Questions

Use the graph of the function to answer each question 2x x 2 f x cot x 2 3 2 a Find all x intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE x b Find all y intercepts of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE y c Find the intervals on which the graph of y f x is increasing and the intervals on which the graph of y f x is decreasing Enter your answers using interval notation If an answer does not exist enter DNE increasing decreasing d Find all relative extrema if any of the graph of y f x Enter your answers as a comma separated list of ordered pairs If an answer does not exist enter DNE relative minima relative maxima e Find all vertical asymptotes if any of the graph of y f x Enter your answers as a comma separated list If an answer does not exist enter DNE

Each problem below refers to triangle ABC In each case find the area of the tri angle Round to three significant digits 1 a 50 centimeters b 70 centimeters C 60 2 a 10 centimeters b 12 centimeters C 120 3 a 41 meters c 34 meters B 151 5 4 a 76 3 meters c 42 8 meters B 16 3 5 b 0 923 kilometers c 0 387 kilometers A 43 20 6 b 63 4 kilometers c 75 2 kilometers A 124 40 7 A 46 B 95 c 6 8 meters 8 B 57 C 31 a 7 3 meters 9 A42 5 B 71 4 a 210 inches 10 A 110 4 C 21 8 c 240 inches 11 A 43 30 C 120 30 a 3 48 feet 12 B 14 20 C 75 40 b 2 72 feet 13 a 4 inches b 6 inches c 8 inches 14 a 5 inches b 10 inches c 12 inches 15 a 4 8 yards b 6 3 yards c 7 5 yards 16 a 48 yards b 75 yards c 63 yards c 17 a 4 38 feet b 3 79 feet c 5 22 feet

Each problem below refers to triangle ABC In each case find the area of the tri angle Round to three significant digits 1 a 50 centimeters b 70 centimeters C 60 2 a 10 centimeters b 12 centimeters C 120 3 a 41 meters c 34 meters B 151 5 4 a 76 3 meters c 42 8 meters B 16 3 5 b 0 923 kilometers c 0 387 kilometers A 43 20

Sketch the graph of the function Include two full periods Use a graphing utility to verify your result y 2 sec 2x 1 I 4 U 4 3 4 2 y

Verify that the function satisfies the three hypotheses of Rolle s Theorem on the given interval Then find all numbers that satisfy the conclusion of Belle s Theorem Enter your answers as a comma separated 1 12 22 12x 1 0 4

Determine the remaining sides and angles of the triangle ABC a 100 m A 39 42 C 25 46 What is the measure of angle B B

Describe the relationship between the graphs of f and g Consider amplitude period and shifts 4 y 3 2 3 2x J 8 0 g 1 1 k X 2 3 B O The graph of g is a horizontal shift 3 units to the right of the graph of f O The graph of g is a reflection of f in the x axis O The amplitude of g is twice that of the amplitude of f O The graph of g is a vertical shift 3 units upward from the graph of f The period of a is 3 times that of f

Find the indicated roots Sketch the roots in the complex plane The fifth roots of 32 b The cube roots of i c The cube roots of 1

Sketch the graph of the y 2 cos x 1 2 37 k k K12 2 k12 3 3 2x 2 3 KIN KIN KIN 2 k KIN 13 X 2 k2 KIN k

Which has a trigonal pyramid structure O SO32 O CO2 OSO3 ONO3 OCH4

Determine the percentage composition by mass of lead in PbCl2 O 74 5 85 4 42 7 57 3 12 7 1 pts Question 4

Which has a tetrahedral structure O SO32 O CO32 OSO3 O NH3 OCH4

Which has a bent structure O H O NH3 O CaCl2 O CO2

EXAMPLE 5 Suppose that f 0 3 and f x 9 for all values of x How large can f 5 possibly be SOLUTION We are given that fis differentiable and therefore continuous everywhere In particular we can apply the Mean Value Theorem on the interval 0 5 There exists a number c such that f 5 f 0 f c 0 SO f 5 f 0 f c 3 f c We are given that f x s 9 for all x so in particular we know that f c s have 5f c s SO 7 f 5 3 f c 3 The largest possible value for f 5 is 29 Multiplying both sides of this inequality by 5 we

Which of the following elements are arranged in an increasing order for both atomic radius and ionization energy OS OF and F O S OFSO and O S F OS F O and S F O OFOS and S O F Onone of these

For the reaction C H4 g 302 g 2CO2 g 2H2O g if 5 0 mol of CO2 are produced how many moles of O2 were reacted 3 3 mol O 6 2 mol 7 5 mol O 12 5 mol O none of these

The molar mass of barium cyanide Ba CN 2 is O 189 4 g mol 300 7 g mol 326 7 g mol 177 4 g mol 163 4 g mol

A supervisor records the repair cost for 17 randomly selected TVs A sample mean of 94 57 and standard deviation of 20 65 are subsequently computed Determine the 80 confidence interval for the mean repair cost for the TVs Assume the population is approximately normal Step 1 of 2 Find the critical value that should be used in constructing the confidence interval Round your answer to three decimal places

Consider the series The interval of convergence goes from x to x The radius of converge is R 8 If needed enter INF for co and INF for 0 n 1 n x 8 8T n 1

Solve the linear programming problem Maximize P 10x 70y Subject to x 6y 18 x y 0 What is the maximum value of P Select the correct choice below and if necessary fill in the answer box to complete you OA P Simplify your answer Type an integer or a fraction

Let A x represent the area bounded by the graph the horizontal axis and the vertical lines at t 0 and x for the graph below Evaluate A x for x 1 2 3 and 4 5 3 M 2 1 A 1 A 2 1 A 3 A 4 2 3 50

13 a 410 meters c 340 meters B 151 5

Each problem below refers to a triangle ABC Any answers that involve angles should be rounded to the nearest tenth of a degree 1 If a 100 inches b 60 inches and C 60 find c 2 If a 100 inches b 60 inches and C 120 find c 3 If a 5 yards b 6 yards and c 8 yards find the largest angle 4 If a 10 yards b 14 yards and c 8 yards find the largest angle 5 If b 4 2 meters c 6 8 meters and A 116 find a

11 a 4 inches b 6 inches c 8 inches Remember Solve for the largest angle first and round to the nearest tenth of a degree

Problem 1 10 points At a certain moment the dimensions of a cylinder are changing as follows The radius is decreasing at a rate of 1 cm s The height is increasing at a rate ofcm s 5 The volume is decreasing at a rate of 87 cm s The surface area is decreasing at a rate of 44 3 cm s Find all the possible values of the radius and the height at this moment

Find all solutions to each of the following triangles 7 A 38 a 41 feet b 54 feet 8 A 43 a 31 feet b 37 feet 9 A 112 2 a 43 centimeters b 22 centimeters 10 B 30 b 42 centimeters a 84 centimeters 11 B 118 b 68 centimeters a 92 centimeters 12 A 124 3 a 27 centimeters b 50 centimeters 13 A 142 b 2 9 yards a 1 4 yards 14 A 65 b 7 6 yards a 7 1 yards 15 C 26 8 c 36 8 kilometers b 36 8 kilometers

Problem 2 10 points Let f x x1 5 3x 22x 99 a Find the critical points of f x on 1 2

Approximate the area under the curve graphed below from x approximation with 4 subdivisions 3 to x 7 using a Left En You will need to approximate the function values using the graph 5 4 3 2 1 1 2 3 A 4 5 6 7 Poot 8

25 Angle of Elevation Figure 11 is a diagram that shows how Colleen estimates the height of a tree that is on the other side of a stream She stands at point A facing the tree and finds the angle of elevation from A to the top of the tree to be 51 Then she turns 105 and walks 25 feet to point B where she measures the angle between her path and a line to the base of the tree and finds that angle to be 44 Use this information to find the height of the tree D h A FIGURE 11 B

21 Angle of Depression A man is flying in a hot air balloon in a straight line at a constant rate of 5 feet per second while keeping it at a constant altitude As he approaches the parking lot of a market he notices the angle of depression from his balloon to a friend s car in the parking lot is 35 A minute and a half later after flying directly over his friend s car he looks back to see his friend getting into the car and observes the angle of depression to be 36 At that time what is the distance between him and his friend Give your answer to the nearest foot

Each problem that follows refers to a triangle ABC 1 If A 40 B 60 and a 12 centimeters find b

What are the two hormones combined in oral contraceptives or the pill A Dopamine and serotonin B Prolactin and oxytocin C Estrogen and progestin D Estrogen and testosterone

XYZ Corporation invests 6 000 into 91 day treasury bills with an interest rate of 1 6 If the broker charges a 30 commission what is the yield yield

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line about x 3 Volume y 1 x5 y 0 x 3 x 4

men is a permanent sterilization surgery meant fo A Vasectomy B Hysterectomy C Pelvic organ prolapse C None of th

Using condoms can cause erectile dysfunction A True B False

Which enzyme makes 5 3 phosphodiester bonds a Helicase b Endonuclease c Topoisomerase d Exonuclase

Introducing this increasingly widespread metaphorical style to the public was a curatorial challenge for museums When organizing The Family of Man an exhibi tion that celebrated universal humanism at the Museum of Modern Art Edward Steichen thought Wynn Bullock s 1902 1975 image Child in Forest symbolized the mythical first woman and he chose it as the show s opening piece Steichen selected Bullock because he believed the photographer s visual language joined the natural environment with the abstract symbolism of the inner world in an ac cessible manner Although the composition of Bullock s work is highly structured the authority of his images lies in their ambiguous temperament that expresses his belief that reality is constructed through personal experience 29 The Family of Man exhibition and book was the major American photographic event of the 1950s Organized by Steichen the director of the Department of Photography at MOMA 1947 1962 as a mirror of the essential oneness of mankind 30 it had a highly enthusiastic public reception in 1955 31 Working on the proposition that photography was a universal language Steichen assembled 508 images from 68 countries by 273 photographers into a giant three dimen sional magazine layout To match its democratic premise that people were all the same Steichen did not treat the photographs as individual works but as pieces of a larger tapestry just as in magazine practice where photographers give up con trol over image quality size placement and context This set aside the achieve ments of individual photographers to support Steichen s collective curatorial stance Jacob Deschin the photography critic for The New York Times called it es editorial achievement Ifor Ste Discussion Board Posts 25 total As a measure of your participation you will write 200 word minin responses to the readings as well as responding to at least one oth post In these posts I want to see concrete examples where you critically reflect on the readings This can include citing specific photographs and photographers theoretical connections between different readings ideas themes and or the author s own argumen

Listen The best classification system is that which most closely a corroborates the classification scheme in use at the time of Charles Darwin b conforms to traditional Linnaean taxonomic practices c reflects evolutionary history d reflects the basic separation of prokaryotes from eukaryotes e unites organisms that possess similar morphologies

What are the health benefits associated with oral contraception A Reduction of severe menstrual cramps B Clearing up acne and improving bone density C Prevention of certain cancers D All of the above

Fill in the blank A colon indicates amino acid positions that have amino acids with A molecular properties

Listen Their primary function of DNA topoisomerase is to cleave DNA strands in order to provide torsional stress relief or to untangle replicating DNA a True b False

Which enzyme makes single strand breaks in DNA backbones a Exonuclease b Topoisomerase c Helicase d Ligase

Topoisomerase does which one of the following a Joins the ends of double stranded DNA molecules b Is required for making recombinant DNA molecules in vitro c Unties knots in DNA molecules d Makes new DNA strands

Which of the following are methods for contraception A Intrauterine device IUD B Sterilization C Diaphragm D All of the above

A phylogenetic tree that is rooted is one a with very few branch points b that illustrates the rampant gene swapping that occurred early in life s history c that extends back to the origin of life on Earth d that indicates our uncertainty about the evolutionary relationships of the taxa depicted on the tree e at whose base is located the common ancestor of all taxa depicted on that tree

What is the role of topoisomerases in eukaryotic DNA replication a Topoisomerise enzymes cut uncoil and reseal the double stranded DNA b Topoisomerise enzymes bind to the origin of replication sites within double stranded DNA c Topoisomerise enzymes join the Okazaki fragments together with phosphodietster bonds d Topoisomerise enzymes open up the double stranded DNA at the replication fork

Fill in the blank A period indicates amino acid positions that have amino acids with properties A molecular

Find the volume of the solid formed by rotating the region enclosed by about the y axis y e 5 y 0 x 0 x 0 8

Find the volume of the solid obtained by rotating the region bounded by y x y 0 and x 1 about the axis 2