Q: The temperature at any point (x, y) in a steel plate is T = 500 - 0.5x2 - 1.2y2, where x and y are…
A: topic - partial differentiation
Q: Find the maximum rate of change of f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.
A: GIVEN DATA : Function fx,y=ex2 TO FIND : Maximum rate of change at 3,0 and the direction The…
Q: Water is draining from a cylindrical tank of water at a rate of 3 m / min . If the radius of the…
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Q: Find the rate of change of f(x,y) = In(x +y +z) – xyz in the direction from (-1,1,1) to (2,1,5) with…
A: solve:
Q: F(X, y,z) = 2x -y? +z?
A: F(x,y,z)= 2x-y^2-z^2 at point (4,-4,2) df/dx= 2 df/dy=-2y df/dz= -2z
Q: Find the rate of change of f(x,y,2) = In(x + y + 2) – ryz in the direction from (-1,1,1) to (2,1,5)…
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Q: A rectangular shaped region is changing with time and increasing in the x direction at the rate of 2…
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Q: A small plane flies horizontally on a line 400 m directly above an observer with a speed of 70 m/s.…
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Q: Let f(x, y) = exy and P(1, 0). Determine the derivative of f at the point P and in the direction of…
A: Given, f(x,y)=e^(xy)
Q: Find the rate of change of the area of a square with respect to the length z of a diagonal. What is…
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Q: Find the maximum rate of change of f(x, y) = (2x - y)3/2 (3,2). at %3D
A: Given, The function is fx,y=2x-y32 at 3,2.We know that, The maximum rate of change…
Q: A vulcanizing shop has a trapezoidal drum that is 5 meters long, 1.5 meter wide at the top, 1 meter…
A: Given information: length of the tank, L=5.0000mwidth of the tank at bottom, wB=1.0000mwidth of…
Q: An open hemispherical container has radius 20 feet. Honey begins flowing into the tank in such a way…
A: Given: Radius of he hemispherical container is 20 feet. Rate of change of depth is 4 feet/hr. The…
Q: Compute Δy/Δx for the interval [2,6], where y=6x−7 (Use decimal notation. Give your answer to three…
A: Given, The interval [2,6], y= 6x−7 We have to find ∆y∆x and the instantaneous rate of change of y…
Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² I in the…
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Q: Water is leaking out of an inverted conical tank at a rateof 10,000 cm min at the same time that…
A: given that an inverted conical tank leaking the water at a rate of 10,000 cm3/min. And the height of…
Q: The temperature at a point in a ball with conductivity K is inversely proportional to the distance…
A: We know:
Q: The temperature at a point (x,y,z) is given by T(x,y,z)=200e^(−(x^2)−(y^2)/4−(z^2)/9) where T is…
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Q: Water is flowing at the rateof 6 m3/min from a reservoir shaped like a hemispherical bowl ofradius…
A: Given The equation of the volume is V=π3y23R-y Radius of the hemisphere is R=13 m Water flowing…
Q: A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x − x2 ), where x and f(x) are…
A: The given function is f(x)=0.048x-x2
Q: Continuity equation is derived using the law of conservation of mass
A: According to the given information, it is required to tell whether the given statement is true or…
Q: 2. A fish is being reeled in by a fishing line that is moving at a rate of - 4 feet per second from…
A: Assume AC=h be the length of the fishing line, BC=x be the distance of fish from the pole and θ be…
Q: Please show your answer to 4 decimal places. Find the maximum rate of change of the function f(r, y)…
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Q: an open hemispherical container has radius 20 feet. honey begins flowing into the tank in such a way…
A: Let depth be h. Volume of the honey in the container is: Also, radius of circular surface is:…
Q: Find the rate of change of f(x,y,2) = In(x + y + 2) – ryz in the direction from (-1,1,1) to (2,1,5)…
A:
Q: Let f(x, y) = exy and P(1, 0). Determine the derivative of f at the point P and in the direction of…
A: Given fx,y=exy
Q: A rectangle is inscribed in the ellipse 16 x2 + 81 y2 = 1296 Find the rate of change of the…
A:
Q: Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and…
A: Given function is
Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² H in the…
A:
Q: The coordinates of a particle in the metric xy-plane are differentiable functions of time t with…
A: The distance of a point (x,y) and the origin is calculated by d=x2+y2 Given rate of change is,…
Q: Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate…
A: for a constant function f(x) = b average rate of change is zero because function is same for all…
Q: The velocity (in centimeters per second) of blood molecules flowing through a capillary of radius…
A: Consider the velocity (in centimeters per second) of blood molecules flowing through a capillary of…
Q: Find the magnitude of the greatest rate of change of f(x, y, z) = (x2 + z2)3 at (1, 3, -2), and…
A: Consider the provided question,
Q: The temperature at any point (x, y) on a steel plate is T = 500 − 0.6x2 − 1.5y2 , where x and y are…
A: Consider the given function T=500-0.6x2-1.5y2
Q: A right circular cylinder has a fixed height of 4 meters. Find the rate of change of its volume V…
A: Given: A right circular cylinder has a fixed height of 6 m.
Q: A rectangular box has sides of length x cm, y cm and z cm. Sides x and z are expanding at rates of 3…
A: This is a problem of the application of derivative.
Q: A leaky 10-kg bucket is lifted from the ground to a height of 12 m at a constant speed with å rope…
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Q: The velocity (in centimeters per second) of blood molecules flowing through a capillary of radius…
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Q: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?
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Q: Find the rate of change of f(x,y) = In(x +y+ z) – xyz in the direction from (-1,1,1) to (2,1,5) with…
A: Given problem is :
Q: Find the rate of change of the function f(x, y,z) =x^2y + 3xz - 5yz^3 + π, at the point (1, -1,1 )…
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Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…
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Q: Find the direction of the maximum rate of increase of f(x,y, z) = y²sinxz² at the point (0,3, –1).…
A: Given the function f(x,y,z)=y2sin(xz2) And the point (0,3,-1)
Q: Water is being drained at a rate of 50 m3/min from a concrete conical reservoir (vertex down). The…
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Q: Let f(z, y) = ze. What is the maximum rate of change of fat the point (2,0)?
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Q: Show that the average rate of change of the linear function f(x) = a over any interval say [x1,x2]…
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Q: Find the rate of change of f(x,y,2) = In(x + y + z) – xyz in the direction from (-1,1,1) to (2,1,5)…
A: The gradient vector to the given scalar function is:…
Q: A right circular cylinder has a fixed height of 4m. Find the rate of change of its volume V with…
A: Let h and r denote the hieght and radius of base of the cylinder.1
Q: Find the maximum rate of change of the function f(r, y) 4y² at the point (4,2) Question Help: OVideo…
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- How are the absolute maximum and minimum similar to and different from the local extrema?Water is flowing at the rateof 6 m3/min from a reservoir shaped like a hemispherical bowl ofradius 13 m, shown here in profile. Answer the following questions,given that the volume of water in a hemispherical bowl ofradius R is V = (π/3)y2(3R - y) when the water is y meters deep. At what rate is the water level changing when the water is 8 m deep?Water is flowing at the rateof 6 m3/min from a reservoir shaped like a hemispherical bowl ofradius 13 m, shown here in profile. Answer the following questions,given that the volume of water in a hemispherical bowl ofradius R is V = (π/3)y2(3R - y) when the water is y meters deep. At what rate is the radius r changing when the water is 8 m deep?
- A draining hemispherical reservoir Water is flowing at the rateof 6 m3/min from a reservoir shaped like a hemispherical bowl ofradius 13 m, shown here in profile. Answer the following questions, given that the volume of water in a hemispherical bowl of radius R is V = (pi/3)y2(3R-y) when the water is y meters deep. a. At what rate is the water level changing when the water is 8 mdeep?b. What is the radius r of the water’s surface when the water isy m deep?c. At what rate is the radius r changing when the water is 8 m deep? note** I have the answer but I can't understand how to differentiate the volume function in terms of (t) without taking the derivative of r and I've provided a photo with the derivative of tha V function that I can't understand. please explain it step by step and Thank You.A metal storage tank with fixed volume V0 = 360π m^3is to be constructed in the shape of a right circular cylinder (including the bottom) surmounted by a hemisphere. A picture is given below.What dimensions will require the least amount of metal? Show and organize your work; use the firstderivative test or the second derivative test or other tools to check that yours is the desired optimalsolution.The linear density of a cable wire is the rate of change of its mass with respect to its length. A nonhomogeneous cable has a length of 9 feet and a total mass of 24 slugs. If the mass of a section of the cable wire of length x (measured from its leftmost end) is proportional to the square root of this length, Compute the density of the cable wire 4 ft from its leftmost end.
- A point moves around a circle x2 + y2 = 17. When the point is at (1, 4), its x coordinate is increasing at the rate of 19 units per second. How fast is its y coordinate changing at that instant?A rectangle is inscribed in the ellipse 16 x2 + 81 y2 = 1296 Find the rate of change of the area of the rectangle with respect to xRate of Change of Area with respect to x =Water is flowing at constant rate of 120 cc/sec in a hemispherical bowl with radius 18 cm. If the height of water is increasing at 0.20 cm/s, determine how fast is the radius of the surface of the liquid a. 0.1669 cm/s c. 0.1169 cm/s b. 0.6119 cm/s d. 0.6911 cm/s
- 20. Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.08 cm thick to a spherical ball with a radius of 90 cm. 17. A 5m ladder is leaning against a wall. Its upper end is sliding down the wall at a rate of 2m/s. Find how fast the bottom end of the ladder is moving at the point 3m from the wall.a particle is moving along the curve y = 2sqrt(5x+1). As the particle passes through the point (3,8) its x coordinate increases at a rate of 3 units per second. Find the rate of change of the distance from the particle to the origin at this instant.A container which has a shape of cone is full of sand. The container stands point down andhas a fixed top radius 5 cm and height 10 cm. Sand is pouring out of the container at a rate of 10 m3/min. When the depth of the sand is 8 cm., at what rate is the depth changing? Is it increasing ordecreasing?
