Column I Column II (A) Circular plate is expanded by heat from radius 5 cm to 5.06 cm. Approximate increase in area is (p) 4 0.6 (B) Side of cube increasing by 1%, then percentage increase in volume is (9) (r) 3 (C) If the rate of decrease of- 2r + Sis twice the rate of decrease of x, then x is equal to 3/3 (D) Rate of increase in area of equilateral triangle of side 15 cm, when each side is increasing at the rate of 0.1 cm/s; is (s) 4.

Q: We have found that the volume of solution in the tank at time t is given by 400 + t. Let A(t) be the…

A: This is a problem of Modelling of Differential Equation.

Q: (A) Estimate the area under the graph of f(x) = 16 – 2? from x = 0 to x = 4 using 4 approximating…

A:

Q: 1. The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast…

A: " Since you have posted a two questions, we will solve first question for you. To get another…

Q: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

A:

Q: tion of the tangent line to f(x) = 4 %3D

A:

Q: L(t) = -173 + 0.578t +0.00760 t^2 : t in years since 1880 Using the sea level formula L(t), estime…

A: Given                                                       Where t in years since 1880. By using…

Q: dv 5000 (i) Water is flowing into a dam at a rate given by dt where V is the volume V31 +4 of water…

A: Given: dVdt=50003t+4 V is volume of water in dam in megaliters, t is time in days At t = 0, V =…

Q: Total differential z = 5(x^3)(y^2)

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Q: A tank contains 100 kg of salt and 2000 L of water. A solution of a concentration 0.025 kg of salt…

A:

Q: y" - y' = -4 y(x) = %3D

A:

Q: (11) tanh(x+ y) =: tanh x+ tanh y 1+tanh x.tanh y

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Q: 13: = 1 = dx 5sinx – 3cosx−2

A:

Q: Marginal profit. The profit, in thousands of dollars, from the sale of x thousand candles can be…

A: Marginal profit. The profit, in thousands of dollars, from the sale of x thousand candles can be…

Q: A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min.…

A: Solution

Q: The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the…

A: Given that the height of the pebble above the water surface after t seconds is y=285-16t2 and t=2.…

Q: A rectangular tank measuring 1 mx 2 m × 3m initially contains w is being pumped into the tank at a…

A:

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.