An arch way is in the shape of a semi-ellipse, the road level being the major axis. If the breadth of the arch way is 30 feet and a man 6 feet tall just touches the top when 2 feet from the side, find the greatest height of the arch.

An arc is in the form of a semi-ellipse. It is 8m wide and 2m high at the centre. Find the height of the arch at a point 1. 5 m from one end.

A grain silo, shown below, is in the shape of cylinder with a half sphere on top . The radius of the base of the cylinder is 10 feet , and the height of the cylindrical part is 60 feet, as marked The silo, when full , can hold 2,100 bushels of wheat . On each of five consecutive days, the farmer sells 150 bushels from an initially full silo. After these sales, approximately what percent of the silo's capacity is still filled with wheat ?

A person standing on the bank of a river observers that the angle subtends by a tree on the opposite bank is 60^(@) . When he retires 40 feet from the bank, he finds the angle to be 30^(@) . Find the height of the tree and the breadth of the river.

A man sitting at a height of 20m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with the foot of tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60^0a n d30^0 respectively. Find the width of the river.

A thin equiconvex glass lens (mu_(g)=1.5) is beign placed on the top of a vessel of height h=20cm as shown figure. A luminous point source is beign placed at the bottom of vessel on the principal axis of the lens. When the air is on both the side of the lens the image of luminous source is formed at a distance of 20cm from the lens out side the vessel. When the air inside the vessel is being replaced by a liquid of refractive index mu_(l) the image of the same source is being formed at a distance 30cm from the lens outside the vessel. Find the mu_(l) .