How would you apply Boyle's Law to the filling of balloon with air?

Please refer to the attachment.
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why is the function [|sinx|+|cosx|] defined only in the interval [1,root2]

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If G is the centroid and I the in-centre of the triangle, with vertices A(-36,7), B(20,7) and C(0,-8), then, find the value of GI.

The number of terms of an A.P. is even; the sum of odd terms is 24, of the even terms is 30, and the last term exceeds the first by 10, find the number of terms and the series.

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Prove and explain in detail that -
Vector A.(vectorA x VectorB) = 0

Write the lewis structure of the nitrate ion NO2¯

three sides of a trapezium are each equal to k cm. find the greatest possible area of the trapezium.
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A bomb is dropped from a plane flying horizontally with uniform speed . Show that the bomb will explode vertically below the plane. Is the statement true if the plane flies with uniform speed but not horizontally?