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Solve the simultaneous equations: x^2 + y^2 = 10 and x + 2y = 5

1.)x 2 + y 2 = 10 2.)x + 2y = 5. Rearrange 2nd equation: x = 5 - 2y. Substitute back into 1st equation: (5 - 2y) 2 + y 2 = 10. Multiply out brackets: 4y 2 - 20y + 25 + y 2 = 10. Rearrange equation: 5y 2 - 20...
EW
Answered by Edward W. • Maths tutor
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What exactly is pi?

Pi is the ratio between a the circumference and the diameter of a circle. It's just a number which happens to describe this ratio for any circle you can think of. Let me explain, using the whiteboard...
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Answered by Harry B. • Maths tutor
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Why does 1/x integrate to lnx?

If we let y = lnx, we then know that x = e y . By differentiating both sides of this equation with respect to y we get:dx/dy = e y , as the exponential function differentiates to itself when differentiated w...
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Answered by Chris L. • Maths tutor
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Solve the equation sec^2 x + 2tanx = 0 , 0 ≤ x ≤ 2π, question from HL Maths exam May 2017 TZ1 P1

We start with sec^2 x + 2tanx = 0 for 0 ≤ x ≤ 2π Note that sec^2 x = tan^2 x +1 tan ^2 x + 2tan x +1 = 0 (tan x +1)^2=0 tan x = -1 x=3π/4 or x=7π/4
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Answered by Michał K. • Maths tutor
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y is proportional to x^2 and that when y = 75, x = 5. Find a formula for y in terms of x and find y when x=3

In a proportional equation, you represent the factor of proportionality as k. In this case it means that y=kx^2. In the question you're given a number for both y and x. Sub these in in order to solve for k. ...
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Answered by Kesem I. • Maths tutor
5097 Views