Discuss the below:
Q1 (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt
(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1m/s how fast is the area of the spill increasing when the radius is 30 m?
Q2 If a snowball melts so that its surface area decreases at a rate of 1cm^2/min, find the rate at which the diameter decreases when the diameter is 10cm.
Q3 A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1m higher than the bow of the boat. If the rope is pulled in at a rate of 1m/s, how fast is the boat approaching the dock when it is 8m from the dock?
Q4 a particle is moving along the curve y=√x. As the particle passes through the point (4, 2) its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant?
Q5 Two sides of a triangle are 12 m and 15 m. The angle between them is increasing at a rate of 2 degrees/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60 degrees?