Amother is her children, of unequal weight, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child simply sinking to the ground. given that her heavier child of weight w is sitting a distance l to the left of the pivot, at what distance l1 must she place her second child of weight w on the right side of the pivot to balance the seesaw?

L₁ = W×L / w

Explanation:

The scenario is shown in the image below.

At the pivot point, the torque acting on this point must be zero so that there will be easy back and forth without the heavier child.

Torque created by lighter child + Torque created by the heavier child = 0

Thus,

According to the axis system, the heavier child is left to the pivot (origin), so,

W×(- L ) + w× L₁ = 0

So,

L₁ = W×L / w

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.