Quadratic equations Questions and Answers

Decimal approximations are not allowed for this problem Enter your answer in exact form Use sqrt to represent Given that a is in quadrant 1 and cos x and also given that is in quadrant 3 and tan 3 give an exact answer for the following a sin a b b cos a b c tan a B 24 41 287 5 533 287 4

Assume that the following functions are periodically extended outside the original interval Sketch their graphs over three intervals Make sure to apply the Fourier Convergence The orem to your graphs 1 f x 3 f x 6 f x 5 f x 10 f x 1 1 0 0 x T L L x 0 L L x 0 x L 0 T X 2 1 2 x T 2 0 2 x T fo 1 x 0 0 2 0 x 1 x 2 2 x 0 2 2x 0 x 2 12 f x x r 1 x 1

1 Use the transformation u 4x 2y v x 2y to evaluate the given integral for the region R bounded by the lines y 2x 2 y 2x 3 y x and y 2x 5xy 2y dx dy R SS 2x R Type an integer or a simplified fraction 5xy 2y dx dy 1 2x 1

A 100 mL to fluid ounces B 5 mL to teaspoonfuls tsp Answer 2 Ophthalmic ointments were formerly packaged in 2 oz tubes What is this size expressed in grams round to 3 significant figures Answer 3 Convert the following round to 3 significant figures A 0 5 gr to mg B 800 mL to pint Answer 4 Convert the following round to 3 significant figures A 165 lb to kg

A 3 g L to mcg mL B 2 mL to dL Answer 2 Convert 6 23 g to micrograms to milligrams and to kilograms Answer 3 Convert the following A 36 mL to L B 2 85 m to cm Answer 4 Are the following concentrations equivalent Answer yes or no 0 1 mg mL and 100 mcg 0 01dL Answer

Round the following quantity as per the rounding inst 27 1258 mg 1 Round to 3 decimal places Answer 2 Round to 3 significant figures Answer 3 Round to the nearest whole number Answer 4 Round to the nearest 10 mg Answer 5 Round to the nearest hundredth Answer

If needed first write the given function as a single rational expression Then factor the numerator and denominator of R x Select the correct choice below and if necessary fill complete your choice x x 12 O A R x Type your answer in factored form Do not simplify B R x cannot be factored further What is the domain of R x Select the correct choice below and if necessary fill in the answer box to complete your choice OA xx Type an integer or a simplified fraction B xlx Type an integer or a simplified fraction Use a comma to separate answers as needed OC xx 2 Type an integer or a simplified fraction OD The domain is the set of all real numbers Write R x in lowest terms Select the correct choice below and if necessary fill in the answer box to complete your choice A R x Simplify your answer

x 6x 40x 0 The solution is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expres

Solve the following inequality algebraically 2x 4 X 4 3 The solution is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression

x 7 x 7 X 50 The solution is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression

Question 3 Solve each equation Give solutions in exact form Show work on checking your answer Circle your final answer a log x 9 log x 3 log 5 b log x 2 log x 1 1 log5 1092 x 2 x 1 1 x 2 x 1 2 log x a x 3 log x 3 logs 2 x 3 5 x 2 not possible x 3x 0 x x 3 0 x 3 x 0 2n 8 x 4 x 2 2 3 c log 2x 2

Solve the following inequality x 3 x 8 0 What is the solution Type your answer in interval notation Simplify your answer Use integers or fractions for any numbers in the expre

Determine which rational function R x has a graph that crosses the x axis at 1 touches the x axis at 4 has vertical asymptotes at x 2 and x 3 and has one horizontal asymptc O A R x OB R x c R x OD R x x 1 x 4 2 x 2 x 3 2 x 1 x 4 x 2 x 3 x 2 3 2 x 3 x 2 x 4 x 1 x 2 3 2 x 1 x 4 21 x 4 1 x 2 3

R x 14x x 5 Find the vertical asymptotes Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The function has one vertical asymptote Type an equation Use integers or fractions for any numbers in the equation C OB The function has two vertical asymptotes The leftmost asymptote is and the rightmost asymptote is Type equations Use integers or fractions for any numbers in the equations OC The function has no vertical asymptote Find the horizontal asymptotes Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The function has one horizontal asymptote Type an equation Use integers or fractions for any numbers in the equation B The function has two horizontal asymptotes The top asymptote is and the bottom asymptote is Type equations Use integers or fractions for any numbers in the equations OC The function has no horizontal asymptote Find the oblique asymptotes Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The function has one oblique asymptote Type an equation Use integers or fractions for any numbers in the equation OB The function has two oblique asymptotes The oblique asymptote with negative slope is Type equations Use integers or fractions for any numbers in the equations and the oblique asymptote with positive slope is

x 5 1 20 The solution is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the express

Question 4 For each function below find f 1 x and give the domain and range of f x a f x ex 3 4 b f x ln x 5 8 a f x Domain of f 1 x Range of f x b f x Domain of f1 x Range of f x

Question 2 Solve each equation Give solutions in exact form For irrational solutions give as decimals correct to the nearest thousandth Show work for each problem to receive full credit Circle the final answer 3 1 4 4 60 b a e 8e 15 0 c 32x12 3 35

Question 1 Let u In a and v In b Write each expression in terms of u and v only without using the In function Show work for each problem to receive full credit b In a b a In 1315 b5

0 3 is one angle of a right triangle with a hypotenuse of length equal to 10 cm Find the exact area of the triangle 5 points

pointa 2 Let C be the parametric curve defined by as depicted below In 1 36 36

a Find the cubic function that is the best fit for the data in the table below b Find the quartic function that is the best fit for the data in the table X y 1 4 2 0 3 10 4 30 5 5 6 190 7 1500 a The cubic function is y 36 639x 350 583x 980 063x 724 857 Simplify your answer Use integers or decimals for any numbers in the expression Round to three decimal places as nee

Fill in the blank to correctly complete the following sentence A polynomial function with leading term 3x 9 has degree

Consider the following polynomial function f x x 2 x 3 x 4 Step 1 of 3 Find the degree and the y intercept Express the intercept as an ordered pair Answer 2 Points

Find the average rate of change of the function from x to X Function x Values f x x 6x x x 1 x 4

A triangle s area is given by the expression 3x 2 x 12 The height is 6x The base of the triangle is the quotien of the area and 1 2 of the height

Which of the following inequalities illustrates the situation below The sum of double a number and six is at least 4 2x 6 4 x 2 6 4 2x 6 4 x 2 6 4

Write equation of the unit vector perpendicular to the wwwww www wwwwwwww 2 surface z 5x xy 5y at point Q 3 2 c

10 Consider the following differential equation on the interval 0 x cos x y sin x cos z y y 0 a 5pts Show that y tan z is a solution b 15pts Use the method of reduction of order to find a general solution on the interval

8x 16x Write the product cos 5 cos 19 COS 3 3 and or cosines NOTE Enter the exact fully simplified answer COS 8x 3 COS 16x 3 as a sum or differe

Convert the polar equation to rectangular form r 5 csc 0

a Solve the system u 3x 4y v x 5y for x and y in terms of u and v Then find a x y the value of the Jacobian a u v b Find the image under the transformation u 3x 4y v x 5y of the triangular region in the xy plane bounded by the x axis the y axis and the line x y 1 Sketch the transformed image in the uv plane x y 0 a x

5 What does the equation x y 2 4 0 represent in the Euclidean space R a A sphere intersecting the plane y 0 in a circle having radius 1 b A sphere intersecting the plane y 2 in a unique point c A sphere intersecting the plane y 0 in a unique point d A circle

Divide If the divisor contains 2 or more terms use long division 5x 2 26x 21 x 6

A 210 seat theater charges 6 for adults and 4 for children If all seats were filled and the total ticket income was 1140 how many adults were in the audience 150 adults 90 adults O 110 adults 130 adults

3 Find the domain of f x 2 2 1 z Use interval notation x 0

Given the function f x z 1 if 4 x 2 if 22 2z Note Assume arrows if no end symbols are shown a Select the correct graph of s Write the domain and range in interval notation b Domain c Range a

Find the area of the region enclosed by 12 25x and x 7 1 2 1 1 2 2 3 5 Q Use horizontal strips to find the area that is integrate with respect to y First find the y coordinates of the two points where y 2 25s meets z 7 1 lower limit c and upper limit d To find the area of the enclosed region from c to d we will integrate s u g y dy where g y

Farmer Jones and his wife Dr Jones decide to build a fence in their field to keep the sheep safe Since Dr Jones is a mathematician she suggests building fences described by y 112 and y x 6 Farmer Jones thinks this would be much harder than just building an enclosure with straight sides but he wants to please his wife What is the exact value of the area of the enclosed region

An 8 ft ladder leans against the side of a house How far is the bottom of the ladder from the side of the house when the angle of elevation of the ladder is 74 Round your answer to the nearest tenth 8 74 2 X 5

f x 5csc x 2 on the interval 0 7 Determine the points of discontinuity x 5 csc x on the interval 0 z If there are multiple discontinuities give your answer in the form of a comma separated list Express numbers in exact form Use symbolic notation and fractions where needed is discontinuous at x

Consider the following polynomial inequality x x 5 x 8 0 Step 2 of 2 Test each interval to find the solution of the polynomial inequality Express your answer in interval notation Answer

6 points Give the equation of any vertical horizontal or oblique asymptotes for the graph of the rational function If there is no asymptote state so f x x 1 x 3 Vertical asymptote s Horizontal asymptote Oblique asymptote

6 12 points Consider the polynomial function f x 15x 61x 2x 8 a List all possible rational zeros b i List all rational zeros and ii factor f x into linear factors

Hint Vertex 6 ats Graph the quadratic function f x 2x2 4x 5 Give the a vertex b axis of symmetry c domain and d range Then determine e the largest open interval of the domain over which the function is increasing and f the largest open interval of the domain over which the function is decreasing 13 points Answer y a vertex b axis of symmetry c domain X y x d range e increasing interval f decreasing interval

7 points Use the synthetic division to decide whether the given number k is a zero of the polynomial function If it is not state so and give the value of f k Show work f x x 3x 5 k 1 2i

7 points Use synthetic division to perform the division Write the answer as quotient 6 3x4 2x 6x 5x 3 x 2 divisor

Solve the system 2x 6y 2 5x 3y 3 Answer x y Enter your answers as integers or as reduced fraction s in the form

Part 3 of Using t sec 8 we must also convert the integration limits If t 2 then 0 sec 2 11 and if t 2 then Submit 8 sec 11 sec

1 x 5 a Complete the table below for x values close to 5 If a value is undefined enter NONE 1 point Let g x X g x X g x 6 Based on the values in the table what happens to the values of g x as x approaches 5 From the left g x help limits From the right g x X g x b Complete the two tables below to see how g x behaves in the long run If a value is undefined enter NONE Enter exact answers using fractions instead of long decimal answers 5 1 10 10 5 01 100 100 5 help limits 1000 1000 Based on the values in your table what happens to the values of g x As x takes very large positive values g x help limits As x takes very large negative values g x help limits c Without a calculator graph y g x on a piece of paper If there is more than one answer below enter your answers as a comma separated list If there are no solutions enter NONE What are the vertical asymptote s x help numbers What are the horizontal asymptote s y help numbers 4 99 4 9 4

Simplify by rationalizing the denominator 13 11 13 11 13 11 13 1 Simplify your answer Type an exact answer using radicals as need