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.
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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
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
A Pentagon has 5 angles. It can have 0, 1, 2, 3 or all 5 equal.
To find the first 5 terms, plug 1, 2, 3, 4 and 5 in for n:3*1-3 = 03*2-3 = 33*3-3 = 63*4-3 = 93*5-3 = 12The first five terms are 0, 3, 6, 9 and 12.