A person standing at the edge of a cliff throws a rock upward from a height of 180ft above ground level with an initial velocity of 64ft/s. Calculate the velocity of the rock when it is exactly 48ft above the person's hand. Separate multiple answers with a comma. (Hint: Use h(t)=−16t2+64t+180 as the position function, where h is in feet, t in seconds. Ignore air resistance.)

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

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8

a 90 degree rotation across the the origin followed by a reflection across the x-axis.

step-by-step explanation: