Mathematics in the london eye answers

1 answer:

6 0

CENTRAL ANGLE:
There are 32 passenger cars, so you want an angle equal to 1/32 of the full circle.

The full circle in degrees is 360°, but you want radians. 
The full circle in radians is 2π. 
2π / 32 
= π/16 radians

ARC LENGTH 
The arc length would be 1/32 of the full circumference. I know you already asked and got answers for the full circumference. Divide that by 32.

AREA OF SECTOR: 
Ditto on this. You have the full area from a prior question. Now just divide it by 32

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$\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================$

$\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================$

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