Subject: Mathematics
Book: Maths Mastery
To convert parametric x=f(t), y=g(t) into Cartesian form y=F(x), eliminate the parameter t. For example, if x=2 cos(t) and y=3 sin(t), solve cos(t)=x/2, sin(t)=y/3, then sin²(t)+cos²(t)=1→ (x/2)²+(y/3)²=1. This is an ellipse in Cartesian form. Conversions matter for analyzing geometry or simplifying integrals in calculus. Recognizing how parametric forms unify with standard shapes fosters deeper insight into motion, design arcs, or advanced transformations. Mastery cements flexible modeling from parametric constraints to direct functional relationships.
If a:b = 7:9 and b:c = 5:6, what is a:c?
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