Quadratic equations Questions and Answers

13 The father s age is six times his son age Four years hence the age of the father wi be four times his son s age The present ages in years of the son and the father are respectively a 4 and 24 b 5 and 30 c 6 and 36 d 3 and 24

A car dealership offers a 1 900 factory rebate and a 9 discount off the price of a new car c Write a function r for the cost of the car after receiving only the factory rebate Write a function p for the cost of the car after receiving only the dealership discount p c

Let A1 A2 such that 1 A A2 An be the vertices of an n sided regular polygon 1 What will be the value of n A A3 1 A A4

There is a linear transformation T V V satisfying T v v for every non zero vetor vand whose matrix representation in some basis B is True False AB 1 0 1 0 0 13 0 0 0 5 3 1 0 6

Divide the polynomial p x by the polynomial g x and find the quotient and remainder in each of the following p x x 3x 5x 3 i ii P x x 3x 4x 5 iii p x x 5x 6 g x x 2 g x x 1 x g x 2 x

2z 4z 4z 5 z z 2 Determine the correct partial fraction decomposition for the expression above Provide your answer below

Suppose that 50 000 from a retirement account is invested in a large cap stock fund After 30 yr the value is 161 946 41 Part 1 of 2 a Use the model A Pe to determine the average rate of return under continuous compounding Round to the nearest tenth of a percent Avoid rounding in intermediate steps The average rate is approximately 3 9 Part 1 2 Part 2 of 2 b How long will it take the investment to reach one quarter million dollars Round to the nearest tenth of a year Round values in intermediate steps to three decimal places

Solve g 27 X Tyne an integer or a simplified fracti

an equation for the rational function graphed below 543 8 1 5 4 3 2 1 4 2 3 4 3 4 11 o Q

40 A lot consists of 48 mobile phones of which 42 are good only 3 have minor defects and 3 have major defects Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect One phone is selected at random from the lot probability that it is i Acceptable to Varnika ii Acceptable to trader

into triangles BCD and AABD by diagonal BD Construct the triangle BD C similar to ABDC with scale factor Draw the line segment D A parallel to DA where A lies on 3 extended side BA Is A BC D a parallelogram Sol Step of construction 3 cm C B 5 cm B 5 cm A A 3cm B B

2 Verify that each of the following is an A P and then write its next three terms 113 424 i 0 14 13 41300 3 3 iii 3 2 3 3 3 iv a b a 1 b a 1 b 1 ii 5 4 v a 2a 1 3a 2 4a 3

13 The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60 and the angle of elevation of the top of second tower from the foot of first tower is 30 Find the distance between the two towers and also the height of the other tower Sol Two vertical tower TW 30 m and ER x m let are standing on a horizontal plane RW y let The angle of elevation from R to top 90 m high tower is 60 and the angle of elevation of second tower from W is 30 E xm R 60 30 ym 30 m W

Fill in the table by performing each implied operation and simplifying the result Write all answers with positive exponents only a 20 b 2k 16k7 4k6 ab 40k o 642 13 q b k 40 13 64 X X X a k 40 13 64 k 196 X X X

Let the polynomial be ax bx c and its zeroes bea and B

15a 3b Sc 15a 5c isa 3b 3b 56 0

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively i 1 ii 2 iii 0 5 iv 1 1 v 11 vi 4 1

of order 1 and a negative leading coefficient 12 marks a Determine a possible equation for f x in factored form

A particle moves along line segments from the origin to the points 1 0 0 1 5 1 0 5 1 and back to the origin under the influence of the force field F x y z z i 5xyj 5y k Use Stokes Theorem to find the work done 6F F dr

match the values of the scatterplost Scatterplot 1 r 0 708

You may use the calculator on the toolbar for this question Let A be the matrix 1 FIRST Find all vectors v so that the distance between Av and the standard unit basis vector ej is minimized Call the set of all such vectors L THEN Find the unique vector va in L such that vo is orthogonal to the kernel of A On a pair of coordinate axes draw ker A and L and vo to check your answer Enter the x coordinate of the vector vo in the box below using 5 decimal points of precision 0 25 Correct Answer 0 09411764705

Rewrite the expression in terms of the first power of the cosine Use a graphing utility to graph both expressions to verify that oth forms are the same 2 sin x tan x

i Consider the function f x x 0 x T a Extend the function in an odd manner and sketch the Fourier S series representation on x E 3 3 b Determine the Fourier sine series of the odd extension c Using the results above and Parseval s identity show that 7 2 21 12 6 n n 1

Find the product 2122 in standard form Simplify your answer completely 2 5 5 3 2 5 3 51 Z1 2 X Write 2 and 22 in trigonometric form and find their product again 2122 3 Finally convert the answer that is in trigonometric form to standard form Are the two products equal Yes O No

What strategy are you using to sketch graph of linear systems and non linear systems

Find v v 10i 24j lyll Tyne an exact answer using radicals as needed Simplify your

2 The angle x lies in the interval and sin x value of sin2x Round your answers to four decimal places Determine th

2 5 points Solve this equation for exact solution s over the interval 0 2 sin 20 cos 20 1

olve the system graphically and indicate whether the solution region is bounded or unbounded Find the coordinates of each corner moint x y 4 x 3y 6 x20 y20

If tan a 24 and cot P Hint Your final answer should have no trigonometric terms a sin a p b cos a c tan a A x d sin a e cos a f tan x 12 for a second quadrant angle a and a third quadrant angle find the following 35 x

Find two functions and a such that the composition fogh expresses the given correspondence Several answers are possible h x x 7 x g x

Determine the equation in standard form of the ellipse that satisfies the given conditions Center at 2 1 one vertex at 3 1 one focus at 1 1

Look at the graphs and their equations below Then fill in the information about the coefficients A B C and D y A x y B x y C x A y D x B a For each coefficient choose whether it is positive or negative Choose one Choose one b Choose the coefficient closest to 0 c Choose the coefficient with the least value C Choose one D Choose one

1 Parallel Line Construction For this part of the assignment you will construct a parallel line through a given line and point First draw a segment AB and point Con your paper Next construct a line through point C that is parallel to AB Label all points and lines used in the construction 2 Perpendicular Line Construction For this part of the assignment you will construct a perpendicular line to a given segment that passes through a given point First draw a segment AB on your paper Draw a point C above that line Construct a perpendicular line through segment AB and point C Label all points and lines used in the construction

a b Prove by mathematical induction that 4 n for all positive integers n A sequence an is defined by a 3 a 7 and an 2 5an 1 6an for all n 1 2 3 Prove by mathematical induction that an 2n 3 1 for all n 1 2 3

v and w c state whether the vectors are parallel orthogonal or neither v 8i j w i 8j a v w Simplify your answer Show Trans a Find the dot product vw b find the angle between v and w c state whether the vectors are parallel orthogonal or neither V 3i j w i j

1 express the solution in terms of natural or common logarithms 2 use a calculator to obtain a decimal approximation correct to 2 decimal places for the solution h 5 3 5 10 0

Caffeine occurs naturally in a variety of food products such as coffee tea and chocolate The kidneys filter the blood and remove caffeine and other drugs through urine The biological half life of caffeine is approximately 6 hours If one cup of coffee has 80 mg of caffeine then the amount of caffeine C in mg remaining after hours is given by C 80 2 6 a How long will it take for the amount of caffeine to drop below 60 mg Round to 1 decimal place b Laura has trouble sleeping if she has more than 30 mg of caffeine in her bloodstream How many hours before going to bed should she stop drinking coff Round to 1 decimal place if necessary Part 0 2 Part 1 of 2 approximately hour s for the amount of caffeine to drop below 60 mg 15

nt e or A P 1 2 where A is the future value of P dollars invested at interest rate r compounded continuously or n times per yea Use for t years 18 000 is invested at 4 interest compounded monthly How long will it take for the investment to double Round to the nearest tenth of a year the model A Pet or A P It will take approximately years for the investment to double X

Solve each equation for the other variable Hint This will involve rewriting each equation in logarithmic form at some step in th a y 9 y 1 b v 4 1 6 c b 3 Preview H Preview

Toutes les ar tes du cube sont de la m me longueur S S S Recharger image Quelle formule peut on utiliser pour calculer l aire du cube A 6 Sx S A S S S OA 6 S S you ces r ponses

Given a square matrix A 231 where al 2 1 1 1 3 ki 1 1 We perform the operation R R 2R Find the matrices E and B such that E A B Hint Find E then perform E A to obtain the matrix B Find value s for k 1 0 whenever possible such that a33 a are the entries of the matrix 4 given above

For each part if the work steps you show are incorrect and or insufficient to show an of the procedures and or calculations involved points will be deducted understanding Complete parts a through c for the equation of a circle x y 4x 2y 1 a Write the equation in standard form by completing the square and showing appropriate work b Identify the center and radius c Graph the circle by showing appropriate work Be sure that your axes and center are properly labeled and your spacing is proportional

Form a third degree polynomial function with real coefficients with leading coefficient 1 such that 1 i and 8 are zeros

Solve the inequality and write the solution set in interval notation If necessary use inf for and capital U for set union as in inf 9 U 10 inf for 9 U 10 Do not enter any spaces in the answer I 8 T 12 0

the method of substitution to solve the following system of equations If the system is dependent express the solution set in ables Leave all fractional answers in fraction form swer 4 Points 2x 4y 2 6x 12y 6 ecting an option will display any text boxes needed to complete your answer O Only One Solution O Inconsistent System Dependent System

Find the equation of the line through the given pair of points in standard form using only integers and the smallest possible positive integer coefficient for x 4 1 4 3 The equation of the line in standard form is

ider the following functions f x x 4 and g x swer 4 Points 2 of 2 Find the formula for gof x and simplify your answer Then find the domain for gof x Round your answer t ces if necessary x 4 5 gof x

If x 85 find the measures of angles 1 2 and 3 m21 m22 m23 o C

Consider the functions f x 6x 7 and g x x 7 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other