which function is a linear function? A. f(x)= x^3+x B. g(s)= 1-4s C. h(t)= 2t+1/t D. f(r)= square root of r
4x-4y-ty+xt = 4x+tx-4y-ty = x(4+t) - y(4+t) = (x-y)*(4+t)
A triangular number is a member of the series which is calculated as follows: t(1) = 1 = 1 t(2) = 1 + 2 = 3 t(3) = 1 + 2 + 3 = 6 t(4) = 1 + 2 + 3 + 4 = 10 and so on. t(n) = 1 + 2 + 3 + 4 + ... + n Fortunately, there is a simpler formula t(n) = n*(n+1)/2 To see why they are called triangular numbers, consider the following pattern: Put one mark in the middle of a line. Then, in the line underneath, put 2 marks. You now have three [=t(2)] marks in the form of a triangle. x x x In the next line, put three marks. You now have six [=t(3)] marks in the form of a triangle. x x x x x x and so on.
Suppose the points are P = (r,s) and Q = (t,u) Then gradient of PQ = (u - s)/(t - r) = m, say. Let Z = (x,y) be any point on the line. Then gradient ZP also = m that is (y - s)/(x - r) = m Equating the two expressions for m, (y - s)/(x - r) = (u - s)/(t - r) or y - s = (x - r)*(u - s)/(t - r) y = (x - r)*(u - s)/(t - r) + s = x*m - r*m - s This is of the form y = mx + b, where m is as defined above and b = -r*m + s
3*4t = 12t
proof of theorem r'(t) x r''(t) K(t) = r'(t)3 proof of theorem r'(t) x r''(t) K(t) = r'(t)3
-1 x 3 x 31 x r x r x r x t = -93r3t
There are 16 possible outcomes, each of which is equally likely. So each has a probability of 1/16 HHHH: X = H*T = 4*0 = 0 HHHT: X = H*T = 3*1 = 3 HHTH: X = H*T = 3*1 = 3 HTHH: X = H*T = 3*1 = 3 THHH: X = H*T = 3*1 = 3 HHTT: X = H*T = 2*2 = 4 HTHT: X = H*T = 2*2 = 4 HTTH: X = H*T = 2*2 = 4 THHT: X = H*T = 2*2 = 4 THTH: X = H*T = 2*2 = 4 TTHH: X = H*T = 2*2 = 4 HTTT: X = H*T = 1*3 = 3 THTT: X = H*T = 1*3 = 3 TTHT: X = H*T = 1*3 = 3 TTTH: X = H*T = 1*3 = 3 TTTT: X = H*T = 0*4 = 0 So, the probability distribution function of X is f(X = 0) = 1/16 f(X = 1) = 4/16 = 1/4 f(X = 2) = 6/16 = 3/8 f(X = 3) = 4/16 = 1/4 f(X = 4 = 1/16 and f(X = x) = 0 for all other x
s - r = 18, so s = 18 + r: t - r = 4(t - s) is t - r = 4(t - 18 + r) ie t - r = 4t - 72 + 4r 3t = 72 - 5r Possible answers: t = 19, r = 3, rt = 16, st = 4; r/s/t = 0, 12, 16 x 1.5 gives 0, 18, 24 t = 14, r = 6, rt = 8, st = 2; r/s/t = 0, 6, 8 x 3 also gives 0, 18, 24 t = 9, r = 9 t = 4, r = 12 The last two are not in fact possible as t must exceed r. The distances starting from r at 0, are rs = 18, st = 6 and rt = 24 The above is unnecessarily complicated! If s is between r and t and rt is 4 times st then rs must be 3 times st. rs is 18 so st is 6 and rt 24. Simple!
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t(1) = a = 54 t(4) = a*r^3 = 2 t(4)/t(1) = r^3 = 2/54 = 1/27 and so r = 1/3 Then sum to infinity = a/(1 - r) = 54/(1 - 1/3) = 54/(2/3) = 81.
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i think it means that each letter represents a number, and because in maths using letters, you don't need to use the x sign so in simple terms it would mean 3 x b x m x s x h x t x r (x=times symbol) so, say b=1 m=2 s=3 h=4 t=5 r=6 then. 3x1x2x3x4x5x6 = 90 and that's what i think it means./ XxX hope it helps
Set x = r*sin(t) and y = r*cos(t) then r = sqrt(x^2 + y^2) and t = arctan(y/x) if x not 0, t = pi/2 if x = 0.
which function is a linear function? A. f(x)= x^3+x B. g(s)= 1-4s C. h(t)= 2t+1/t D. f(r)= square root of r
T = 3x + 7y; x = 4; y = 6T = 3x + 7y (substitute 4 for x, and 6 for y)T = 3(4) + 7(6) = 12 + 42 = 54