(1) A rock is thrown into a lake causing a wave to ripple outward. Suppose the radius of the circle bounded by the rippling is changing at a rate of 2 m/s at the moment when the circle's radius is 3m. Determine how fast the area of the circle is changing at this same moment. (a) Draw a picture and be sure to label it appropriately. (b) Write an equation relating the area of the circle and the radius. (c) Differentiate with respect to time.

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A: Shown below

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A: We can solve as follows

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A:

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A:

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A: Follow the procedure given below.

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A: Let X be the distance of man from lamppost .

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Q: he measure of the angle subtended at

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A: Solved below.

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.