1. Water is being drained at a constant rate from an inverted conical tank into a tank in the shape of an inverted square pyramid. The concial tank has a semivertical angle of 30 degrees. The dimensions of the square pyramid tank are 2x2 for the base and the height is 4. The dept of the water in the concial tank is Hm, the depth of the water in the pyramid tank is h m.
Show tha tthe magnitudes of the rates of change of the depth in each tank are equal when h:H = 2[(pi)^1/2] : (3)^1/2
2. Three circles of equal radius r are touching each other. A triangel is drawn so that each side is a tangent to two circles, without touching the other circle.
(a) find the are of the triangle in terms of r.
(b) if the radii of the circles are increasing at a rate of 2cm/min, find the rate at which the area of the triangle is increasing when the sum of the areas of the circles is 75pi cm^2.
please help thanks.
Show tha tthe magnitudes of the rates of change of the depth in each tank are equal when h:H = 2[(pi)^1/2] : (3)^1/2
2. Three circles of equal radius r are touching each other. A triangel is drawn so that each side is a tangent to two circles, without touching the other circle.
(a) find the are of the triangle in terms of r.
(b) if the radii of the circles are increasing at a rate of 2cm/min, find the rate at which the area of the triangle is increasing when the sum of the areas of the circles is 75pi cm^2.
please help thanks.
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