Questions

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

y varies jointly as x and z and inversely as the square of w and y 12 5 when x 16 z 3 and w 5

A sheriff in the Hudson River Valley near Albany New York about to go into the hills in the fall of 1839 to collect back rents from tenants on the enormous Rensselaer estate was handed a letter the tenants have organized themselves into a body and resolved not to pay any more rent until they can be redressed of their grievances The tenants now assume the right of doing to their landlord as he has for a long time done with them viz as they please You need not think this to be children s play if you come out in your official capacity I would not pledge for your safe return A Tenant When a deputy arrived in the farming area with writs demanding the rent farmers suddenly appeared assembled by the blowing of tin horns They seized his writs and burned them That December a sheriff and a mounted posse of five hundred rode into the farm country but found themselves in the midst of shrieking tin horns eighteen hundred farmers blocking their path six hundred more blocking their rear all mounted armed with pitchforks and clubs The sheriff and his posse turned back the rear guard parting to let them through This was the start of the Anti Renter movement in the Hudson Valley described by Henry Christman in Tin Horns and Calico It was a protest against the patroonship system which went back to the 1600s when the Dutch ruled New York system where as Christman describes it a few families intricately intermarried controlled the destinies of three hundred thousand people and ruled in almost kingly splendor near two million acres of land The tenants paid taxes and rents The largest manor was owned by the Rensselaer family which ruled over about eighty thousand tenants and had accumulated a fortune of 41 million The landowner as one sympathizer of the tenants put it could swill his wine loll on his cushions fill his life with society food and culture and ride his barouche and five saddle horses along the beautiful river valley and up to the backdrop of the mountain By the summer of 1839 the tenants were holding their first mass meeting

is incorrect e function y 6 x 15 2x algebraically wers in increasing order If there is only one zero

Use the graph to state the absolute and focal maximum and minimum values of the function Assume each point lies on the gridlines Enter your answers as a comma separated list If an answer does not exist enter Da 0 1 absolute maximum value absolute minimum value local maximum value s local minimum value s y fix

Explain the difference between an absolute minimum and a local minimum There is no difference OA function has an absolute minimum at x ciftc is the smallest function value when x is near c whereas f has a local minimum at c if c is the smallest function value on the entire domain of f OA function f has an absolute minimum at x cific is the smallest function value on the entire domain of f whereas has a local minimum at c if c is the smallest function value when x is near c OA function f has an absolute minimum at x cif c is the largest function value on the entire domain of f whereas has a local minimum at c if c is the largest function value when is near c OA function has an absolute minimum atx cific is the largest function value when x is near c whereas has a local minimum at c if c is the largest function value on the entire domain of

When comparing the value 13 to 13 which statement is TRUE O 13 13 O 13 13 O 13 13 O 13 13

andard 6 1 Which statement can be represented by 20 dollars O Joe deposited 20 into his savings account O Janet earned 20 mowing her neighbor s yard O Kyle withdrew 20 from his checking account O Sally found 20 on the sidewalk

H 2 and 2 Let T R2 R2 be the linear transformation satisfying T 51 18 and T 52 13 Find the image of an arbitrary vector x T

1 to 2 2 to 5 3 to 1 1 to 1 5 to 1 5 1 52 8 11 5 4 3 2 1 1 2 5 2 2 figure The points of each preimage are represented by circles and the points of each image are represented by squares

Find the critical numbers of the function Enter your answers as a comma separated list If an answer does not exist enter DNE F x x4 5 x 3 2 x

Graph y x vertically stretched by a factor of 4 reflected across the x axis and shifted left 4 When graphing first select the correct shape from the options below the grid

4x Suppose that 8 x Cnx n 0 Find the first few coefficients Co 4 1 C C2 C3 87 88 87 3 C4 87 Find the radius of convergence R of the power series D C

Find the critical numbers of the function Enter your answers as a comma separated list If an answer does not exist enter DNE f x 2x 3x 12x

Find the absolute minimum and absolute maximum values of f on the given interval f t t 9 2 1 3 absolute minimum absolute maximum

Changes in the timbre or tone color in a piece of music

The right rectangular prism is packed with unit cubes of the appropriate unit fraction edge lengths Find the volume of the right rectangular prism in centimeters Figure not to scale 4 3 85 cm 67 cm 45 cm O 12cm S

Rewrite the logarithm as a ratio of common logarithms and natural logarithms log 98 a common logarithms b natural logarithms

A car is driving away from El Paso with constant velocity At 1 p m it is 145 miles away from El Paso At 3 p m it is 275 miles away from El Paso Part A Write a linear function d t that describes the distance d in miles the car is from El Paso in terms of time t in hours after 12 00 p m Answer Part B How long after 12 00 p m in hours will the car be 300 miles away from El Paso Round answer to the nearest hundredth Answer Part C Describe the process for determining how long the car has been driving from El Paso

A company is considering three different plans for car rentals from Ajax Rentals Bargain Rentals and Cheap Rentals Ajax Rentals has the lowest fixed cost and the highest cost per mile while Bargain Rentals has the highest fixed cost and the lowest cost per mile Part A The company has obtained a graph displaying the cost functions for each rental company but the graph is not labeled Determine which lines are associated with which companies 400 150 100 Miles 200 Miles Cheap a solid b dashed Bargain c dotted Ajax Part B Match each company with the interval where it has the lowest price compared to the other two companies Bargain a 125 175 Ajax b 175 200 C 100 125

8 Determine the scale factor of the geometric figure The points of each preimage are represented by circles and the points of each image are represented by squares 1 to 1 Sto 2 2 5 to 0 2 to 1 1 25 201

The velocity of a falling object is 12 4 m s at 2 seconds after being dropped and 22 2 m s at 3 seconds after being dropped Part A Graph the velocity of the falling object as a function of time in seconds Use t 0 to represent when the object was dropped 30 velocity m s 20 10 10 2 time seconds 3 Clear All Draw Part B Estimate when the object was falling with a velocity of 18 m s seconds

Next Find the area of the region enclosed by y 1 25z and z 5 y 2 1 2 3 2 a 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 1 25z meets z 5 y 4 2129 lower limit c 10 upper limit d 4 2129 10 B and To find the area of the enclosed region from to d we will integrate where g y d g y dy

A window has the shape of a parabola above and a circular arc below Find the area of the window 10 7 10 ft 6 34 Use the dotted line as your y axis and the solid gray line as the x axis Find the distance from the z axis to the top of the circle Write the equation of the circle Write the equation of the parabola feet

Assume that you have agreed to use a cellular plan that charges a price of p 4q 500 dollars for using q GB of data Determine a formula for a that describes the amount of data you can use in terms of the amount of money that you are willing to spend Answer

Given the following voltage and current i t 5 sin 377t 57 A u t 10 cos 377t 41 V Determine the phase relationship between i t and u t Notes on entering solution Enter your solution with respect to V leads i by Enter your solution in degree Do not include units in your answer ex 5 is entered as 5

The shaded region between the graphs of y 2x 20 and y 3x 15 is displayed 25 F 6 141 below in orange The shaded region lies between 2 5 40 and 3 5 A typical rectangle is shown in the diagram located at position x What is the height of this rectangle in terms of Now find the total area of the orange shaded region

Find the area of the region enclosed by y 1 25x and x 5 72 2 1 2 3 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 1 25z meets 2 5 y lower limit c upper limit d and To find the area of the enclosed region from to d we will integrate C where g y d g y dy

Consider the function In 1 72 00 Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms For example if the series were 3 you would write 1 322 32z 33 3z Also indicate the radius of convergence Partial Sum Radius of Convergence 7

1 Find c 0 such that the area of the region enclosed by the parabolas y x c and y c x is 90

4 A reporter from the Sacramento Bee claims that more than 14 of California workers say it is likely they will quit working this year In a simple random sample of 250 California workers 18 said it is likely they will quit working this year At the significance level of 5 is there enough statistical evidence to support the report s claim Simple Random Sample Requirements 1 2 3 P 14 P214 Step 1 State the hypothesis Ho P 14 P 14 Tall Ha n 250 Step 2 Draw your distribution and find critical number s Step 3 Compute the test statistics Step 4 Make a Decision Step 5 Summarize the result Restate the level of significance and discuss the claim

Find the first five non zero terms of power series representation centered at x 0 for the function below f x ln 6 x Answer f x In 3 1 2 18 What is the radius of convergence Answer R 3 81 4 x 324 1215

A factory selling cell phones has a marginal cost function C x 0 01x 3x 229 where represents the number of cell phones and a marginal revenue function given by R x 429 2x Find the area between the graphs of these curves and x 0 What does this area represent total profit for 200 cell phones sold total profit for more than 200 cell phones sold total revenue for 200 cell phones sold for 200 cell phones cold

There is a line through the origin that divides the region bounded by the parabola y 8x 3x and the x axis into two regions with equal area What is the slope of that line

Sketch the region enclosed by y 5x y 7x and x 1 Find the area of the e region

Set up the definite integral required to find the area of the region between the graph 15 and y 3x 13 of y x da

Find c 0 such that the area of the region enclosed by the parabolas y x 2 and y c x is 460

Determine which graph corresponds to the area enclosed by the curves y 4x and y x 3 6 8 65 5 4 3 2 1 23 5 4 3 2 1 1 2 3 4 2 Find the area of the region between y 4x and y x 3

Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Then find the area of the region 2y 3 y 3 and 2y 3x 6

4 A reporter from the Sacramento Bee claims that more than 14 of California workers say it is likely they will quit working this year In a simple random sample of 250 California workers 18 said it is likely they will quit working this year At the significance level of 5 is there enough statistical evidence to support the report s claim Requirements 1 2 Simple Random Sample Binomial 3 np 250 Step 1 State the hypothesis Ho Ha Tail Step 2 Draw your distribution and find critical number s Step 3 Compute the test statistics Step 4 Make a Decision Step 5 Summarize the result Restate the level of significance and discuss the claim

c Write down the minimum height of point P 1 Later the cat is tired and it takes twice as long for point P to complete one revolution at a new constant rate d Write down the new value of b

74 90 1 01 M n 0

A rectangular soccer field has dimensions 70 yards by 110 yards as shown in the figure A sprinkler placed at point P rotates 15 and sprays across the entire field as shown in the figure What percent of the soccer field is watered by thi one sprinkler Round to the nearest hundredth P 95 yd 15 110 yards 70 yards

8 Wayne wants to plant a triangular garden in his backyard and he will enclose the garden with 204 feet of fencing a Give two possible sets of side lengths for the garden one making an acute triangle and one making an obtuse triangle b Find the semiperimeter of each garden c Find the area of each garden d Wayne decides that he will have one side length of the garden be 50 feet If another side length is x write an expression for the 3rd side length e Write an equation in terms of x for the area of the garden f Use technology to find the lengths of the sides of the garden that give the maximum area and state the maximum area

If you reflected the point 3 4 across the x axis what would be the coordinates of the new point The new coordinates would be Select Select Select 3 4 3

Two planes leave the Atlanta airport at the same time and fly for three hours Flight 1504 flies 34 West of North at 245 miles per hour and Flight 168 flies 70 East of North at 271 miles per hour After 3 hours how far apart are the planes Round to the nearest hundredth 34 N 70

A statistics lab required students to draw cards numbered between 1 and 6 and track the results Drawing a number between 1 and 6 xx 1 2 3 4 5 6 Number drawn How many students drew a number greater than 4 students Submit

2 The figure shows ABRO B 18 9 R 13 a Find the semi perimeter of ABRO b Find the area of ABRO Round to the nearest tenth

While working as a summer camp counselor Jessica monitored how many candy necklaces each child made Making candy necklaces 12 x 01 3 x 234 56 Candy necklaces made How many children are there in all children