Ex. : The dimen sions of a rectangular solid at agiven instant (to) are and H=5cm. at 2 cm/s ec and (w) is decreasing at 4em/ses Find the rates of change of volume (V) and Sur face area at time t.) Are (V) and (S) -ncreasing, decreasing L=13 cm,W=9 cm IF L) and CH) are increasing ) or neither.

Q: A 100 gal-tank initially contains 50 gal of fresh water. At t = 0, a salt solution containing 1 Ib…

A: Given: A 100 gal-tank initially contains 50 gal of fresh water. At t=0, a salt solution containing 1…

Q: 12) A PARTIUE is movING ALONG A ITYBERBOLA xy =8. AS IT REAUHES tHE POINT (4,2), THE Y-COOR DINATE…

A:

Q: Assume that after  months, butterflies’ populace  in 1000 is calculated as: f(w) = 12w + cos(16w) +…

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Q: Suppose that the Celsius temperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2y and…

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Q: 2. The moment the batmobile passes through the point (-1, /3), the angle 0 is changing at a rate…

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Q: The volume of a right circular cone of radius r and height h isV = π/3 (r^2h). Suppose that r = h =…

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Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

A: Application of differentiation

Q: which then evaporates at a rate proportional to the area of the surface of the water. Show that the…

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Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

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Q: 3. A tiny organism begins to move in a straight line with velocity v(t) = t(t – 1)'/3 microns per…

A: Let the expression for the velocity is v(t)=t(t2-1)1/3. Integrate the expression to find the…

Q: Assume that after months, butterflies’ populace in 1000 is calculated as: f(w) = 12w + cos(16w)…

A: Given f(w) = 12w + cos(16w) +n * 100

Q: Suppose that the temperature T (x, y, z) of a spherical metal part satisfies, for each point (x, y,…

A: We will use directional derivative.

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Q: Consider the ideal gas law PV = kT, where k > 0 is a constant. av a.) Determine the rate of change…

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Q: Suppose a spaceship of length Lo is traveling at a high speed v relative to an observer. To the…

A: topic - functions

Q: Suppose a particle begins to move from the origin (t = 0) following the curve in space r(t)= (5sint,…

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Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A: A detailed solution is given below.

Q: . A vertical line segment of length 8 ft is moving horizontally at a rate of 3 ft/sec. At what rate…

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Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A: Given: Let A is the area of a circle with radius r Then we have A = πr2

Q: EXAMPLE 5 In an oil refinery, a storage tank contains 2000 gal of gasoline that ini- tially has 100…

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Q: Suppose a spherical balloon grows in such a way that aftert seconds, its volume V is given by V = 4…

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Q: A particle moves along a hyperbola xy = 12. As it reaches the point (3, 4), the y-coordinate is…

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Q: 03/ The dimensions of a rectangular solid at a given instant (t.) are : L(t) 13 cm. W(t)-9 cm. H(t.)…

A: Given problem:- The dimensions of a rectangular solid at a given instant (t0) are: L(t )=13 cm.…

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Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

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Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find da/dt in…

A: Given that  Area of the circle =A  Radius of the circle =r  To find the rate of change of area

Q: 4. A T meter long chain hangs from the top of a tall building as shown. If the linear density of the…

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Q: A 32-lb weight stretch a spring 2ft. At t = 0, the mass is released 1 ft above the cquilibrium…

A: The solution is given below

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

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Q: 2. Find the temperature distribution inside a solid parallelepiped with sides (a, b, c) whose faces…

A: Here, uxx + uyy +uzz = 0                                  .......1 with conditions, ux,y,z,0 = A…

Q: 1. The surface area of a sphere of radius r is S = 4t r2 and the volume is V = ar. A spherical…

A: Given,

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Mathematical modeling is the real-life application of the differential equation. One such important…

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A: a (i) Given dVdt=3 m3/sec And radius r=5 meter and  height h=4 meter ⇒rh=54⇒r=54h The volume of the…

Q: Suppose water is leaking from a tank through a circular hole of area An at its bottom. When water…

A:

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given: Let us consider the given, dhdt=-56h32 c=0.6, g=32 ft/s2 Vertex angle=60°

Q: in terms of dt dt (a) If A is the area of a circle with radius r and the circle expands as time…

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Q: Suppose that the Celsiustemperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2yand…

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Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

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Q: 6- The dimension of a solid rectangular at given instant ( to ) are (L = 13 cm) ,(W = 9 cm ) and ( H…

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Q: A stone is tossed vertically into the air from ground level with an initial velocity of 15 mis. Its…

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Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given: Water is leaking from a circular hole(in the bottom) whose area is Ah. When water leaks…

Q: B. The dimensions of a rectangular solid at a given instant (t.) are (a = 13 cm). (b=9 cm) and (c =…

A: Given  Dimensions of rectangular solid  a=13cm, b=9cm, c=5cm .Rate of change of a and c increase…

Q: dh _10. A cylindrical piston with fixed radius r = 3 cm is being compressed so that How h =- dt fast…

A: Given

Q: e surface area of a sphere increases at a rate of 90 m2/sec Then the rate at which the radius…

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Q: In an industrial process, water flows through three tanks in succession, as illustrated in Figure 1.…

A: From the figure in tank (1) total inflow is u and outflow is 8x-8y So we have 8x-8y+u=0…

Q: 45. A cylindrical tank of radius R and length L lying horizontally as in Figure 21 is filled with…

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Q: A)If A is the area of a circle with radius r and the circle expands as time passes, find  dA dt  in…

A: a) Given A is the area of a circle of radius r A=πr2 Then, dAdt=2πrdrdt...(1)

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

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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.