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GCSE or A-level Maths: How can I find the x and y intercepts of a cubic function?

Assume we have the function: y = x ( x 2 + 8x - 9) This function is known as a cubic function as when multiplying out the brackets, the highest function of x would be x 3 .Note: If the highest order of x was...
AM
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Prove that the sum of squares of the first n natural numbers is n/6(n+1)(2n+1)

In order to do this we must follow the standard procedure for a proof by induction which is to first check a base case:Let n = 1, then the sum can be written as 1 2 = 1/6(1+1)(2+1) = 1 as required. Next, ass...
TD
6465 Views

Solve these simultaneous equations: 3xy = 1, and y = 12x + 3

From first equation: 3xy = 1 => x = 1/(3y)Substitute expression for x into second equation: y = 12x + 3 => y = 12(1/3y) + 3 = 4/y +3Multiply through by y: y 2 = 4 + 3y => y 2 - 3y - 4 = 0Factorise: ...
HM
3174 Views

Solve the following simultanious equations: zy=28 and 2z-3y=13

zy=28 so y=28/z13=2z-3y13= 2z - (28 x 3)/z13=2z-84/zmultiply each side by z to give 13z = 2z 2 -84rearange for a quadratic2z 2 -13z-84=0solve by factorising(2z+8)(z-21/2)z= -4 0r 21/2substitute -4 into both ...
OB
2744 Views

Prove that sin(x)^2 - 5cos(x)^2 = 6sin(x)^2 - 5

5 = 5(cos(x)^2 + sin(x)^2) = 5cos(x)^2 + 5sin(x)^2=> 5 - 5cos(x)^2 = 5sin(x)^2=> sin(x)^2 + 5 - 5cos(x)^2 = 6sin(x)^2=> sin(x)^2 - 5cos(x)^2 = 6sin(x)^2 - 5
NT
2575 Views