Water is leaking out of an inverted conical tank at a rate of 14300.0 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has a height of 6.0 m and the diameter at the top is 6.5 m. If the water level is rising at a rate of 16.0 cm/min when the height of the water is 2.0 m, find the rate at which water is being pumped into thr tank in cubic centimeters per minute.

Q: 2. Sand is being dropped at the rate of 10ft.3/min into a conical pile. If the height of the pile is…

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Q: A conical tank has height 3 m and radius 2 m at the base. Water flows in at a rate of 2 m^3/min.…

A: Given Height of canonical tank=3 m and Radius of canonical tank =2 m and dvdt=2 m3/min.     .....1

Q: Water is leaking out of an inverted conical tank at a rate of 14700.0 cm3/min at the same time that…

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Q: A water tank has the shape of an inverted circular cone (point down) with a base of radius 6 feet…

A: We can consider two similar triangles from the question and using that we can make an expression for…

Q: Water is leaking out of an inverted conical tank at a rate of 10000.0 cm3/min at the same time that…

A: Given that, diameter is 5.5 m which is equivalent to 550 cm.. Therefore, radius is 5502=275 cm.…

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A: To express r in terms of h, use the the ratio between the height and radius of the cone is constant…

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Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

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Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

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Q: The surface area of a sphere increases at a rate of 90 m/sec. Then the rate at which the radius…

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Q: Water is being released from a conical reservoir (vertex down) 20 ft in radius and 40 ft deep at a…

A: Use similar triangle to shoe that  r/20 = h/40 where r and h are the radius and height of water in…

Q: Water is leaking out of an inverted conical tank at a rate of 6000.0 cm/min at the same time that…

A: Please see the below picture for detailed solution.

Q: Question 4

A: Let a be the acceleration, v be the velocity, s be the position and t be the time of braking.

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Q: Water is leaking out of an inverted conical tank at a rate of 11800.0 cm/min at the same time that…

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Q: A system of storm severs in a coastal city is designed to capture water runoff during heavy rains…

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Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

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Q: Water is leaking out of an inverted conical tank at a rate of 11600.0 cm3/min at the same time that…

A: Given: The diameter of the tank is 4m. that is, 400cm. Then the radius of the tank will be 200cm.…

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

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Q: The height h and radius r of the base of a straight circular cone are varying at constant rates of…

A: Topic:- application of derivatives

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Q: A 75 kg box is pushed off of a 120 m tall building with an initial horizontal speed of 15 m/s. How…

A: We have to first sketch the given situation.

Q: Sugar juice is filtering through a conical funnel 20cm deep and 12cm across the top into a…

A: Given that,Sugar juice is filtering through a conical funnel 20cm deep and 12cm across the top into…

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Q: a water tank has the shape of an inverted circular cone with a base radius of 2m and a height of 4m.…

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Q: Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12rcm³ / s. If…

A: Given: Radius of the funnel r=8 cm. Height of the funnel h= 16 cm. rate of change of volume…

Q: Water is leaking out of an inverted conical tank at a rate of 6000.0 cm3/min at the same time that…

A: It is given that the height of the tank is h = 10.0 m and the diameter at the top is 6.0 m, that is,…

Q: water is running out of a conical funnel at the rate of 1 cu inches per second. If the radius of the…

A: This question is related to application of derivatives.

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Q: 4. A vertical right circular cylindrical tank measures 24 ft high and is 8 ft in diameter. It is…

A: Given:The height of the right circular cylindrical tank is 24 ft and diameter is 8 ft. It is full of…

Q: Water is leaking out of an inverted conical tank at a rate of 11700.0cm^3/min  at the same time that…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate at…

A: To find the rate at which the diameter decreases when the diameter is 12 cm and surface area…

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Q: A 35-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 8…

A: Let BC = x = distance from the base of wall to bottom of the ladderAB = y = distance from the base…

Q: Water is leaking out of an inverted conical tank at a rate of 13000.0 cm^3/min at the same time that…

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Q: If a spherical balloon is being filled with air at a constant rate of 2 cm³/s, at what rate is the…

A: Let r be the radius of the balloon in cm and V be the volume in cm3. The variable t stands for time…

Q: 15. Water is being poured at the rate of 150 cm³/s into an inverted cone with a diameter of 3 meters…

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Q: Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12rcm³ /s. If…

A: Given-  dVdt=12π cm3sec.,R=8 cm and H=16 cm To find- depth of sand after 15seconds and the rate of…

Q: If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at…

A:

Q: If a snowball melts so that its surface area decreases at a rate of lcm²/min, find the rate at which…

A: Snowball represents a sphere So , Surface Area of sphere is 4πr2.  And , d=2r.  Using this we solve…

Q: 19. Water is leaking out of an inverted conical tank at a rate of 10,000 cm³/min at the same time…

A: I am attaching image so that you understand each and every step.

Q: A cylindrical tank, shown to the right, has height 8 m and radius 3 m. Suppose the water tank is…

A: Here, the density of water  ρ=1000 kg/m3&g=9.8 m/s2 Here, the radius of the cylindrical tank is…

Q: 3) Water is being poured at the rate of 2TT m3/min. into an inverted conical tank that is 12-meter…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.