Differential equations Questions and Answers

Evaluate the integral 3 2x 7 dx 1 3 2x 7 dx 1

Use substitution to find the indefinite integral 4x 3 dx 4x 6x 5 cx S 4x 3 4x 6x 5 dx

Evaluate the following indefinite integral 1 11t 6t 1 11t4 6t dt dt 0 Type an exact answer

Solve the following partial differential equation 2 y cos 3x y e x y 8 z dy 2x 3 axdy

er 10 d S 10 ng an option will display any text boxes needed to complete your answer Increasing on one interval Decreasing on one interval Constant on one interval O Increasing on one interval and Decreasing on another Increasing on Decreasing on 10

finding solutions of differential equations X 3 x y 3x 6 y 9x e 4 3 y

A manufacturer produces two models of a gas grill Grill 4 requires 0 6 hr for assembly and I hr for packaging Grill B requires 1 2 hr for assembly and 0 5 hr packaging The production information and profit for each grill are given in the table Grill A Grill B Part 0 3 Assembly 0 6 hr 1 2 hr Part 1 of 3 Packaging 1 hr 0 5 hr The manufacturer has 600 hr of labor available for assembly and 400 hr of labor available for packaging Profit 150 100 a Determine the number of grill A units and the number of grill B units that should be produced to maximize profit assuming that all grills will be sold The manufacturer should produce grill 4 units and grill R units to maximize profit

4 Consider 1 cycle of a shifted sine function graph below The function below can be modeled by p x Asin Kx B D Determine the exact values of A K B and D 3 HG E SIT 12 2 T 3 312 st

Find the average value of f x 4 sina 2 cos a on the interval 0 1 Average value

uiz in D Instruction Question 1 solve for x 23x 1 32 x 2 O x 1 Ox 2 Onone of these answers Question 2 Solve for x 3x 1 25 Ox 0 93 Ox 2 93

b 2 4 2 Find an equation in standard form for the ellipse that satisfies the given conditions It may be helpful to start by drawing a picture with the given information a Major axis length 14 on x axis minor axis length 10 b Foci 0 3 major axis length 10 c Minor axis endpoints 12 0 major axis length 26 d Foci 2 1 and 2 5 major axis endpoints 2 1 and 2 7 for vertices and foci of the ellipse

5 Show that the solution of the differential equation x kx x 0 is x t kt ez A cos nt B sin nt where n un ER A and B are arbitrary constants

1 point 4 letter words are formed using the letters A B C D E F G How many such words are possible for each of the following conditions a No condition is imposed Your answer is b No letter can be repeated in a word Your answer is c Each word must begin with the letter A Your answer is d The letter C must be at the end Your answer is e The second letter must be a vowel Your answer is

Find the area of the region enclosed by the curve a 14 cos t 7 sin 2t y 4 sin t with 0 t 2m Graph it and it will make you cry

Given the following graph 3 2 16 14 01 4 12 10 8 20 0 2 3 What is the value of the slope of the trendline S 6

walues of e a b and c for the conic 16 3 cos 0 se se se se 9

Find the average rate of change of f x 4x 9 on the interval 1 6 Your answer will be an expression involving b

Write the Mayan numeral as a The equivalent Hindu Arabic numeral is What is the equivalent Babylonian numeral Choose the correct answer below O A WWW O B WWW Oc WWW WWW OD WWW WWWWW

Differentiate and simplify y x Og 2 21 2 y 2 Oy z 2 21m y x 2 1 In x Oy x 2 Oy z 2 2m z y x 28

Multiply in the indicated base 25 45 25 45 5

Listen Determine the equation of the tangent line to the curve y 9 tan x at the point 9 Oy x 9 2 1 Oy 18x 9 1 Oy x 9 1 7 Oy 18x 9 1 7 Oy 18x 9 1

Let C be the function whose graph is given to the right This graph represents the cost C of using m anytime cell phone minutes in a month for a five person family plan a Determine C 0 Interpret this value C Cost dollars 2000 1000 3000 3001 0 108 1000 00 0 13865 1754 5000 10000 m Number of minutes 15000

Convert the following base ten number to a number in the indic 188 to base 3 188 3

Write the Mayan numeral as a Hindu Arabic numeral 0 1 10 11 2 EN 12 3 HEE 4 wwww 5 15 6 CLE 16 The squivalent Hindu Arabic numeral is 7 17 8 www 9 18 19 www

Find the intercept s of the following equation y 2x 8 Select the correct choice below and if necessary fill in the answer box to complete yo OA The intercept s is are Type an ordered pair Use a comma to separate answers as needed OB There are no intercepts

Find f a f a h and the difference quotient for the function given below where h 0 8 x 7 f a f a h f x f a h f a h

In the given right triangle find the side labeled x X X 16 80 X

For what values of a in 0 27 does the graph of r x x 2 sin x have a horizontal tangent Enter your response as a comma separated list of numbers Verify your result by plotting the graph of r a on 0 2

Estimate the area under the graph of f x from x 1 to x 6 by using 5 approximating rectangles Estimate with right endpoints Estimate with left endpoints

Evaluate the formula for the given quantity C F 32 Find C when F 76 76 degrees Fahrenheit is equal to degrees Celsius

Evaluate the function for the given value f x ex x 1 f 1 Type an integer or a decimal Round to the nearest thousandth

When playing bingo 125 balls are placed in a bin and balls are selected at random Each ball and number as indicated in the chart below For example there are balls marked B1 B2 up to B25 126 127 up 150 and so on Assume one bingo ball is selected at random B 1 1 25 26 50 G 51 75 76 100 101 125 What are the odds in favor of it having the letter G on it Simplify your answer

S 104 S 10 10 Use the graph to answer the following questions a Over which intervals is the function decreasing Choose all that apply 7 0 7 2 2 4 4 8 2 8 8 b At which r values does the function have local minima If there is more than one value separate them with commas C

To determine premiums life insurance companies must compute the probable date of death On the basis of a great deal of research Mr Duncan age 39 is expected to live another 47 58 years Does this determination mean that Mr Duncan will live until he is 86 58 years old If not what does it mean Choose the correct answer below OA Yes because 39 47 58 86 58 OB No it means that all 39 year old men will live another 47 58 years OC No it means that the average person with traits similar to Mr Duncan will live another 47 58 years OD No it means that Mr Duncan will live at most another 47 58 years

Consider the given equation cot y csc y sec y a Verify algebraically that the equation is an identity sin y This answer has not been graded yet b Confirm graphically that the equation is an identity

Use a calculator to approximate the square root 22 22 22 Round to three decimal places

depth width The strength of a beam is proportional to the width and the square of the depth A beam is cut from a cylindrical log of diameter d 22 cm The figures show different ways this can be done Express the strength of the beam as a function of the anc the figures Use k as your proportionality constant s 0 242k sin 20 sin 0 X NOTES e ASK YOUR TEACHER PRACTICE ANOT

n 3 of 5 1 point Attempt 2 of Unlimited View c nes leave the same airport The first plane aves at 5 15 pm and averages 436 mph a 0 2 1 of 2

Sol Angles Watch the video and then complete parts a and b below Click here to watch the video a Identify an equation that could be used to find the marked and 3x 15 Z 2x 5 3x 15 2x 5 2x 5 3x 15 2x 5 2x 5 3x 15 90 L M L 2

Determine the quantity ne distance on both sides of 6 kg 4 m

Compare the torsion of f t cost sint t and g t cost sint t 4 at the point t 2

The amount of bacteria present in a medium after thours is given by A t 65e 0 2t At what rate is the amount of bacteria changing after 10 hours O O a 480 289 bacteria per hour b 1248 750 bacteria per hour c 960 578 bacteria per hour d 96 058 bacteria per hour

The number of different mammal species observed along a transect through a forest is a random variable X with CDF 0 01 0 0 16 2 0 36 i 9 0 71 13 0 96 i 16 i 21 What is the expected value of the random variable X Round your answer to five decimal places F Answer

Minimize f x y x y subject to 8x 2y 136 X 16 y

Minimize f x y x y2 subject to 8x 2y 136 2 X

Let f x y 4x y2 2x 8y 6 A Find the minimum value of f x y when y 2 B Explain why the answer to part A is not the minimum value of the function f x y A The minimum value of f x 2 is Simplify your answer

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Which of the following describes a population and a sample from that population College students college students from a local university O College students high school students High school students high school teachers Adults college students

The figure to the right suggests a number of lines and planes the planes may be described by naming three points Use the A line and a plane whose intersection is a point

K Determine which figure shows vertical angle a d 1 2 1 b e