Differential equations Questions and Answers

zilldiffeqmodap11 7 4 009 EP consider the following initial value problem y y tsin t y 0 0

Solve the equation for a where x is in radians State the exact solutions if any that lie in the interval 0 2 If the equation has no solutions respond with DNE 4 4 sec x sec x sec x 3 3 Separate multiple solutions with a comma

Given f x 5x 6 and f 2 1 and f 2 3 Find f x 5x2 and find f 1 2 6x 21 297 6

Find three real numbers x y and z whose sum is 12 and the sum of whose squares is as small as possible Identify the function of f and the constraint of g The function of fis x y 2 2 The constraint of g is x y z 12 The three numbers are Simplify your answers Use a comma to separate answers as needed

Determine the polar trigonometric form of each of the following complex numbers Write angle measures in radians a 2 2i 2 2 cos i isin b 2 2i 2 2 1 X 2 2 cos i sin c 2 21 2V 2 cos sin 2 4 X

13 find the particular solution for the equation 9 8 given y 4u given y 4 when x 0 The solution to the d efferal equation is y dy 3x y dx

Find the domain and intercepts f x x 9 Find the x intercept s Select the correct choice below and if necessary fill in the answer box to complete your choice OA The x intercept s of the graph is are x Simplify your answer Type an integer or a decimal Use a comma to separate answers as needed OB There is no x intercept Find the y intercept s Select the correct choice below and if necessary fill in the answer box to complete your choice OA The y intercept s of the graph is are y Simplify your answer Type an integer or a decimal Use a comma to separate answers as needed B There is no y intercept

raw the phase portrait of the Autonomous equatio y t y 4 y e 2y 1

Using the expanded accounting equation calculate and enter the answers for each question You will need to use the answers you calculate for beginning and ending equity to answer the rest of the questions Beginning of Year End of Year Beginning Equity Assets Net Income Loss 25 000 60 000 Dividends Liabilities 1 What is the equity at the beginning of the year 18 000 29 000 3 If the company issues common stock of 9 500 and pay dividends of 40 200 how much is net income loss 5 If the company issues common stock of 16 300 and net income is 17 500 how much is dividends 2 What is the equity at the end of the year Ending Equity 4 If net income is 1 100 and dividends are 9 700 how much is common stock Common Stock 6 If the company issues common stock of 42 000 and pay dividends of 2 000 how much is net income loss Net Income Loss

A bakery sells 3 lemon poppy muffins for every 4 bran muffins sold Which table represents the relationship between lemon poppy and bran muffins A Lemon Poppy Bran 12 16 C 9 12 18 Lemon Poppy Bran 9 18 21 12 20 24 24 B D Lemon Poppy Bran 3 4 8 16 Lemon Poppy 3 6 12 6 12 Bran 4 7 13

2 Determine the equation of the following graph All parts of your function should provide justification of how you arrived at each term N 10 11 10 9 8 7 6 5 4 3 Note y 2 is a horizontal asymptote Note x 1 and x 1 are vertical asymptotes Note there is a zero at x 0 5 and at x 2 2 3 4 5 8 9 10 11 12 13 14 15 16 1

Indicate whether the following table specifies a function Domain 399 Range 435 Choose the correct answer below OA The table specifies a function D The table dans no specifica

Solving A Pet for P we obtain P Aet which is the present value of the amount A due in t years if money earns interest at an annual nominal rate r compounded continuously A Graph P 19 000e 0 071 0 t 70 B Find limt 19 000e 0 07t Guess using part A Conclusion The longer the time until the amount A is due the smaller is its present value as we would expect A Choose the correct graph of P 19 000e O A AP 19000 70 Q B limt 19 000e 0 07t 0 07t OB AP 19000 0st 70 70 27 TORI O C AP 19000 0 Q D 19000

Use the price demand equation x f p 144 2p to find the values of p for which demand is elastic and the values for which demand is inelastic Assume that price and demand are both positive Demand is inelastic for all values of p in the interval Type your answer in interval notation Type integers or decimals Demand is elastic for all values of p in the interval Type your answer in interval notation Type integers or decimals www

Determine the domain of the function of two variables f x y y 4x The domain is x y Type an inequality Use a comma to separate answers as needed Use integers or fractions for any numbers in th

The series 12n 5 3n 5 is neither convergent nor divergent 2 conditionally convergent 3 absolutely convergent 4 NOTA

Solve for x Show work 1 2 XIO 1 x 10 3 4x 1 21

Assume T 0 If cot 0 5 what are cos 0 sin 0 tan 0 sec 0 and csc 0 Give your answers in fraction forms with exact values ie leave the square root in the solution if there is square root

Sketch the graphs of the functions f and g f x x 3 g x x 9 y 10 5 10 5 5 10 5 square units 10 X io 10 5 10 y 5 5 zx6 Find the area of the region enclosed by these graphs and the vertical lines x 2 and x 1 5 10 X GO 10 5 10 y 5 5 10 5

Use the chain rule to find z s z at z s and z t z e cos 0 r st 0 s8 t

Match each linear equation with its graph G P I Equation Y Y www c 4 71 1 4 1 2 T x 1 3 3 K B R Q Graph Color a purple P b green G c black K d red R e blue B

Find three real numbers x y and z whose sum is 21 and the sum of whose squares is as small as possible Identify the function of f and the constraint of g The function of fis The constraint of g is

Calculate the definite integral 4 4 f2e 9 0 gx dx

Question Select the image below that represents 1 a 300 angle in standard form and 2 its reference angle 30 60 30 Ref Ref Ref Ref

Find the general solution for the differential equation 36x dy dx

dy dx Find the general solution for the differential equation 3y Choose the correct answer below OA O C y OD OB 9x3 ya 8x y 9 C 8 C 8x3 8 C C

Evaluate the definite integral 2 2 0 e t 6 et 2 e t 6 et 2 dt dt

Find f x f x 8x 6e f x Type an exact answer in terms of

Check Point 6 Among all pairs of numbers whose difference is 8 find a pair whose product is as small as possible What is the minimum product

dy Find the particular solution for the equations dx 3x 1 Y 6 given y 8 when x 0 The solution to the differential equation is y Type an expression using x and y as the variables Use integers or fractions for any numbers in the expression

nd the general solution for the differential equation 22x e dx

y y ax y 0 0 where a R show that the above Problem Satisfies the conditions of Picard s theorem and calculate the first Pour terms of Picard s iterations

Find the general solution for the differential equation dy 40x dx ey

Find the general or particular solution as indicated for the following differential equation dy dx 0 4y y 0 90

nd the particular solution for the equation dy 9x 1 dx y 5 given y 2 when x 0 e solution to the differential equation is y pe an expression using x and y as the variables Use integers or fractions for any numbers in f

Find the particular solution for the differential equation dy 6x2 dx 7y at y 2 and x 0 The particular solution to the differential equation is y Type an expression using x as the variable Use integers or fractions for any numbers in the expression

Find the general solution for the differential equation X dy 24y dx 11

Find the general solution for the differential equation dy 1 dx 24y 4 The general solution is Type an equation Do not explicitly include arguments of functions in your answ

Find the general solution for the differential equation Verify that the solution satisfies the original differential equatio dy dx 4x 6x

IN dw as a function of t both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t Then b evaluate dt For the given functions a express w 8ye Inz x In 1 y tan t z e 1 1 dw dt at the given value of t

13 The rate of growth dP dt of a population of bacteria is proportional to k times the square root of t where P is the population growth and t is the time in days the days are between 0 and 10 inclusive The initial size of the population is 700 After 1 day the population has grown to 1000 What is the population after 5 days Round the answer to the nearest integer In the above k is the constant of proportionality That is dP dt is directly proportional to the square root of t that is dP dt k times the square root of t

1 The reproduction function for the North American duck is estimated to be f p 0 02p 7p where p and f p are measured in thousands Find the size of the population that allows the maximum sustainable yield and also find the size of the yield

local minima x shown to the right find the absolute maximum and the absolute minimum if they exist Identify any local maxima or Select the correct answer below and if necessary fill in the answer boxes to complete your choice O A The absolute maximum of y f x is f Type integers or simplified fractions OB There is no absolute maximum for y f x Select the correct answer below and if necessary fill in the answer boxes to complete your choice OA The absolute minimum of y f x is f Type integers or simplified fractions B There is no absolute minimum for y f x to complete your choice 1 2 3 2 6 4 4 0 0 S

Calculate the exact value of sin 165 using the half angle formula Rationalize the denominator if necessary sin 165 2 Enter your answer in simplest form Ente

2 Review basic computational skills 3 Simplifying polynomials 4 Adding subtracting and multiplying polynomials 1 Simplify fractions Simplifying fractions To simplify a fraction one cancels the greatest 18 pr P common factor 9 24 1 Write each fraction in lowest terms 28 49 a b Example 18 6 24 6 75 125 2 Perform the indicated operations and simplify the result a 4 b 2 3 3

Given the initial condition y 0 1 find the particular solution of the equation y e3x 2y A

Assume that the amount of time T a job takes is inversely proportional to the number of people P doing the job Does it make sense to use differential equations to model how long a job takes If so write the differential equation If not explain why A

Find the general solution to y x2 1 y 0 for y 0

Bob heats up a bottle of milk for his baby Jill every morning Jill will only drink the bottle if it is at 98 degrees So Bob places the bottle in a cup of hot water 170 degrees The bottle starts off at 35 degrees After 2 minutes the bottle is 80 degrees Use Newton s heating cooling law that the rate of change in the temperature H is proportional to the difference between the object and the surrounding temperature to determine how long Bob should leave the bottle in the hot water Assume that the water stays at 170 degrees

If the rate of change in the number of horses H in a population is proportional to 300 H t where t is measured in years Write the differential equation to solve for H t Do not solve