Questions

4 Oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a constant rate of 2000 cubic centimeters per minute The oil slick takes the form of a right circular cylinder with both its radius and height changing with time Note the volume V of a right circular cylinder with radius r and height his given by V r h b A recovery device arrives on the scene and begins removing oil The rate at which oil is removed is R t 400 t cubic centimeters per minute where t is the time in minutes since the device began working Oil continues to leak at the rate of 2000 cubic centimeters per minute Find the time when the oil slick reaches its volume Just

3 4 pts Find the directions in which the function increases and decreases most rapidly AND the derivatives of the function in those directions g x y a xe z P 1 42

Find the area of the composite figure 1 111 6 yd 8 yd 12 yd 2 13 mm T 15 mm 17 mm 8 mm 3 9 cm 2 8 cm 5 2 cm 4 8 cm

1 3 pts Find all second order partial derivatives 2 Xe x 5

1 Do not use a calculator for this one 5 2 Graph of f 4 4 slope 2 The function fis defined on the closed interval 5 4 The graph of consists of three line segments and is shown in the figure above Let g be the function defined by g x a b f t dt Find g 3 On what open intervals contained in 5 x 4 is the graph of g both increasing and concave down g x The function is defined by h x 9 Find h 3

3 pts Find Vf at P f x y z e cos z y 1 sin x P 0 0

2 A particle moves along the y axis so that its velocity at time t 0 is given by v t 1 tan et At time t 0 the particle is at y 1 Note tan 1 y arctanx a Find the acceleration of the nesti 1

g f r dr where f x da where f x is given by f x 3 2 12 if x 0 if x 0

You have arrived at Steinert its to see the music concert held every spring and unfortunatay Only seats were available in the last row There are 23 rows The stage which seats all per fofing s Is Positioned such that it is in line with the 5th row of seats in each section The stage is 20 feet from the first row seats The dexth of the seats are 17 inches and the height is 32 inches what is the approximate and OF depression from the last row to the stage as you listen to music

Twenty sections of bilingual math courses taught in both English and Spanish are to be offered in introductory algebra intermediate algebra and liberal arts math The preregistration figures for the number of students planning to enroll in these bilingual sections are given in the following table Use Webster s method with d 29 6 to determine how many bilingual sections of each course should be offered Course Enrollment Introductory Algebra 120 Intermediate Algebra 282 Liberal Arts Math 186 Course Number of Apportioned Sections Introductory Algebra

A large hotel chain needs to apportion 28 new staff members among three hotels based on the numbers of rooms in each hotel as shown below Use the table to answer parts a and b Hotel A B C Total Number of rooms 308 218 286 812 a What is the standard divisor 29 Type an integer or a decimal rounded to the nearest hundredth as needed b Find each hotel s standard quota The standard quota for hotel A is 10 62 Type an integer or a decimal rounded to the nearest hundredth as needed The standard quota for hotel B is

A resort management company plans to apportion 58 new beach umbrellas among four resorts based on the number of rooms in each resort as shown in the table Determine each resort s apportionment using Jefferson s method Hint Some divisors between 10 and 11 will work Resort A B C D Total Number of Rooms 93 105 137 265 600 Resort A Number of Umbrellas 9 Type an integer Resort B Number of Umbrellas

3 x y z 3 x 3y 4z 12 x 3y 5z 3 A 3 0 5 C 1 0 0 B 5 3 4 D 1 3 1 4 4 5x 4y 2z 14 5x y 2z 5 2x y 2z 5 A 1 3 5 B 5 3 1 C 3 1 5 D 0 3 1

Mr Young built a greenhouse 42 feet wide 110 feet long 5 feet to the eaves and 14 feet to the ridge cap How many square feet of plastic does it take to enclose the greenhouse

What is the sum of the series 6 5k 20 k 3 Enter your answer in the box

Which answer represents the series in sigma notation 1 1 1024 4096 0 0 1 0

Find the indicated side length Round your answer to the nearest tenth 1 Find HK H 103 9 in 51 K HK P

Find the indicated side length Round your answer to the nearest tenth 1 Find BC A 9 in 107 B BC 7 in C

What equation is solved by the graphed systems of equations LT 2 3 1 4 4 7x 3 x 3 7x 3 x 3 7x 3 x 3 7x 3 x 3

At the end of April Mandy told Bill that she has read 16 books this year and reads 2 books each month Bill wants to catch up to Mandy He tracks his book reading with a table on his door Using his table below what month will Bill have read the same amount of books as Mandy Month Books May 4 June 8 July 12 September October August December

Label the Meninges

Solve the system y 3x 2 and 3y 9x 6 by using graph paper or graphing technology What is the solution to the system No solutions Infinite solutions 3 2

8 Nancy is in her apartment on the sixth floor of a building She spots two cars that are parked 10 ft apart If she measures the angle of depression to the closest car to be 50 and then the further car to be is 38 How far is the first car parked from the base of her apartment building to the nearest foot

7 Ana and Baker are on opposite sides of a tall tree Anna is closer and measures the angle of elevation to the top of the tree to be 74 and Baker measures an angle of elevation of 43 If Ana and Baker are 50 meters apart how tall is the tree to the nearest meter

4x 8 28

In general there are two basic costs for cell phone plans the cost of the phone and the monthly cost for talk text and data usage Alexi buys a phone for 620 and then signs up for a phone plan that costs 45 per month with all taxes included Part A Let C represent the total cost that Alexi will pay if he uses this phone for m months How much has Alexi paid after 1 month How much has he paid after 8 months How much has he paid after 11 months Write each answer as an ordered pair of the form m C Hint 1 month 8 months 11 months Part B Identify the slope and vertical intercept for this situation Do not include units in your answers Hint Slope Vertical Intercept per month Part C Use the slope and vertical intercept to write a linear function that gives the total cost Alexi pays in terms of the number of months Hint Answer Part D Interpret the slope as a rate of change by filling in information into this for each additional month that he is using his phone Alexi pays an

What happens if you try to use l Hospital s Rule to find the limit X lim Repeated applications of l Hopital s Rule result in the original limit or the limit of the reciprocal of the function You cannot apply l Hopital s Rule because the function is not continuous You cannot apply l Hopital s Rule because the denominator equals zero for some value x a You cannot apply l Hopital s Rule because the numerator equals zero for some value x a You cannot apply l Hopital s Rule because the function is not differentiable Evaluate the limit using another method

18 What happened to Wade the day after he completed the first task that changed his life for the better

Label the Meninges

If f is continuous f 2 0 and f 2 9 evaluate lim 2 4x 2 6x x 0 x

each of the statements as DD for density dependent or DI as density independent 2pts each ch of the statements below involves a situation that will affect the growth of a population Classify C d e f g a b Rainbow smelt and yellow perch attempt to occupy the same area The more aggressive smelt survive the perch do not A severe flood brings a lot of sediment and dirt into the lake The turbidity of the lake increases greatly A drought decreases the water level in the lake The carrying capacity of the lake decreases Due to the introduction of rainbow smelt an invasive species the lake becomes too crowded and some species of fish do not survive Many fish die due to an increase in water temperature Parasites present in the lake are killing off fish in great numbers Since yellow perch migrate long distances to spawn many do not survive the trip

a Investigate the existence of equilibrium point s for the following nonlinear difference equation xn 1 rxn 1 xn and state the condition under which an equilibrium is stable if it exists b Consider the following nonlinear difference equation for population growth kxn b k 0 xn 1 b xn i ii iii Does the population reach a steady state If your answer in i is yes is the steady state stable Discuss when a conclusion from your investigation is biologically meaningless c Discuss the equilibrium and stability of the balls in the following diagram

3 B A C D FL

Determine whether each pair of tr 13 T W

d Name the postulate if possible that makes the triangles congruent A N B SAS AAS ASA Not Possible M C

Cevation 3x 1 2y y e x 1 dx

A A camper wants to protect her bag of food from bears She decides to tightly stretch a rope between two trees and hang her bag from a point exactly halfway along the length of the rope The first tree is 10 feet east and 6 feet north of her firepit The second tree is 5 feet west and 8 feet north of her firepit The rope is attached at a height of 8 feet to the first tree and a height of 9 feet to the second tree Let the firepit represent the origin movement east of the firepit represent movement in the direction of positive x movement west of the firepit represent movement in the direction of negative x movement north of the firepit represent movement in the direction of positive y and movement above the firepit represent movement in the direction of positive z 1 Write the coordinates of the points on the trees where the rope is attached 2 Find the distance between the points in part a Use sqrt to indicate a square root For example 3 would be written sqrt 3 3 Find the coordinates of the point where the food bag is hung 4 If the food bag is 1 2 feet long when hung and bears can reach a height of 7 5 feet when standing is the camper s food safe from bears Explain why or why not U pointol

sted in the accompanying table are heights in of mothers and their first ughters The data pairs are from a journal kept by Francis Galton Use the listed ired sample data and assume that the samples are simple random samples and at the differences have a distribution that is approximately normal Use a 0 05 gnificance level to test the claim that there is no difference in heights between others and their first daughters Mother 68 0 60 0 63 0 67 0 66 0 66 0 64 0 Daughter 70 5 61 7 63 0 66 0 65 0 63 0 68 0 65 0 65 0 68 0 this example a is the mean value of the differences d for the population of all pairs of data where each individual difference d is defined as the daughter s height I d minus the mother s height What are the null and alternative hypotheses for the hypothesis test Ho Hd in Type integers or decimals Do not round

the number of a certain type of bacteria y present in a culture is determined by the equation y 3000 2 where x is the number of days the culture has been growing Find the number of baclela fter 5 days After 5 days bacteria will be present

The formula y ghi gives the velocity v in feet per second of an object after it tails hi feet accelerated by gravity 9 in foot per second squared if g is approximately 32 teet per second squad Sed in object has fallen if its velocity is 120 feet per second

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y 0 y cos 3x x 0 about the axis y 7

What can be inferred from the following statement from the essay Society and Solitude by Ralph Waldo Emerson The solitary river was not solitary enough

1 x 3 x 5

2 2c 10c 11

2

7 25c 8146

8 163

9 54 5

5 x sy x

6 w y y3 3 4