Each week our school’s team travels to other schools for competitions. today the five members of the gymnastics team and seven weight lifters are on the way to our rival school for meet. the coaches would like the athletes on the two teams to get to know one another, so they will assign them to ride together in two vans. in how many ways can give gymnast and seven weight lifters ride in two vans if no van contains more than eight passengers and there is at least one member of each team in each van?

The answer is 9.

Step-by-step explanation:  Given that five members of gymnastics team and 7 members of weight lifting team are travelling in two vans  to the rival school for competition. We are to find the number of ways in which they can ride in two vans such that no van contains more than eight passengers and there is at least one member of each team in each van.

Let 'g' and 'w' denote a member of gymnastics team and weight lifting team respectively.

Then, the possibilities are

For 1 g, we can choose 3w, 4w, 5w, 6w.

For 2g, we can choose 2w, 3w, 4w, 5w, 6w.

For 3g, we can choose 1w, 2w, 3w, 4w, 5w.

For 4g, we can choose, 1w, 2w, 3w, 4w.

Therefore, there are (4 + 5 + 5 + 4) = 18 ways.

Since, here the position of the vans does not matter, so the options are double here. Hence, we must divide it by 2.

Thus, the total number of ways = 9.

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 answer is 62.8 cubic units