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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=2pir C=10pi2 = 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.

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)...

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

Answered by Jordan G. • Maths tutor

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Solve simultaneously, x+y=2 and 4y^2-x^2=11

(1) x + y = 2(2) 4y²- x² = 11
Rearrange (1) to x= 2-y & substitute x=2-y into equation (2)
Simplify the new equation to 3y²+4y-15 = 0, use quadratic formu...

Answered by Nicholas N. • Maths tutor

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The equation of the line L1 is y=3x–2. The equation of the line L2 is 3y–9x+5=0. Show that these two lines are parallel.

The first thing that you should know when wanting to find out if two lines are parallel are the features of a parallel line. These key features include never intersecting lines which means they continue f...

Answered by Karina P. • Maths tutor

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