Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

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Question 1103087: pleas help me solve this question: A full grain silo empties at a constant rate, if the rate is 3.5 ft3/s. Write an expression to determine the amount of grain left after s seconds.
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Question 1103209: What are two numbers multiplied together when you get negative 270 but when you add you get 39
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Question 1103208: What are two numbers multiplied together that give you negative 270 but when added you get 30?
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Question 1103245: Solve the equation with the method of factorization method
4x square-4a square x +(a ki power 4 -b ki power 4)

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Question 1103626: My questions is write a polynomial function h that has 3 and -5 as zeros of multiplicity 2?

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Question 1103626: My questions is write a polynomial function h that has 3 and -5 as zeros of multiplicity 2?

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Question 1103561: Susan purchased a painting in the year 2000 for $4000. Assuming an exponential rate of
inflation of 3.1% per year, how much will the painting be worth 8 years later?

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Question 1103671: N =4; -4(⅓), and 2 +3i are zeros; f(1) = 100
1)Since 32+3i are zeros. Conjugate them making it 2-3i.
2)Then set x to each one.
3) x=-3, x=¼, x=3+2i, x=3-2i
x+3=0, 4x=1, x-3-2i=0, x-3+2i=0, x+3=0, 4x=1,x-3-2i=0, x-3+2i=0, 4x-1 =0
4) Use the zero factor property in reverse. When doing that multiply it by a constant “a”
a(x+3)(4x-1)(x-3-2i)=0
5)
F(x) = a(x+3)(4x-1)(x-3-2i)(x-3+2i)
F(x) = a(x+3)(4x-1)[(x-3)-2i][(x-3)+2i]
F(x) = a(4x²+11x-3)[(x-3)²-(2i)²]
F(x) = a(4x²+11x-3)[x²-6x+9-4i²]
F(x) = a(4x²+11x-3)[x²-6x+9-4(-1)]
F(x) = a(4x²+11x-3)[x²-6x+9+4]
F(x) = a(4x²+11x-3)(x²-6x+13)
F(x) = a(4x4-24x³+52x²+11x³-66x²+143-3x²+18x-39)
F(x) = a(4x4-13x³-17x²+161x-39)
F(1) = 100 = a(4∙14-13∙1^3-17∙1^2+161∙1-39)
F(1) = 100 = a(4∙16-13∙8-17∙4+161∙2-39)
F(1) = 100 = a(96)
100/96=a

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Question 1103898: what is the x-intercepts of f(theta)=sin(theta) and how does it relate to the unit circle definition of sine.
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Question 1103951: Maria is 12 years older than her cousin Andy
Maria is x years old
Andy is y years old

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Question 1103939: Mr. Jordan plans to leave the total of his savings to his four children. If they all are to receive the same amount of inheritance and the total savings that he has is $501,052.40, how much will each of them receive?
Click here to see answer by richwmiller(17219) About Me 

Question 1103935: the coach wants to spend three-eighths of basketball practice time on defense. He plans to spend 45 min. on this. how many hours will the team spend practicing?
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Question 1104063: Simplify the expression.
quantity cosecant of y plus cotangent of y times quantity cosecant of y minus cotangent of y divided by cosecant of y.

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Question 1104061: Find sin θ if cot θ = - 2 and cos θ < 0.
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Question 1104117: Find all solutions to the equation.
7 sin^2 x - 14 sin x + 2 = -5

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Question 1104192: Degree 4; zeros: 3-5i; -1 multiplicity 2

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Question 1104181: Factor each denominator completely
A. 17/40x^2
B. x+25/2x^2-6×

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Question 1104404: What is a polynomial function in standard form with zeros 1, -1, 2, and 4?
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Question 1104511: Place the indicated product in the proper location on the grid.
(a + 3)(a - 2)

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Question 1104687: what is 10% of 50% of one half kg? solution
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Question 1104642: Find all solutions in the interval [0, 2π).
cos^2(x) + 2 cos x + 1 = 0
Find all solutions in the interval [0, 2π).
(sin x)(cos x) = 0
Find all solutions to the equation.
cos^2(x) + 2 cos x + 1 = 0

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Question 1104951: Find the number of possible values of p so that +6x%5E2%2Bpx%2B12+ can be factored as the product of two integral first degree polynomials.
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Question 1104917: Which of these statements are true about scientific theories and hypotheses?
A hypothesis is a tentative statement.
A theory is the same as a fact.
A theory has strong predictive power.
A theory is formed before experimentation begins.
A hypothesis is formed after experimentation is complete.

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Question 1105250: A Polynomial Function for Volume
The polynomial function given below represents the volume of a rectangular prism with a square base. Each binomial factor of the polynomial represents one dimension of the rectangular prism.
f(x) = x^3 + x^2 – 21x – 45

g(x) is a fourth-degree polynomial function with the following properties.
•g(x) has the same real zeros as f(x).
•g(x) has at least one imaginary zero.
Find a possible equation for g(x). Write your equation in standard form. Enter your answer and explanation in the box.

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Question 1105250: A Polynomial Function for Volume
The polynomial function given below represents the volume of a rectangular prism with a square base. Each binomial factor of the polynomial represents one dimension of the rectangular prism.
f(x) = x^3 + x^2 – 21x – 45

g(x) is a fourth-degree polynomial function with the following properties.
•g(x) has the same real zeros as f(x).
•g(x) has at least one imaginary zero.
Find a possible equation for g(x). Write your equation in standard form. Enter your answer and explanation in the box.

Click here to see answer by greenestamps(13198) About Me 

Question 1105249: A Polynomial Function for Volume
The polynomial function given below represents the volume of a rectangular prism with a square base. Each binomial factor of the polynomial represents one dimension of the rectangular prism.
f(x) = x^3 + x^2 – 21x – 45
Use the Remainder Theorem to determine whether the binomials x – 5 and x + 1 represent dimensions of the rectangular prism. Enter your answer and explanation in the box.
Rewrite the given function as a product of binomial factors. Enter your answer and explanation in the box.
The area of the base of the rectangular prism is 289 cm2. What are the dimensions of the rectangular prism? Enter your answer and explanation in the box.

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Question 1105299: Find the the domain of the following expression x+3/x-12
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Question 1105338: If a turbine generates 500kW in a 10m/s wind, how much power does it generate in 12 m/s wind?
A step-by-step process on how to solve this would be great, thanks!

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Question 1105536: Given that +x%5E2-3x%2B2+ is a factor of +x%5E4%2Bkx%5E3-10x%5E2-20x%2B24+, evaluate the sum of the four roots of the equation: +x%5E4%2Bkx%5E3-10x%5E2-20x%2B24=0+
Click here to see answer by Boreal(15235) About Me 
Question 1105536: Given that +x%5E2-3x%2B2+ is a factor of +x%5E4%2Bkx%5E3-10x%5E2-20x%2B24+, evaluate the sum of the four roots of the equation: +x%5E4%2Bkx%5E3-10x%5E2-20x%2B24=0+
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Question 1105526: create a trinomial with 6xy as a common factor
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Question 1105543: express this in factored form using the greatest common factor. Show work.

10xy + 25ax

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Question 1105543: express this in factored form using the greatest common factor. Show work.

10xy + 25ax

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Question 1105544: Put into factored form using greatest common factor
24x^3 - 18x^4

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Question 1105545: Put into factored form using the greatest common factor
36x^4y^3 + 20 x^3y^5

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Question 1105623: Prove why synthetic division works like algebraic long division. (Use y=Ax^2+Bx+C)
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Question 1105638: prove why synthetic division works. (do a proof)
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Question 1105638: prove why synthetic division works. (do a proof)
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Question 1105691: Please help me solve the monomial -2^8 times 5^3 over 5^4 times 2^10 times 10
The problem asks me to calculate but my teacher taught us an easier way of solving the monomial instead of simplifying and multiplying every expression but i just forgot how

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Question 1105721: How many pairs of integers (a, b) satisfy the equation +a%5Eb+=1296+
Click here to see answer by ikleyn(52775) About Me 
Question 1105721: How many pairs of integers (a, b) satisfy the equation +a%5Eb+=1296+
Click here to see answer by Boreal(15235) About Me 

Question 1105792: do a constant polynomial have leading term, leading coefficient ? if yes then what will be the constant term of constant polynomial ?? all the leading term, leading coefficient and constant term will be same??
suppose i want to express this polynomial(x^2 - 3x + 4) in a variable of y. what will be he leading term, leading coefficient and constant term??

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Question 1105874: find the zeros of the polynomial by prime factorisation method 2x^2 + 7/2x + 3/4
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Question 1105890: Determine a value of b that will NOT allow the expression n^2-3n-b to be factored.
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Question 1105889: Determine a value of b that will make the expression 16x^2+bx+49 become a perfect square trinomial
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105