Algebra Questions

1 cot e 2 7 16 Find the value of the six trigonometric functions of 0 where is the angle formed by the positive x axis and the line segment from 0 0 to 2 7 sin 0 cos 0 tan 0 sec 0 csc 0

C 55 A 9 B If angle C measures 55 and BC has length 9 find Angle B in degrees The length of AB The length of AC If you use a calculator to find a decimal approximation your answer must be accurate to at least 3 decimal places

Find the vertex of y x 6x 6 using the vertex formula Step 1 Find the x coordinate of the vertex For any parabola y Az Bz C the x coordinate of the vertex will always be t Using this formula what is the x coordinate of the vertex for the parabola y x 6x 6 Step 2 Find the y coordinate of the vertex lue the vertey of the serab

12 A If angle B measures 27 and AC has length 12 find Angle C in degrees The length of AB The length of BC 27 B

Given a right triangle with sin 0 1 cos 0 2 tan 0 3 sec 0 4 csc 0 5 cot 0 5 8 determine the value of the other trigonometric ratios of 0

Find the area if the distance between two adjacent dots in a row or column is one unit 9 What is the ratio of the area of B to the area of A 3 A B 9 19 D 1

D redit 8 How high can you go using s 2 4 1 1 7 4 2 3 2 1 32 2741 24 2 2 3 7 4 3 4 4 5 7 4 2 5 6 4 2 6 7 7 8 4x2 8 D 9 7 2 9 10 11 7 4 11 12 7 2 17 14 2 12 13 7 4 2 11 2 13 14 7 4 2 28 2 14 15 2x4 7 8 7 15 16 42 16 7x2 4 14 4 10 17 24 7 17 18 72 4 18 19 41 7 2 24 7 17 2 19 20 4 21 22 41 2 24 2 22 23 27 4 23 24 7x4 2 28 2 24 25 7 4 49 24 25 26 41 2 24 2 26 27 27 28 7x4 28 72 49 74 2401 42 16 27 128 47 16384 2 4 4 14 2 47 74 42 42 312 29 24 42 27 72 7 5040 4 24 21 2 16384 128 2401 49 149 7

D redit 8 How high can you go using s 2 4 1 1 7 4 2 3 2 1 32 2741 24 2 2 3 7 4 3 4 4 5 7 4 2 5 6 4 2 6 7 7 8 4x2 8 D 9 7 2 9 10 11 7 4 11 12 7 2 17 14 2 12 13 7 4 2 11 2 13 14 7 4 2 28 2 14 15 2x4 7 8 7 15 16 42 16 7x2 4 14 4 10 17 24 7 17 18 72 4 18 19 41 7 2 24 7 17 2 19 20 4 21 22 41 2 24 2 22 23 27 4 23 24 7x4 2 28 2 24 25 7 4 49 24 25 26 41 2 24 2 26 27 27 28 7x4 28 72 49 74 2401 42 16 27 128 47 16384 2 4 4 14 2 47 74 42 42 312 29 24 42 27 72 7 5040 4 24 21 2 16384 128 2401 49 149 7

9 Suppose f x 0 for all x and f x dx 18 Let R be the region in the first quadrant bounded by the coordinates axes y f x and x 3 Find the volume of the solid generated by 0 revolving R around the y axis BELEM Set up the integral that gives the volume of the solid Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OA JOf x dx OB SD x dx

weather balloon has a volume of 720 L when filled with helium at C at a pressure of 385 torr Part A What is the new volume of the balloon when the pressure is 0 18 atm the temperature is 45 C and n remains constant Express your answer to two significant figures and include the appropriate units Vnew Value Units

10 10 x B 2 0 10 2 0 10 Find the coordinates of in the ordered basis B a b Hint The preview shows the picture of a with the coordinates you pro

O Points 0 of 1 all fence runs parallel to the wall of a house at a distance of 10 ft Find the length of the shortest ladder that extends from the ground to the house without touching the fen Assume the vertical wall of the house is 20 ft high and the horizontal ground extends 20 ft from the fence PEND The length of the shortest ladder is ft Round the final answer to the nearest tenth as needed Round all intermediate values to the nearest thousandth as needed S

ided by the following curves Let S be the solid generated when R is revolved about the given axis If possible find the volume of S by both the disk washer and shell methods Check that your results agree y x y x OA S 1 11 in the first quadrant revolved about the x axis Set up the integral s that gives the volume of the solid as a single integral if possible using the disk washer method Use increasing limits of integration Select the correct choice below and fill in any answer boxes within your choice OB dx S dx Type exact answers www dx Type exact answers

Write the equation of the quadratic with Vertex 3 1 and point 7 3 Hint do the same as above

1 y 3 2 cos x Choose the correct graph O A UNS HILLE AV 10 1 IN Ay S 10 VAN loft H ON pehod interval Do not use a graphing calculator OB O C HERINE TOTTE HILLSITTE HISHHHHHH HISSITH 0 of 1 O D Ay GOO Save

Select the correct asnwer The volume of a rectangular prism is a minimum of 25 cubic feet The height of the prism is 3 feet more than its width and its length is at most 5 feet more than the width Carla wrote this system of inequalities to represent this situation where Vis the volume of the prism and wis the width V w 8w 15w V 25 A OB C OD Carla wrote the system incorrectly the first equation has the wrong volume expression Carla wrote the system incorrectly the second equation has the wrong inequality symbol Carla wrote the system correctly Carla wrote the system incorrectly the first equation has the wrong inequality symbol

Type the correct answer in the box Tiffany is monitoring the decay of two radioactive compounds in test tubes at her lab Compound A is continuously decaying at a rate of 12 and compound B is continuously decaying at a rate of 18 Tiffany started with 30 grams of compound A and 40 grams of compound B Create a system of inequalities that can be used to determine when both compounds will be less than or equal to the same mass M where t is time in weeks PA is the initial amount of compound A PB is the initial amount of compound B and ris the rate of decay Enter the inequalities in the field by replacing the values of PA PB and r olo O 0 101 0 Vo 0 X TT a B A P sin cos tan sin cos tan 9 PO csc sec cot log log In 0 11 0 L VO A U 00 L00

Select the correct answer from each drop down menu Two different species of deer are housed in two separate areas of a wildlife park The initial population of species A was 300 and the population is increasing by 15 every year The initial population of species B was 400 and the population is increasing by 7 every year Use the given information to determine when the two species will have the same population After years the populations of the two species will be approximately equal with deer of each species

Select the correct answer The height of a pelican as it swoops down to catch a fish in the lake is modeled by this equation where x represents the time in seconds and y represents the height of the pelican in feet y r 6x 8 75 At the same time a second pelican flies in a straight line modeled by this equation y 5 Which statement describes the number and viability of the system s solutions The system has only one solution and it is viable because it results in positive values of time The system has two solutions but only one is viable because the other results in a negative value of time C The system has only one solution but it is not viable because it results in a negative value of time D The system has two solutions and both are viable because they result in positive values of time A B

Use the given conditions to find the exact values of sin 2u cos 2u and tan 2u using the double angle formulas cos u 15 17 2 U sin 2u cos 2u tan 2u

Select the correct answer Using graphing what are the approximate solutions to this equation 2x 1 1 x OA B C OD 0 913 and 1 803 0 761 and 1 217 x 0 761 and 1 803 0 913 and 1 217

Solve the equation Check your answer in the original example 4m 6 9 3

Select the correct answer Consider this equation 12 42 1 2 2 Approximate the solution to the equation using three iterations of successive approximation Use the graph as a starting point N LIN 2 2 OA OB a z IN

Select the correct answer Consider functions fand g 5 2 1 3 Using a table of values what is an approximate solution to the equation f x g x to the nearest quarter of a unit A B C 2 2x 1 D 2 50 1 75 1 50 22 25 Next

Calculate 7 9i Give your answer in a bi form Give the solution with smallest positive angle Round both a and b to 2 decimal places

9 Given A ABC answer the following round each answer to the nearest tenth A If a 10 b 6 and c 7 find a 2 points find ZA b 2 points find ZB c 2 points find ZC 6 C 7 10 B

2 7i 3 4i 6 points Given the following expression a 1 point State the conjugate b 4 points Simplify the expression in a bi form

8 10 points Find the all solutions of this equation in the interval 0 2 3 tan 0 3 6 tan

A C C If a 8 b 8 and ZC 60 then find the length of side c b B a

12 5 points Prove identity sin x csc x cos x csc x

points Given the following expression 5278 a a 1 point State the LCD b 4 points Simplify the complex fraction a PIA88

Consider the following vectors given in polar form 3 3 70 Write the polar form for each of the following resultant vectors a 50 7 Preview 13 325 6 67 Preview Hint your answers will be in the form c and you do not need to enter a degree symbol Enter your angle as a degrees between 0 and 360

Find the standard deviation for the following data Round your answer to 2 decimal places as needed 90 63 53 96 26 4 52 73 13 10 19 standard deviation

Find the periodic payment which will amoun to a sum of 18000 if an interest rate 8 is compounded annually at the end of 14 consecutive years

An arch shaped monument is often mistaken to be parabolic in shape In fact it is a catenary which has a more complicated formula than a parabola The arch is 614 feet high and 614 feet wide at its base Assume that the x axis represents ground level and that the y axis goes through the center of the arch Complete parts a b and c a Find the equation of a parabola with the same dimensions Let x equal the horizontal distance from the center of the arc Simplify your answer Use integers or fractions for any numbers in the expression

A certain game involves tossing 3 fair coins and it pays 19 for 3 heads 10 for 2 heads and 4 for 1 head Is 10 a fair price to pay to play this game That is does the 10 cost t blay make the game fair

A researcher wants to know if the news station a person watches is a factor in the amount of time in minutes that they watch The table below shows data that was collected from a survey Local FOX CNN 55 42 Ho H1 H2 H3 H At least two of the means differ from each other 1 For this study we should use ANOVA 2 The test statistic for this data 3 The p value for this sample 37 65 25 53 65 24 29 51 47 35 26 63 62 40 50 Assume that all distributions are normal the three population standard deviations are all the same and the data was collected independently and randomly Use a level of significance of a 0 01 49 69 17 46 60 17 46 Please show your answer to 3 decimal places Please show your answer to 4 decimal places

Solve the equation Write the solution set with the exact solutions Also give approximate solution to 4 decimal places log q 8 4 7 O There is no solution O The exact solution set is DO 9 0 0 10 O D

8 58 X 19w 45 5

Suppose that In 5 s and In 11 t Use properties of logarithms to write the logarithm in terms of s and t In 55

Write the following expression as a sum and or difference of logarithms Express powers as factors In e x 7

Use properties of logarithms to find the exact value of each expression Do not use a calculator log 86 8 log 26

Use common logarithms or natural logarithms and a calculator to evaluate the expressi log 15 17 Use the change of base property to rewrite the given expression log 17

Provide your answer below 2 0 14 0 6 DC

Given the function C n n 1 n 7 n 4 the coordinates of its C intercept are the coordinates of its n intercepts are

4x y 1 What is the slope of this line What is the y intercept of this line

Convert this equation to slope intercep form 2x 3y 6

4 Which expression below is equivalent to 3 2x 4 3 x 5 a 3x 27 3x 27 c 9x 27 d 3x3

3 Which value for x below is a solution to the equation 2x 8x 20 5x a 1 b 2 C 4 d 5

2 Is x 4 a solution to the equation 4x 5 21 No