Q 7(c) The differential equation describing a tank filled to a height h (metres) at timet (seconds) is dh given by = -/2gh, where g = 9.81 metres/second?, and A and Ao are the cross A V sectional areas of the tank and the outlet respectively. A cylindrical tank of diameter 1.5 m contains water of height h. The water drains through a square hole of side 0.05 m. Show that the differential equation representing the height h at any timet is given by (i) -6.2 dh -0.00627Vh dt (ii) Given that when t 0, h = 1.6 m, solve this differential equation to give an expression for h in terms of t. (Please do your workings to 2 decimal places). Z.- ..e How long (in minutes) does it take to empty the tank if it is 1.6m in depth when full. (Please do your workings to 2 decimal places). (ii)

Q: 6. An ant crawls along a linear path with a velocity of v(t) = cos(3t) inches per minute. (a) What…

A: Given, Velocity of the ant  v(t) = cos(3t) Let's assume the initital position = x = 0  at time t = 0…

Q: Suppose an object is moving along a line such that the acceleration after t seconds is 6t -8t…

A:

Q: An object is suspended from the end of a spring. Its displacement, in cm, from the starting position…

A: We will find out the required values.

Q: Use implicit differentiation to find dv/dL.

A: We will use concepts of differentiation in this.

Q: At time t in seconds, an object's distance from a point is given by s(t) = t³ + 1 centimeters. (a)…

A:

Q: For y = 1/x^2 , use differentials to approximate the change in y when x changes from 4 to 4.125.…

A: Topic- differentials WE are given y=1x2and x changes from 4 to 4.125and we know thatddxxn=nxn-1

Q: Number 6

A: 6The velocity of a car is given by : v(t)=t2+2t here, v(t) is measured in ft/sec and t is measured…

Q: a)    Determine the rate of change for the following functions (i) to (iii):   B=10 B is the value…

A:

Q: The pressure, volume and temperature of an ideal gas are related by the equation 8.31T P(T,V) = V…

A: Given, P(T,V)=(8.31T)/V At centre V=12litre and T=310k

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.