In Problems 9 - 10, set up each problem algebraically and solve. Be sure to state what your variables represent.
9. The stopping distance (ds) of a car after the brakes are applied varies directly as the square of the
speed (v). If a car, traveling 100 km/h can stop in 90 m, how fast can a car go and still stop in 45 m?

yes

step-by-step explanation:

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584