Math - Others Questions

Find f x f x 4x 12x xw c 3

d y 2 dx y 6x 4 Find d y dx

Find d y 6 2 d y 2 dx y 11 6x5 5 2x

g x et powered by desmos X 5 5 0 5 5 t e shown in red and blue respectively in the graph above By zooming in and out view the Compare the functions f x x7 and g x functions using several viewing scales When does the graph of g finally surpass the graph of f The graphs intersect for the last time at Round your answer to four significant figures Hints You can manually adjust the axes of the graph by clicking on the settings tool in the top right To get this much accuracy you may need to zoom in very close to the intersection point You must round your answer or it will be marked wrong

Write the numeral in the Babylonian numeration system 0000 199 ADDDAAA wwwwwwwwwwww wwwwwwvY A DDDDDDDDDDDD

Two brothers Steven and Michael each inherit 36000 Steven invests his inheritance in a savings account with an annual return of 3 2 while Michael invests his inheritance in a CD paying 4 2 annually How much more money than Steven does Michael have after 1 year Answer How to enter your answer opens in new window Keypad

Solution The required numbers are 1 2 3 4 5 6 So the given set in the roster form is 1 2 3 4 5 6 Example 3 Write the set A 1 4 9 16 25 in set builder form Solution We may write the set A as A x x is the square of a natural number Alternatively we can write A x x n where n N Example 4 Write the set 1 2 3 4 5 6 2 3 4 5 6 7 in the set builder form Solution We see that each member in the given set has the numerator one less than the denominator Also the numerator begin from 1 and do not exceed 6 Hence in the set builder form the given set is n Isns6 where n is a natural number and 1 n 6 n 1 ed Example 5 Match each of the set on the left described in the roster form with the same set on the right described in the set builder form 1 P R I N C A L a x x is a positive integer and is a divisor of 18 b x x is an integer and x 9 0 ii 0 ii 1 2 3 6 9 18 c x x is an integer and x 1 1 iv 3 3 d xx is a letter of the word PRINCIPAL Solution Since in d there are 9 letters in the word PRINCIPAL and two letters P and I are repeated so i matches d Similarly ii matches c as x 1 1 implies x 0 Also 1 2 3 6 9 18 are all divisors of 18 and so iii matches a Finally x 9 0 implies x 3 3 and so iv matches b EXERCISE 1 1 1 Which of the following are sets Justify your answer i The collection of all the months of a year beginning with the letter J ii The collection of ten most talented writers of India in A team of eleven best cricket batsmen of the world iv The collection of all boys in your class v The collection of all natural numbers less than 100 vi A collection of novels written by the writer Munshi Prem Chand vii The collection of all even integers

Note In roster form the order in which the elements are listed is immaterial Thus the above set can also be represented as 1 3 7 21 2 6 14 42 b The set of all vowels in the English alphabet is a e i o u c The set of odd natural numbers is represented by 1 3 5 The dots tell us that the list of odd numbers continue indefinitely Note It may be noted that while writing the set in roster form an element is not generally repeated i e all the elements are taken as distinct For example the set of letters forming the word SCHOOL is S C H O L or H O L C S Here the order of listing elements has no relevance ii In set builder form all the elements of a set possess a single common property which is not possessed by any element outside the set For example in the set a e i o u all the elements possess a common property namely each of them is a vowel in the English alphabet and no other letter possess this property Denoting this set by V we write P V x x is a vowel in English alphabet It may be observed that we describe the element of the set by using a symbol x any other symbol like the letters y z etc could be used which is followed by a colon After the sign of colon we write the characteristic property possessed by the elements of the set and then enclose the whole description within braces The above description of the set V is read as the set of all x such that x is a vowel of the English alphabet In this description the braces stand for the set of all the colon stands for such that For example the set A x x is a natural number and 3 x 10 is read as the set of all x such that x is a natural number and x lies between 3 and 10 Hence the numbers 4 5 6 7 8 and 9 are the elements of the set A If we denote the sets described in a b and c above in roster form by A B C respectively then A B C can also be represented in set builder form as follows A x x is a natural number which divides 42 B y y is a vowel in the English alphabet C is an odd natural number Example 1 Write the solution set of the equation x x 2 0 in roster form Solution The given equation can be written as x 1 x 2 0 i e x 1 2 Therefore the solution set of the given equation can be written in roster form as 1 2 Example 2 Write the set x x is a positive integer and x 40 in the roster form

Write the number given below as a binary numeral 53

Write the number given below as a decimal numeral 11110000 two

Managers need to find the right balance between which two concerns to meet the needs of the healthcare organization HCO O Centralization and current structure O Horizontal coordination and centralization O Vertical control and horizontal coordination O Current structure and vertical control

Write the number given below as a decimal numeral 1100 two

Change 514 to base eight eight

The mass of a sample of a saturated soil is 540 grams The dry mass after onven drying is 420 grams The specific gravity of solids is 2 7 Determine 1 Degree of saturation is S 100 2 The mass of water is 120 3 The volume of water is 120 4 The volume of solid is 155 55 5 The water content w 6 The void ratio e 0 77 28 6 7 Saturated unit weight Ysat 8 Dry unit weight Yd 15 9 Porosity n 43 5 10 If emax 9 cm 19225 cm kN m kN m 1 and emin 0 6 the relative density Dr 83 25

Organizations are all of the following select all that apply O Social Governed by individual behavior Linked to the external environment Recursive Scientific Goal directed

When organizing tasks into jobs and positions managers must determine all of the following except O qualifications for the job O opportunities for the job specific tasks for the job authority for the job

Change the number to base ten 326 5 eight

The organization and management of hospitals are different from and more complex than they are in other types of organizations because some workers are O members of a labor union O contractors O part of a clinical medical staff volunteers

Change the number to base ten 424 five

Write the numeral in the Roman numeration system 1 034

Write the numeral in the Roman numeration system 44

Change 527 to base eight

Write the number given below as a decimal numeral 11110010 two

Write the number given below as a binary numeral 54

Change the number to base ten 413 five

Anwyn the Bold must rescue her fianc Marcin the Mighty along with his troop of soldiers from the evil clutches of the Baron of Oxmoore They are located on the top floor of the round tower To facilitate the rescue she is going for a bold move the use of a catapult to assault the castle that is 62 m away The Baron and his archers are ready to shoot from the top of the tower This position is 15 m above the release point of any projectile Anwyn the Bold sends their way when she aims the catapult at an angle of 60 above the horizontal Determine a how fast the projectile must be launched so that it hits the archers b the velocity of the projectile when it reaches the archers and c what direction the projectile is moving when it reaches the archers Place your final answers in the spaces provided

Change the number to base ten 325 1

Give the meaning of the numeral 6 in the number 6 104 6 tens 6 hundreds 6 thousands 6 ten thousands 6 hundred thousands

In a simplified model for taxes a person will pay 10 on the first 40 000 earned 20 on the next 50 000 earned 40 on the rest For instance a person earning 30 000 will pay 3 000 in taxes and a person earning 100 000 will pay 10 x 40 000 20 x 50 000 40 x 10 000 18 000 dollars in taxes 1 If a person has an income of x 0 write down the function T describing the amount of money that they pay for taxes Explain and simplify the formulas as much as possible Do not use the sign 2 2 Write down the function M1 describing the net income of a person income minus taxes as a function of their gross income x Explain and simplify the formulas as much as possible 3 Draw the graph of M1 for x between 0 and 120 000 You can do it by hand or copy from a graphing calculator 4 A common misconception about taxes is that earning more money can make you fall into another tax bracket and you will then earn less money Explain why this is wrong Your answer should be We see that the function M1 is which means

ore than six times a number results in

5 less than a number

Consider f x 2 5 x 4 a Find f x using the Quotient Rule and the Extended Power Rule b Note that f x x 5 x 4 Find f x using the Product Rule and the Extended Power Rule c Compare your answers to parts a and b a f x

ntiate the function 5 x 8 x

4 fix x 4x 2x 3 What is the sum of the solutions to jx g x 0 g x 3 x N f 4 g OA OB OC OD 0 1 3 4

Let a cost function be defined by Cost in dollars 100 5x 10 C x 3 x 8 50 if x 8 where C is the cost in dollars for x kilograms of bulk cashews Its graph is shown Solve for x C x 110 O 10 C Weight in kilograms if 0 x 8 20 OA OB OC OD 20 25 27 28

Given the piecewise function defined by ax b if x 2 F x cx d if x2 2 where a b c and d are real constants Its graph is shown Determine the sum of a b c d 4 2 3 2 10 1 2 F 2 3 4 OA 2 OB 5 OC OD 6 7

What is the perimeter of the rectangle type in you answer Type in your answer 13 5 cm

1 i The term 2 1 i where i 1 is most nearly O 1 i O 0 O 1 i O 1

Firms A B T E F I Markets for goods and services Markets for factors of production C D G H Households Answer Bank Money

Consider a function of x equal to the determinant shown below f x 0 2 2 3 The first derivative f x of this function with respect to x is equal to O O 4x 6x5 3x 3x 8x4 5 x6 O 3x4 1 6

A company that processes fruits and vegetables is able to produce 500 cases of canned pears in one half hour with 7 workers Material cost is 7 200 and overhead is 1 900 What is the labor productivity Your Answer

9 points Solve the Bernoulli equation xy xy Obtain an explicit solution dx

6 15 a Show that the differential equation 3x ydx x y dy 0 is exact h Obtain an implicit solution

dy 7 9 Solve the differential equation 1 x 2y 3 by using an appropriate substitution Obtain an explicit solution dx

Select ALL statements below that are part of a CORRECT list of steps when your choices are read in order top to bottom for the Clown to act out the computation 3 4 6 Start on 3 Start on 3 Face left and walk forward 4 steps Face left and walk backward 4 steps Face right and walk forward 4 steps Face right and walk backward 4 steps Face right and walk forward 6 steps Face right and walk backward 6 steps Face left and walk forward 6 steps Face left and walk backward 6 steps They end on 7 They end on 5 They end on 1

2 10 Consider the initial value problem dy dx x y y 0 0 Does the Existence and Uniqueness Theorem guarantee the existence of a unique solution for this problem Answer yes or no and justify your answer DO NOT SOLVE THE DIFFERENTIAL EQUATION

Demand for the first six periods are shown below The weights are 0 1 0 3 and 0 6 where 0 6 is applied to the most recent period Compute a three period weighted moving average forecast for period seven That is F7 Period Demand 1 2 3 4 5 6 1 976 2 084 2 192 2 292 2 318 2 345 Do not round intermediate calculations Round your final answer to a whole number Your Answer

5 10 Use an integrating factor to solve the differential equation x x y 2x dy dx Give an explicit solution

3 10 Given that the general solution to the differential equation y y 6y 0 is y C e x c e 2x give the solution to the initial value problem y 6y 0 y 0 0 y 0 5

4 12 Solve the initial value problem 3exdy2e 1 dx y 0 2 Give an explicit solution