 7

Determine the different possibilities for the numbers of positive negative and nonreal complex zeros for the following function 3 f x x5 3x4 x 2x 9 What is the possible number of positive real zeros of this function Use a comma to separate answers What is the possible number of negative real zeros of this function Use a comma to separate answers What is the possible number of nonreal complex zeros

Simplify m 49 m 14m 49 O 1 m 7 m 7 m 7 1 Om 7 m 7

Divide by using synthetic division Check your answer by multiplication h h 2 h 2 19

Find and simplify the function f g 10 given that f x x 4 and g x x 2 Provide your answer below

Find and simplify the function Assume that 1 x 9 7 x given that f x x 1 and g x x 1 f Select the correct answer below O x 1 O x 1

Given the following table of values compute fog 3 Do not include fog 3 in your answer Provide your answer below x f x g x 1 14 4 2 6 1 3 9 4 11 2 3

Given the graphs of f x and g x provided below find the composition of functions f g 2 5 1 g x 4 1 3 K f x 1 0 0 1 2 3 4 5 6 Provide your answer below 1

Divide the polynomials by using long division Check your answer by multiplication 24a 35a 4 5a 2 3

Factor the polynomial by grouping if possible Select Cannot be factored if applicable 3mx 12nx my 4ny Cannot be factored

Video Example 2 b D 0 100 Sketch the curve r 1 sin 0 Solution Instead of plotting points we first sketch the graph of r 1 sin 0 in Cartesian coordinates in the top figure by shifting the sine curve up one unit This enables us to read at a glance the values of r that correspond to increasing values of 0 For instance we see that as so we sketch the corresponding part of the polar curve in figure a As 0 increases from to the top figure shows that r decreases from 3 2 0 increases from 0 to r the distance from O increases from to to so we sketch the 2 as shown in part d If we let 0 increase beyond 2n or decrease 3r as shown in part c Finally as 0 increases from r decreases from to 2n r increases from next part of the curve as in figure b As increases from it to 2 beyond 0 we would simply retrace our path Putting together the parts of the curve from figures a d we sketch the complete curve in part e It is called a cardioid because it s shaped like a heart 2 2 n 0 to to

Factor out the common binomial factor 3x x 2y y x 2y x 2y

3x 6xy xy 2y Part 0 2 Part 1 of 2 possib Step 1 Identify and factor out the GCF from all four terms In this case the GCF is 1 Group the first pair of terms and the second pair of terms 3x 6xy xy 2y 3x 6xy xy 2y Step 2 Factor out 3x from the first pair of terms Factor out y from the second pair of terms The terms now contain a common binomia 3x x 2y Y X

Your firm is considering a project that requires 2 000 000 of fixed assets that are classified as 7 year property for MACRS What is the book value of these assets at the end of year 6 with the following depreciation rates Year Percent 1 2 14 29 24 49 3 17 49 4 12 49 5 6 8 93 8 93 7 8 93 8 4 45

Graph 120 10 10 10 20 Sign of Even or Leading Odd Coefficient Degree h x x 4 x 3 Degree End Behaviour Symmetry 2 For the following function complete the table and sketch a graph Leading Coefficient End Behaviour Number of turning points x intercepts Number of x intercepts y intercept Least Possible Degree

Use quadratic regression to find a function that models the data Plot the data and the quadratic regression curve The table to the right shows the price of soybean meal in dollars per metric ton With x 0 corresponding to the year 2000 what does the graphing calculator model estimate for the year 2014 Years 2011 2012 2013 2014 2015 R and D Spending 397 523 546 527 395 Use quadratic regression to find a function f x that models the data f x x x Use integers or decimals for any numbers in the expression Round to three decimal places as needed

ign in Apex Leam DgmoookOndykxfmv dzsazoqh3ssivo viewform hr vainly com For st 14 Find the equation of the polynomial graphed below y f x 6 x x x 2 x 1 x 1 A F X x 25 x 1 x 1 B x x x 2 x 1 x 1 8 F x x 2 x 1 x 1

13 James deposits 8000 into an account that pays 2 35 interest compounded quarterly How long will it take until he has 10000 in the account O A OB O C D 4 97 years 9 52 years 9 61 years 98 years

19 A degree 2 polynomial has x intercepts at x 5 and x 2 The graph goes through the point 1 24 Find the exact equation of this polynomial y x 5 x 2 O A y 2x 3x 10 y x 3x 10 OB y 2x 6x 20

5 In 1990 the city of Andover had a population of 15 000 people Since then the population has grown by 3 3 each year In 1990 the city of Minneapolis had a population of 370 000 and has been decreasing by 1 7 each year If these patterns continue how many more people will be living in Minneapolis compared to Andover after 25 years O A 207 237 B C 234 530 530 155 O D Because Andover is increasing and Minneapolis is decreasing Andover will have more people

6 Using the same scenario from earlier Rynn wants to know if people in their town consume movies more often in theaters or at home They want to use a survey and create a representative sample of people to answer their research question Which sampling method would give Rynn a sample that most accurately reflects the population in their town O A Rynn asks every 5th person who exits the local movie theater how they prefer to consume movies O B Rynn walks through her neighborhood and asks everyone who is at home how they prefer to consume movies O C Rynn uses a phonebook and an online phone listing and calls every 5th person to ask them how they prefer to consume movies O D Rynn surveys everyone that works in her office how they prefer to consume movies

Find the solution using the undetermined co efficient metho A y y 2y tet 1 B y 2y 2y 4te cos t

3 The information in the table describes a polynomial function Leading Coefficient Degree Zeros Local Minimum Local Maximum y intercept 1 3 1 2 4 4 1 8 2 8 T a Sketch a graph of the function Identify and label the zeros local maxima and y inte b Describe the end behavior of the graph of the function c How many turning points does the graph of the function have Justify your answer d Write an equation of the polynomial

2 8cm 2 Find the value of Theta 0 Angle A 6 marks K U 18 6 cm 52 3

Problem 1 Let F x y y x a Sketch the vector field with at least 15 vectors drawn b Suppose at t 0 a particle is placed a the point 1 2 in the vector field one can imagine that the vector field describes the velocity of a fluid Find the location of the particle r t at time t c In the same scenario as the previous part write down an equation in x and y that describes the curve traced out by the particle s motion

w shows for different countries the average number of Country France Germany Greece United Kingdom United States Annual Number of Hours Worked 1 551 1 320 2 118 1 644

1 point Let L R R be the linear operator defined by a Find the dimension of the range of L b Find the dimension of the kernel of L let She the subspace of R3 spanned by 2 and 25e L x 8x120x2 8x3 10x2 24x1 24x3 25e Find the dimension of L S

The problem that follows reviews material we covered in Section 2 3 The following problem refers to right triangle ABC in which C90 Solve the triangle Round your answers to the nearest whole number A 34 c 42 56

Which of the numbers below is closest to the monthly payment needed to pay off a loan of 1550 in 12 equal monthly payments if the annual interest on the loan is 3 compounded monthly 1 131 28 2 127 34 3 135 21 AY 120 15

For the polynomial function f x x3 3x 13x 15 a Use the degree to determine the maximum possible number of real zeros b Use the Rational Zeros Theorem to list all possible rational zeros c Use the Bounds Theorem to find a bound for the real zeros of the function d Graph the function and identify all rational zeros of the function e Use the rational zeros and synthetic division to completely factor the function Paragraph a Degree b P q c Bound d Zeros e f x B UA

nd a basis for the subspace of R4 consisiting of all vectors of the form X1 6x1 x2 6x1 3x2 Gm

Factor the trinomial completely by using any method Remember to look for a common factor first Select Prime if the polynomial cannot be factored 157 2 291 0 Prime

60 degrees A small object with an initial temperature of 135 degrees Fahrenheit is dropped into a tub with a temperature Fahrenheit The function f t Cel kt 60 represents the situation where it is time in minutes C is a constant and k is a constant After 6 minutes the object has a temperature of 85 degrees What is the approximate value of k Round to three decimal places Provide your answer below