A tennis ball is dropped from an initial height of 30 feet. It bounces 5 times, with each bounce height being about 2/3 of the height of the previous bounce.

Step-by-step explanation:

I'm thinking you want to know the height of the ball on that 5th bounce, right? This is of the form

where a is the initial height and b is the decay factor.  If the ball comes up to 2/3 of its height from the previous bounce, then b = 2/3 and our equation is

If you want to know the height y of the 5th bounce x, sub in a 5 for x and solve for y:

and get that

y = 320/81 or as a decimal, 3.9506 feet

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)