The question is ambiguous since it is not clear what the question means.
If there is a mapping such that
t(0) = 1
t(1) = 1
t(2) = 2
t(3) = 6
and you require t(5), then the answer is anynumber. It is easy to find a rule based on a polynomial of order 4 such that the first four numbers are 1, 1, 2 and 6 followed by the chosen next number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
Here, fitting the 3rd degree polynomial,
t(n) = (2n^3 - 3n^2 + n + 6)/6 for n = 0, 1, 2, ...
gives t(5) = 31.
How to solve: 3x - 2y = 1 3x2 - 2y2 + 5 = 0 Rearrange the first equation to make x or y the subject (that is x = something or y = something) and then substitute into the second equation and solve that: 3x - 2y = 1 => y = (3x - 1)/2 3x2 - 2y2 + 5 = 0 => 3x2 - 2((3x - 1)/2)2 + 5 = 0 [substitute for y] => 3x2 - 2(9x2 - 6x + 1)/4 + 5 = 0 [expand the square term] => 3x2 - (9x2 - 6x + 1)/2 + 5 = 0 [spot that 2w/4 is the same as w/2] => 6x2 - (9x2 - 6x + 1) + 10 = 0 [multiply equation by 2] => 6x2 - 9x2 + 6x - 1 + 10 = 0 [remove the brackets by multiplying by -1 as it is -1 x (..)] => -3x2 + 6x + 9 = 0 [collect together terms] => 3x2 - 6x - 9 = 0 [multiply whole equation by -1] => x2 - 2x - 3 = 0 [divide whole equation by 3] => (x - 3)(x + 1) =0 [factorize) => x = 3 or -1 [as one factor or the other must be zero] Now use first equation to find corresponding y terms: x = 3:y = (3 x (3) - 1) / 2 = 8 / 2 = 4 x = -1: y= (3 x (-1) - 1) /2 = -4 / 2 = -2 So the solution is the (x, y) pairs, or points, (3, 4) and (-1, -2). The answer can be checked using the second equation: (3, 4): 3(3)2 - 2(4)2 + 5 = 3 x 9 - 2 x 16 + 5 = 27 - 32 + 5 = 0 (-1, -2): 3(-1)2 - 2(-2)2 + 5 = 3 x 1 - 2 x 4 + 5 = 3 - 8 + 5 = 0
Point of contact: (3, 4) Circle equation: x^2 +y^2 -2x -6y+5 = 0 Completing the squares: (x-1)^2 +(y-3)^2 -1 -9 +5 = 0 So: (x-1)^2 +(y-3) = 5 Centre of circle: (1, 3) Slope of radius: (3-4)/(1-3) = 1/2 Slope of tangent: -2 Equation of tangent line: y-4 = -2(x-3) => 2x+y = 10 Tangent line meets the x axis at: (5, 0) Using formula distance from (1, 3) to (5, 0) = 5 units
A Pentagon has 5 angles. It can have 0, 1, 2, 3 or all 5 equal.
If y = -3x - 2 then substituting x from each ordered pair gives :- A) (1,1) y = (-3*1) - 2 = -5 ☒ B) (0,-1) y = (-3*0) - 2 = -2 ☒ C) (0,0) y = (-3*0) - 2 = -2 ☒ D) (-1,0) y = (-3*-1) - 2 = 1 ☒ So the answer is ALL OF THEM are not solutions to the equation y = -3x - 2.......BUT, you've used the word Inequality so depending whether y > -3x - 2 or y < -3x -2 clearly affects the results.
1-1 1-2 1-3 1-4 1-5 1-6 2-1 2-2 2-3 2-4 2-5 2-6 3-1 3-2 3-3 3-4 3-5 3-6 4-1 4-2 4-3 4-4 4-5 4-6 5-1 5-2 5-3 5-4 5-4 5-6 6-1 6-2 6-3 6-4 6-5 6-6 So there ARE 36 possible outcomes, you see. Answer BY: Magda Krysnki (grade sevener) :P
+4 +3 +3 -4 -3 -2 0 -1 +3 +1+1 0 +1
each row has the contents of 8 5 3 in that order 8 0 0 5 0 3 5 3 0 2 3 3 2 5 1 7 0 1 7 1 0 4 1 3 4 4 0 the other solution is 8 0 0 3 5 0 3 2 3 6 2 0 6 0 2 1 5 2 1 4 3 4 4 0 See related link "Dividing" for more info
3. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4 9 4 4 5 9 2 3 0 7 8 1 6 4 0 6 2 8 6 2 0 8 9 9 8 6 2 8 0 3 4 8 2 5 3 4 2 1 1 7 0 6 7 9 8 2 1 4 8 0 8 6 5 1 3 2 8 2 3 0 6 6 4 7 0 9 3 8 4 4 6 0 9 5 5 0 5 8 2 2 3 1 7 2 5 3 5 9 4 0 8 1 2 8 4 8 1 1 1 7 4 5 0 2 8 4 1 0 2 7 0 1 9 3 8 5 2 1 1 0 5 5 5 9 6 4 4 6 2 2 9 4 8 9 5 4 9 3 0 3 8 1 9 6 4 4 2 8 8 1 0 9 7 5 6 6 5 9 3 3 4 4 6 1 2 8 4 7 5 6 4 8 2 3 3 7 8 6 7 8 3 1 6 5 2 7 1 2 0 1 9 0 9 1 4 5 6 4 8 5 6 6 9 2 3 4 6 0 3 4 8 6 1 0 4 5 4 3 2 6 6 4 8 2 1 3 3 9 3 6 0 7 2 6 0 2 4 9 1 4 1 2 7 3 7 2 4 5 8 7 0 0 6 6 0 6 3 1 5 5 8 8 1 7 4 8 8 1 5 2 0 9 2 0 9 6 2 8 2 9 2 5 4 0 9 1 7 1 5 3 6 4 3 6 7 8 9 2 5 9 0 3 6 0 0 1 1 3 3 0 5 3 0 5 4 8 8 2 0 4 6 6 5 2 1 3 8 4 1 4 6 9 5 1 9 4 1 5 1 1 6 0 9 4 3 3 0 5 7 2 7 0 3 6 5 7 5 9 5 9 1 9 5 3 0 9 2 1 8 6 1 1 7 3 8 1 9 3 2 6 1 1 7 9 3 1 0 5 1 1 8 5 4 8 0 7 4 4 6 2 3 7 9 9 6 2 7 4 9 5 6 7 3 5 1 8 8 5 7 5 2 7 2 4 8 9 1 2 2 7 9 3 8 1 8 3 0 1 1 9 4 9 1 2 9 8 3 3 6 7 3 3 6 2 4 4 0 6 5 6 6 4 3 0 8 6 0 2 1 3 9 4 9 4 6 3 9 5 2 2 4 7 3 7 1 9 0 7 0 2 1 7 9 8 6 0 9 4 3 7 0 2 7 7 0 5 3 9 2 1 7 1 7 6 2 9 3 1 7 6 7 5 2 3 8 4 6 7 4 8 1 8 4 6 7 6 6 9 4 0 5 1 3 2 0 0 0 5 6 8 1 2 7 1 4 5 2 6 3 5 6 0 8 2 7 7 8 5 7 7 1 3 4 2 7 5 7 7 8 9 6 0 9 1 7 3 6 3 7 1 7 8 7 2 1 4 6 8 4 4 0 9 0 1 2 2 4 9 5 3 4 3 0 1 4 6 5 4 9 5 8 5 3 7 1 0 5 0 7 9 2 2 7 9 6 8 9 2 5 8 9 2 3 5 4 2 0 1 9 9 5 6 1 1 2 1 2 9 0 2 1 9 6 0 8 6 4 0 3 4 4 1 8 1 5 9 8 1 3 6 2 9 7 7 4 7 7 1 3 0 9 9 6 0 5 1 8 7 0 7 2 1 1 3 4 9 9 9 9 9 9 8 3 7 2 9 7 8 0 4 9 9 5 1 0 5 9 7 3 1 7 3 2 8 1 6 0 9 6 3 1 8 5 9 5 0 2 4 4 5 9 4 5 5 3 4 6 9 0 8 3 0 2 6 4 2 5 2 2 3 0 8 2 5 3 3 4 4 6 8 5 0 3 5 2 6 1 9 3 1 1 8 8 1 7 1 0 1 0 0 0 3 1 3 7 8 3 8 7 5 2 8 8 6 5 8 7 5 3 3 2 0 8 3 8 1 4 2 0 6 1 7 1 7 7 6 6 9 1 4 7 3 0 3 5 9 8 2 5 3 4 9 0 4 2 8 7 5 5 4 6 8 7 3 1 1 5 9 5 6 2 8 6 3 8 8 2 3 5 3 7 8 7 5 9 3 7 5 1 9 5 7 7 8 1 8 5 7 7 8 0 5 3 2 1 7 1 2 2 6 8 0 6 6 1 3 0 0 1 9 2 7 8 7 6 6 1 1 1 9 5 9 0 9 2 1 6 4 2 0 1 9 8 9
(0 + 1 + 5 + 3 + 3 + 3 + 0 + 2 + 2) / 9 = 2.1 recurring (that is, 2.1111...)
No sorry you can't Actually, you can: 0 - 2 + 3 * 5 = 5 0 - 2 = -2 -2 + 3 = 1 1 * 5 = 5
1 2 0 3 -1 4 -2 5 -3 6 or 1 2 3 4 5 6 ... interlaced with 0 -1 -2 -3 -4 -5 .....
Intro/outro: e-|-7-8-------5-7------------------------| B-|-7-8-------3-5------5-7------8-5------| G-|--------------------2-4---------------| D-|-----------------------------0-2------| A-|--------------------------------------| E-|--------------------------------------| Riff 1: P.M. P.M.... e-|-------------------| B-|-------------------| G-|-------------------| D-|-------------------| A-|-/8-----/8---------| E-|-/6-0-0-/6-0-0-0-0-| Riff 2: P.M e-|-------------------| B-|-------------------| G-|-------------------| D-|-----------2-----5-| A-|-4---2---4-0-4---3-| E-|-2---0---2---2-2---| Add 1: e-|--------| B-|--------| G-|--------| D-|-4------| A-|-4------| E-|-2------| Add 2: e-|-------| B-|-------| G-|-------| D-|-5---4-| A-|-3---2-| E-|-------| Riff 3: P.M P.M....| e-|-------------------| B-|-------------------| G-|-------------------| D-|-/5-----/5---------| A-|-/3-----/3---------| E-|----2-2----2-2-2-2-| Chorus: P.M...........| P.M.........| e-|-----------------------------------------------------------| B-|-----------------------------------------------------------| G-|-----------------------------------------------------------| D-|-6---5-4---6-----------------6---5-4---6-------------------| A-|-4---3-2---4-0-0-0-0-0-0-0-0-4---3-2---4-0-0-0-0-0-0-0-2br-| E-|-----------------------------------------------------------| Riff 4: P.M |.| |.....| |-------| e-|-------------------------------------------------| B-|-------------------------------------------------| G-|-------------------------------------------------| D-|-9\8\7---5-----4---------------------------------| A-|-7\6\5---3-----2-5-----------5-2-----------5-2---| E-|-------0---0-0---3---0-0-0-0-3-0-0-0-0-0-0-3-0---| Riff 5: P.M...| |.........| |.........| |.........| e-|----------------------------------------------------------- B-|----------------------------------------------------------- G-|----------------------------------------------------------- D-|---------5---------------5---------------4---------------4- A-|-4-4-4-4-3---3-3-3-3-3-3-3---3-3-3-3-3-3-2---2-2-2-2-2-2-2- E-|----------------------------------------------------------- P.M.......| |.........| |.........| |.........| --------------------------------------------------------------- --------------------------------------------------------------- --------------------------------------------------------------- -------------3---------------3---------------2---------------2- -2-2-2-2-2-2-1---1-1-1-1-1-1-1---0-0-0-0-0-0-0---0-0-0-0-0-0-0- --------------------------------------------------------------- P.M....| |.........| |..........| |..........| -------------------------------------------------------------| -------------------------------------------------------------| -------------------------------------------------------------| -------------------------------------------------------------| ---------3---------------3---------------5---------------8---| -1-1-1-1-1---1-1-1-1-1-1-1---1-1-3-3-3-3-3---3-3-6-6-6-6-6---| Riff 6: P.M. e-|----------------| B-|----------------| G-|---------5------| D-|-9\8\7---5------| A-|-7\6\5---3------| E-|-------0--------| Add 3: e-|--------| B-|--------| G-|-4------| D-|-4------| A-|-2------| E-|--------| Riff 7: P.M |...| e-|----------------------------------| B-|----------------------------------| G-|-------------5--------------------| D-|-2-----------5--------------------| A-|-2-----------3---3-----5/---7-7---| E-|-0-------0-0-----3-3-3-3/---5-5---| Riff 8: P.M....| |......| |.| |.| |.| e-|----------------------------------------------------------| B-|----------------------------------------------------------| G-|----------------------------------------------------------| D-|-------------7--------------------------------------------| A-|-4-----------5-----------7/---7---7-------7-------7-------| E-|-2---2-2-2-2-----5-5-5-5-5/---5---5---5-5-5---5-5-5---5-5-| Riff 9: e-|----------------------------------------| B-|----------------------------------------| G-|----------------------------------------| D-|----------------------------------------| A-|-7---7---7------5---5------3------------| E-|-5---5---5------3---3------1------------| Riff 10: P.M...................................| e-|-------------------------------------------------------| B-|-------------------------------------------------------| G-|-------------------------------------------------------| D-|-------------------------------------------4---5---4---| A-|---------4-5-----------4-5-----------4-5---2---3---2---| E-|-0-0-0-0-2-3---0-0-0-0-2-3---0-0-0-0-2-3---------------| Riff 11: P.M....| |.........| |.........| |.........| e-|------------------------------------------------------------ B-|------------------------------------------------------------ G-|------------------------------------------------------------ D-|---------5---------------5---------------4---------------4-- A-|-3-3-3-3-3---3-3-3-3-3-3-3---3-3-2-2-2-2-2---2-2-2-2-2-2-2-- E-|------------------------------------------------------------ P.M........| |..........| |.........| |..| ----------------------------------------------------- ----------------------------------------------------- ----------------------------------------------------- -------------3---------------3---------------2------- -2-2-1-1-1-1-1---1-1-1-1-1-1-1---1-1-0-0-0-0-0---0-0- ----------------------------------------------------- P.M.....| |..| -----------------| -----------------| -----------------| ---------2-------| -0-0-0-0-0---0-0-| -----------------| Riff 12: P.M....| P.M........| P.M........| P.M.......| e-|-----------------------------------------------------------| B-|-----------------------------------------------------------| G-|-----------------------------------------------------------| D-|---------10--------------10--------------7---------------8-| A-|-8-8-8-8-8---8-8-8-8-8-8-8---8-8-5-5-5-5-5---5-5-6-6-6-6-6-| E-|-----------------------------------------------------------| Add 4: e-|-------------| B-|-------------| G-|-------------| D-|-5---4---3---| A-|-3---2---1---| E-|-------------| Riff 13: e-|------------------------| B-|------------------------| G-|------------------------| D-|-----------2-----5------| A-|-4---2---4-0-4---3------| E-|-2---0---2---2----------| Riff 14: e-|---------------------| B-|---------------------| G-|---------------------| D-|-----------2---------| A-|-4---2---4-0-4---2---| E-|-2---0---2---2---0---| Riff 15: P.M. |.| |.| |.| e-|-------------------------------------------------------| B-|-------------------------------------------------------| G-|-------------------------------------------------------| D-|-----------2-----5-------5-------5-------5-------5\4---| A-|-4---2---4-0-4---3---3-3-3---3-3-3---3-3-3---3-3-3\2---| E-|-2---0---2---2-----------------------------------------| Add 5: P.M.......... .| e-|-----------------| B-|-----------------| G-|-----------------| D-|-----------------| A-|-----------------| E-|-0-0-0-0-0-0-0-0-| That was all the riffs, lads! This will show you when to play them: Intro x4 Riff 1 x12 Riff 2 x4 Add 1 x1 Add 2 x1 Riff 1 x4 Add 2 x1 Riff 1 x4 Add 2 x1 Riff 3 x4 Chorus x1 Riff 3 x2 Chorus x1 Riff 2 x4 Riff 1 x4 Add 2 x1 Riff 1 x4 Add 2 x1 Riff 3 x4 Chorus x1 Riff 3 x2 Chorus x1 Riff 4 x4 Riff 5 x1 Riff 4 x3 Riff 6 x1 Add 3 x1 Riff 7 x4 Riff 8 x4 Riff 9 x1 Riff 10 x4 Riff 11 x2 Riff 12 x1 Riff 11 x1 Riff 12 x1 Riff 4 x4 Riff 5 x1 Riff 4 x3 Riff 6 x1 Riff 1 x12 Add 4 x1 Add 1 x1 Riff 1 x4 Add 1 x1 Riff 1 x4 Add1 x1 Riff 3 x4 Chorus x1 Riff 3 x2 Chorus x1 Riff 2 x4 Riff 13 x1 Riff 14 x1 Riff 13 x1 Riff 14 x1 Riff 15 x1 Riff 14 x1 Add 5 x1 Riff 15 x1 Riff 14 x1 Add 5 x1 Outro x1
8
1. Start with any two numbers . ( Use 0 and 1 to get the standard sequence) 2. 0 1 Rule: Add each pair of numbers to get the next term 0 1 1 ( add 0 + 1 to get 1) 0 1 1 2 ( add 1 + 1 to get 2) 0 1 1 2 3 (1+2 = 3) 0 1 1 2 3 5 (2 + 3 = 5) 0 1 1 2 3 5 8 and so on forever.
1 (0+1) 3 (0+1+2) 6 (0+1+2+3) 10 (0+1+2+3+4) 15 (0+1+2+3+4+5) 21 (0+1+2+3+4+5+6) Notice these are the numbers you can arrange into equalateral triangles.
slope = change_in_y/change_in_x = (2 - 5)/(0 - 1) = -3/-1 = 3
INTRO: E-----------------------3-------------------------------5----------| B---5---5----3-------3--3--------3---1----1--1------0---6----------| G---4-4-4----3----3--3--3-----3--3---3----2--2------0---5---5--4---| D-----------------------------------------------------------5--3---| A---3---3----3--3----------3---------3--------------2---5---5--5---| E-----------------------------------------1------0----------3--3---| E-----------------------3--------------------------------5----------| B---5---5----3-------3--3--------3---1----1--1------0----6----------| G---4-4-4----3----3--3--3-----3--3---3----2--2------0----5---5--4---| D------------------------------------------------------------5--3---| A---3---3----3--3----------3---------3--------------2--3/5---5--5---| E-----------------------------------------1------0-----------3--3---| VERSE 1: E------------------------------------------------------------| B---1--1---1--1--1---1-----0--0----0------1--1---------------| G---0--0--0---0--0--0------0--0--0--------2--2---------------| REPEAT THIS 3X D-----------------------------------------3--3---------------| A---0---------0-----------------------------------------0----| E--------------------------0---------------------0---3-------| E--------------------------------------------------------| B---1--1---1--1--1---1-----0--0----0---------------------| G---0--0--0---0--0--0------0--0--0------5--5---4---------| D---------------------------------------5--5---3---------| A---0---------0-------------------------5--5---5---------| E--------------------------0------------3--3---3---------| REFRAIN: E----0----0--0----0--0-----0--------------------------------------------| B----1----1--1----0--0-----0---1-1-------1-1----1---3-3-----------------| G-------2----------------------0-0--0----0-0--0-----3-3----5-5--4-------| D----3-------3---------------------------------------------5-5--3-------| A--------------------------2---0------0--0-0---------------5-5--5---4---| E-----------------0--0--0---------------------------3-3----3-3--3---2---| E----0----0--0----0--0-----0-----------------------------------------| B----1----1--1----0--0-----0---1-1-------1-1----1--------------------| G-------2----------------------0-0--0----0-0--0------3--5-4----------| D----3-------3---------------------------------------3--5-3----------| A--------------------------2---0------0--0-0---------5--5-5----------| E-----------------0--0--0----------------------------3--3-3----------| CHORUS: E-----------------------3--------------------------------------5--5------------| B---5---5----3-------3--3--------3---1----1--1----1---0----0---6--6---6--------| G---4-4-4----3----3--3--3-----3--3---3----2--2--2-----0--0-----5-----5--5--4---| D-----------------------------------------3-----------------------------5--3---| A---3---3----3--3----------3---------3----------------2--------5--------5--5---| E---------------------------------------------------0-------------------3--3---| E-----------------------3----------------------------------------5--5------------| B---5---5----3-------3--3--------3---1----1--1----1---0----0-----6--6---6--------| G---4-4-4----3----3--3--3-----3--3---3----2--2--2-----0--0-------5-----5--5--4---| D-----------------------------------------3-------------------------------5--3---| A---3---3----3--3----------3---------3----------------2--------3/5--------5--5---| E---------------------------------------------------0---------------------3--3---| VERSE2: REFRAIN & CHORUS........Before you do the bridge "Gsus nalang" wala ng "G7" (wat i mean 2 say is,the last chords from Chorus) BRIDGE: E-----------------------------------------|--------------------------0-X-X-X--| B-------------6------6---------8------8---|--------6------6------8---2-X-X-X--| G-------------5------5---------7------7---|--------5------5------7---0-X-X-X--| D-----------------------------------------|--------------------------2-X-X-X--| A------0-3-5-----5-5----5--/7-----7-7-----|--0-3-5----5-5----5/7-----0-X-X-X--| E---3-------------------------------------|-----------------------------------| E-------------------------|--------------------------------------| B-----6-----6-----8---8---|---6-X-X-X---8-X-X-X---9-X-X-X----3---| G-----5-----5-----7---9---|---5-X-X-X---7-X-X-X---9-X-X-X----5---| D---------------------9---|----------------------------------5---| A---5---5-5---5/7-----7---|---5-X-X-X---7-X-X-X---8-X-X-X----5---| E-------------------------|----------------------------------3---| Freestyle- So Slow Intro: CM7-C9-C7-F7-Em7-Dm7-Gsus-G7 2x Hmmmmm........ Verse 1: Am7 Em7 FM7(/E/G) I been with you boy 3 years is quite a while Am7 Em7 FM7(/E/G) Getting sensual is really not my style Am7 Em7 FM7(/E/G) You know i love and i like it just like this Am7 Em7 Gsus-G7 Sometimes i feel like givin you more than just a kiss Refrain: FM7 Em7 But baby its wrong, Baby its not the kind of game Am7 Gm7 Gsus G7 If i give it to you now, our love will never be thesame F# FM7 Em7 It won't be long, we got to play a love just right Am7 Gm7 Gsus G7 I know you know the will come, but baby for tonight Chorus: CM7 C9 C7 Lets take slow, so slow, any where you wanna go FM7 Em7 Dm7 Gsus-G7 Baby for you i lay it all the light CM7 C9 C7 You are to know, i know, Boy i ain't got no where to go FM7 Em7 Dm7 Gsus-G7 I give it to you, only to you, we got to take it real slow Verse 2: When we get together, you know i feel the fire It burns up inside, oh that natural desire I know that you feel it too, i know you wanna flow Keep dreami'n about it, and the fire starts to grow (Repeat Refrain & Chorus) Bridge: /G /A /C Dm7 Em7 I know tommorrow it will still be you and me /A /C Dm7 Em7 A7 I'm save it all for you specially... Dm7 Em7 Em pause Trust in me baby when i say to you Dm7 Em7 F Gsus brake If we wait a little longer, our love will be forever true (Repeat Chorus 2x) CM7........