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- A particle moves along a hyperbola xy=8. When it passes through a point (2,4), its x-coordinate increases at a rate of 3cm/s. How is the distance from the particle to the origin changing at this moment?A rectangular shaped region is changing with time and increasing in the x direction at the rate of 2 units/sec and decreasing in the y direction at the rate of 0.5 units/sec. How does the diagonal change when x=4 and y=6? Is the diagonal increasing or decreasing at this moment?3. The perimeter of an isosceles triangle is 24 cm. What is the maximum area possible? 4. A 5m ladder leans against a vertical wall. If the top starts sliding downward at the rate of 4.30 ft/sec, find how fast the lower end moves when it is 3m from the wall
- Water is leaking out of an inverted conical tank at a rateof 10,000 cm3/min at the same time that water is beingpumped into the tank at a constant rate. The tank has height6 m and the diameter at the top is 4 m. If the water level isrising at a rate of 20 cm/min when the height of the wateris 2 m, find the rate at which water is being pumped into thetank.Water is leaking out of an inverted conical tank at a rate of 13000.0 cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 m and the the diameter at the top is 5.0 m. If the water level is rising at a rate of 17.0 cm/min when the height of the water is 2.5m, find the rate at which water is being pumped into the tank in cubic centimeters per minute.Water is leaking out of an inverted conical tank at a rate of 9400.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 13.0 meters and the diameter at the top is 3.5 meters. If the water level is rising at a rate of 28.0 centimeters per minute when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
- A ladder 35 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 3 feet per second. 1. How fast is the top of the ladder moving down the wall when its base is 7 feet from the wall? 2. Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall. 3. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.A reservoir has the shape of a right-circular cone with its vertex down. The altitudeis 10 m, and the radius of the base is 4 m. Water is poured into the reservoir at aconstant rate 20π m3/min. How fast is the water level rising when the depth of thewater is 5 m?Water flows through a circular pipe of cross-sectional area 6.16cm2 at a uniform speed of 10 cm per second. At 6 a.m, water starts flowing through the pipe into an empty rectangular tank of base area 3 m2. a) what is the depth of water in the tank at 8.30 a.m ? b) If the tank is 1.2 m high and has a hole at the bottom through which water leaks at the rate of 11.6cm3 per second, determine the time at which the tank will be filled.
- Water is leaking out of an inverted conical tank at a rate of 0.0137 m3/min. At the same time water is being pumped into the tank at a constant rate. The tank has height 6 meters and the diameter at the top is 3.5 meters. If the water level is rising at a rate of 0.18 m/min when the height of the water is 2 meters, find the rate at which water is being pumped into the tank.A spaceship is moving in a straight line at 36,000 miles per socond. Suddenly it accelerates at a(t) = 18t miles per second squared. Assume that the speed of light is 186,000 miles per second and that relativistic effects do not influence the velocity of the spaceship. How long does it take the ship to reach the speed of light and how far does it travel during that time?A hand-tossed pizza base starts off as a ball of dough with a volume of 400π cm3. First,the cook stretches the dough to the shape of a cylinder, then the cook tosses the dough. Ifduring tossing, the dough maintains the shape of a cylinder and the radius is increasing ata rate of 15 cm/min, how fast is its thickness changing when the radius is 20 cm?[