Complete three problems from each section.7. A tank of water in the shape of a cone is being filled with water at a rate of 12m3sec. The base radius of the tank is 26 meters and the height of the tank is 8 meters. At what rate is the depth of the water in the tank changing when the radius of the top of the water is 10 meters? Note the image below is not completely to scale....8. The angle of elevation is the angle formed by a horizontal line and a line joining the observer's eye to an object above the horizontal line. A person is 500 feet way from the launch point of a hot air balloon. The hot air balloon is starting to come back down at a rale of 15ttSoC. At what rate is the angle of elevation, 0, changing when the hot air balloon is 200 feet above the ground. See the (probably bad) sketch below to help visualize the angle of elevation if you are having trouble seeing itComplete three problems from each section.A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5m2sec at what rate is the radius decreasing when the area of the sheet is 12m2?A person is standing 350 feet away from a model rocket that is fired straight up into the air at a rate of 15fsec. At what rate is the distance between the person and the rocket increasing (a)20 seconds after liftoff? (b)1 minute after liffoff?A plane is 750 meters in the air flying parallel to the ground at a speed of 100ms and is initially 2.5 kilometers away from a radar station. At what rate is the distance between the plane and the radar station changing (a) initially and (b)30 seconds after it passes over the radar station?Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of 2ftsec and the other person starts going up in the elevator at a rate of 7ftsec. What rate is the distance between the two people changing 15 seconds later?Complete three problems from each section.A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5m2sec at what rate is the radius decreasing when the area of the sheet is 12m2?A person is standing 350 feet away from a model rocket that is fired straight up into the air at a rate of 15ftsec. At what rate is the distance between the person and the rocket increasing (a)20 seconds after liftoff? (b)1 minute after liftoff?A plane is 750 meters in the air flying parallel to the ground at a speed of 100ms and is initially 2.5 kilometers away from a radar station. At what rate is the distance between the plane and the radar station changing (a) initially and (b)30 seconds after it passes over the radar station?Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of 2ftsec and the other person starts going up in the elevator at a rate of 7ftsec. What rate is the distance between the two people changing 15 seconds later?