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Find the points of intersection of the line y+x=8 and a circle with centre at (3,-2) and radius 5.

1 Circle Equation: (x-3) 2 +(y+2) 2 =5 2 2 Line Equation: y=-x+8Sub Equation 2 into 1 (x-3) 2 +(10-x) 2 =25x 2 -13x+42=0(x-7)(x-6)=0x=7,x=6 Sub Values back into equation 2 Points = (7,1)&(6,2)
JB
Answered by Jamie B. • Maths tutor
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A field is 90m x 45m, next to a circular lake, 20m across. For training, the coach says your team can either run around the lake 3 times or run along 2 sides of the pitch and then back along the diagonal. Which run is the shortest?

C=2 pi r C=10 pi 2 = 20pi = 62.83185 62.83185 * 3= 188.5m z= root(90^2 + 45^2) = 100.62 l=100.62+90+45 = 235.6 m They should run around the lake.
OK
Answered by Orla K. • Maths tutor
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Solve the simultaneous equations 4x + 2y =20 and 8x + 6y =45

Let (1) be 4x + 2y =20 and (2) be 8x + 6y =45.First we want to eliminate either x or y so that we have an equation in terms of only one unknown. Lets eliminate x. If we multiply (1) by 2 we have2(4x + 2y) = ...
JR
Answered by Jade R. • Maths tutor
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Prove algebraically that the difference between the squares of any two consecutive odd numbers is always a multiple of 8

(2n+3)^2-(2n+1)^2 4n^2+12n+9-4n^2-4n-1 8n+8 8(n+1), which is a multiple of 8
JG
Answered by Jordan G. • Maths tutor
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how do you calculate a percentage of a number?

The easiest way to do it is by using a simple equation. You know that the number N you want to find the percentage of is the "total", which means it is 100%. Let's call X the result of the percenta...
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Answered by Francesca B. • Maths tutor
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