Algebra Questions

The flow system shown in the figure is activated at time t 0 Let Qi t denote the amount of solute present in the ith tank at time t Assume that all the flow rates are a constant 10 L min It follows that the volume of solution in each tank remains constant assume this volume to be 1000 L The concentration of solute in the inflow to Tank 1 from a source other than Tank 2 is 0 7 kg L and the concentration of solute in the inflow to Tank 2 from a source other than Tank 1 is 0 kg L Assume each tank is mixed perfectly a Set up a system of first order differential equations that models this situation 1 50 HGGI 1 100 Qi Q 1 100 1 50 2 b If Q 0 30 kg and Q2 0 30 kg find the amount of solute in each tank after t minutes Q t kg Q t kg 7 0

Solve 2 2x x 21x The solution set is Type your answer in interval notatic

Suppose a sample of a certain substance decayed to 77 8 of its original amount after 300 days Round your answers to tv decimal places a What is the half life in days of this substance days b How long would it take the sample to decay to one third of its original amount days

x 1 234 2 345 3 456 y 12 342 11 45 16 56 which of the following is the equivalent of y of type x A 10x 30 B 9x 27 D 7x 21 C 8x 2 E 5x 20

About the sequence x kEZ we have the following 1 EB x b for each t to b t b a b x 1 1 5 0 MK te to b te bk20 k 1 c x keZ is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x 1 8 to 8B x b C which is given by x t lim x 1 1E1 b to b Thus X 1 lim x f s x s ds 6 X 1 1 da kix x lim ff s x s ds x flim f s x s ds Finally the validity of this integral equation has the following two implications X t x s x s ds x 0 x 1 x f f s lim x s ds x ff s x s ds Thus the function 1 x 1 satisfying the integral equation x 1 x ff s x s ds for all t t b t b 2 dx 0 aff s x s ds f 1 X 1 dt d This now proves that the curve X To 8 to 85 thus obtained is a solution of the initial value problem

and passes through both the front and back sides of the figure 7 Directions Sketch and state the figure that is the cross section described for the given figure stated al

Patricia has 250 000 saved for retirement in an account earning 4 05 interest compounded monthly How much will she be able to withdraw each month if she wants to take withdrawals for 24 years Round your answer to the nearest dollar

If cos a 0 118 and cos 3 0 546 with both angles terminal rays in Quadrant l find the values of tan a Your answers should be accurate to 4 decimal places

Sketch two periods of the graph for the following function f x 3 tan 4x 20 1 TEL 3R KI K y 8 6 4 2 3x t

Find the sum of the infinite series 1 9 8 9 1 975 86 9a7 18 for those values of r for which it converges O83 92 8r 1 1 A O9r3 8r2 9r 1 1 A O 93 82 9r 8 1 A 8 92 8r 9 1 14

About the sequence keZ we have the following a x 1 EB xo b for each 1 to b t b MKk b 1 x 1 te to b t b k20 k 1 x keZ is uniformly Cauchy on t b to b verification of these properties is left for the reader We consider the uniform limit of the sequence x 10 8 to 8 B x b C which is given by 1 l b to b Thus X 1 lim x x t lim x 1 1 2 f s X s ds Finally the validity of this integral equation has the following two implications X t x f s x s ds x 0 X x lim ff s x s ds x f lim f s x s ds x f f s lim x s ds x ff s x s ds Thus the function rx 1 satisfying the integral equation x 1 x f s x s ds for all 1 18 b t b dx 0 ff s x s ds 1 X 1 dt This now proves that the curve X to 8 4 82 thus obtained is a solution of the initial value problem

Graph the trigonometric function x 34 y cos x Espanol Plot all points corresponding to x intercepts minima and maxima within o cycle Then click on the graph a function button

given the graph of the function y f x evaluate F 1 Given the graph of the function y f x evaluate f 1 undefined 02

From a window 32 0 ft above the street the angle of elevation to the top of the building across the street is 52 0 and the angle of depression to the base of this building is 15 0 Find the height of the building across the street 2 The height of the building across the street is Round to the nearest whole number as needed ft C This question 6 point s possible 52 0 15 0

given the graph of the function y f x find x such that f x 7 2 4 2 0 2 4 A f 4 6 6

Prove the fencity lept CSC X sin 2x Note that each Statement must be based on a Rule chosen from the Rule menu To see a detailed description of a Rule select the More Information Button the right of the Rule Statement RE Im Tue Select Rule 0 0 DID 0 0 0 0 D B D D 0 0 D D

ne the signs of the six trigonometric functions of an angle in standard position with the given measure 675 Determine if the value of sin 6 5 is positive or negative Positive O Negative Is the value of cos 675 positive or negative Positive Negative What is the sign of the value of tan 675 Positive Negative Is the sign of the value of csc 675 positive or negative Positive Negative Determine if the value of sec 675 is positive or negative O Positive O Negative What is the sign of the value of cot 675 CCCC

Factor by grouping sometimes called the ac method 10x x 2 First choose a form with appropriate signs Then fill in the blanks with numbers to be used for grouping Finally show the factorization Form O O 10x 2 0 O 10 2 0 0 2 10x O 0 0 10x Factorization 10x x 2 X S

Solve the initial value problem y 3y 4y 0 y 0 1 y 0 11 The general solution is y x www

Simplify the expression below when x 1 and y 3 2y X 2

Example Use Theorem 4 to find the horizontal asymptote s for the following functions 8x42x 10 3x 3x x 3x 2x 2 4x 7x x a y b y 10x6 5x 13 1 2x 3x 4 c y

Baby Zia has 10 less than 9 times as many toys as Baby Zion Together Baby Zia and Baby Zion have 180 toys How many toys does Baby Zia have

Post a short discussion on Double Angle Half Angle and Reduction Formulas at least 50 words minimum and in your own words and not copying from a website or your textbook

Which of the following power functions is the most dominant in the long run Of x 1000x O g x 3x4 Oh x 99x Om x 101x

Solve the absolute value inequality Graph the solution set 3t 2 4 Select the correct choice below and fill in any answer boxes within your choice OA The solution set in interval notation is Type your answer in interval notation Use integers or fractions for any numbers in the expression OB The solution is the empty set Graph the solution set Choose the correct answer below OA O C 4 4 2 2 0 0 2 4 O B O D 4 2 2 0 0 2 LIN 4

Use the graphs of the functions to solve the problem f x x 3 g x 6 a f x g x b f x g x c f x g x 12 Tex 6 to co 6 12 compound inequality O D The solution set is the empty set c Solve f x g x Select the correct choice below and if necessary fill in the answer box to complete your answer OA The solution set is x Simplify your answer Type a compound inequality OB The solution set is Simplify your answer Use a comma to separate answers as needed OC The solution set is x x or x Simplify your answer Type inequalities OD The solution set is the empty set

Determine the extreme values for each function on the interval 3 x 4 and include if any extreme values found are maximum or minimum values 10 f x 3 12 f x 3x 8

10 Evaluate the expression below given the replacement values 1 2x 42 if x 9 and y 3 A 68 B 42 C 60 D 53 E 55 to impress everyone to promote world peace to show how cool math is to win a bet to end world hunger

7 Given the graph of the function y f x find the domain A 0 00 B 1 2 C 2 1 D 1 5 E 0 1 F None of the above y f x 5 I 132S 4 3 2 5 4 3 2 11 2 3 4 5 1 2 3 4 5

Evaluate the expression below given the replacement values p 2q 7r if p 1 q 8 and r 4 A 24 B 12 C 20 D 11 E 13 pajamas bow ties gorilla costumes tu tus sunglasses

What is the end behavior of the graph As x approaches infinity f x approaches infinity O As x approaches negative infinity f x approaches negative infinity As x approaches infinity f x approaches negative infinity O As x approaches negative infinity f x approaches negative infinity As x approaches infinity f x approaches negative f x

Which functions have graphs that are steeper than the graph of f x 3x Select each correct answer g x 4x m x 4x j x 2x h x 2x k x 3x

2 Evaluate the expression below given the replacement values 10m n if m 3 and n 7 A 277 B 20 C 83 D 263 F 07 excited nervous shocked confused thrilled

Score 0 37 0 11 answered Question 6 1 2 a 2 a 1 a Solve the following equation Be sure to check each answer in the original equation if you multiply both sides by an expression that contains a variable V 2 a 3a 2 Question Help Video Post to forum

Score 0 37 0 11 answered Question 1 Choose the correct words to fill in the blanks below multiply denominators least common denominator 1 The first step to solving a rational equation is to find the in the equation 2 The second step to solving a rational equation is to by the LCD 3 Multiplying a rational equation by the LCD clears the equation of all 4 If we get a then we write the equation in standard form factor and solve Question Help Post to forum quadratic for all denominators both sides of the equation equation once we have multiplied a rational equation by the LCD

3 2 Score 0 14 0 7 answered Question 3 I For the following exercise solve the radical equation Be sure to check all solutions to eliminate extraneous solutions x 7 2 Question Help VIDEO OPost to forum

Which graph represents f x 2x O 6 5 4 3 2 151 6543 2 1 IN 1 2 3 1 2 3 4 5 X 6 O 5 4 3 2 6 5 4 3 2 1 2 3 2 PN 3 4 5 6 X

3 a Find f 1 b Find f 3 4 c Find x if f x 3 2 d Find the domain of f x e Find the range of f x 2 f x 5

A D 1 F x 3x 1 ii G x x 1 iii H x x 1 iv I x x 1 B C

Here are four graphs Match each graph with a quadratic equal Column A 1 2 T N O 2 2 Column B a b C d y x 3 y x 1 x 3 y x 1 x 3 y x 3

Which equation is represented by the graph yf 10 O a O b Oc Od 3 1 y x 1 3 2 y x 3 1 y x 3 1 r 3 2 11 6 X

1 Find the slope of each line GIVEN a graph or an equation 2 1 2

5 7 3 8 2y x 4 Find the slope of each line 7 y x 3 4 y 2x 2 0 Find the slope of the line through each pair of points 5 13 9 9 4 6 6 2 12 14 0

1 3 SUM Find the slope of each line GIVEN a graph or an equation 2 1 3 8 2y x 4 2 4 y 2x 2 0

8 0 Write the point stope form of the equation of the line through the given point with the given slope 8 through 3 2 slope 2 A y 2 2 x 3 B 3 x 2 0 3 1 D y 3 4x 2 9 through 2 5 slope A 2 x Cl y 2 x 5 Dj J 5 x 2 Write the point slope form of the equation of the line through the given points 10 through 5 1 and 5 1 O A 0 S B y 1 5 y 1 x 5 D I 5 11 through 11 3 and 0 3 A j 1 6x 3 B y 3 dz 11 C y 3 x 1 D p 1 6x 3 1

Find the real solutions of the equation 3 5t 3 21 Select the correct choice below and fill in any answer boxes within your choice O A The solution set is OB The solution set is all real numbers OC The solution set is the empty set Use a comma to separate answers as needed

According to a particular test a normal score is 400 It can be shown that anyone with a score x that satisifies the 1 23 has an unusual score Determine the scores that would be considered unusual X 400 inequality 11 What values of x represent an unusual score Select the correct answer below and fill in the answer box es to complete your choice Simplify your answer O A Test scores between and would be considered unusual OB Only test scores less than would be considered unusual OC Test scores less than or greater than would be considered unusual OD Only test scores greater than would be considered unusual

Solve the absolute value inequality Graph the solution set 2 3x 5 The inequality 12 3x 5 is equivalent to 2 3x or 2 3x Select the correct choice below and if necessary fill in the answer box to complete your choice O A The solution set in interval notation is Type your answer in interval notation Use integers or fractions for any numbers in the expression OB The solution is the empty set Graph the solution set Choose the correct answer below O A 4 2 0 2 4 6 8 O B 2 0 N 2 st 6

Use the graphs of the functions to solve the problem x x 4 g x 6 a f x g x b f x g x c f x g x 12 Xxx 6 0 6 1 12 N a Solve f x g x Select the correct choice below and if necessary fill in the answer box to complete your answer OA The solution set is x Simplify your answer Type a compound inequality O B The solution set is x x or x Simplify your answer Type inequalities OC The solution set is Simplify your answer Use a comma to separate answers as needed O D The solution set is the empty set b Solve f x g x Select the correct choice below and if necessary fill in the answer box to complete your answer

If f x 2 3x 1 and g x 8 solve the following a f x g x b f x g x c f x g x a Solve f x g x Select the correct choice below and if necessary fill in the answer box to complete your a OA The solution set is x x or x Simplify your answer Type inequalities OB The solution set is x Simplify your answer Type a compound inequality OC The solution set is Simplify your answer Use a comma to separate answers as needed The solution set is the empty set