Find the maximum and the minimum values of f(x.y.z) = 4x - 5y + 3z on the sphere x +y° +z? = 50. %3D The maximum value is (Simplify your answer.)

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A: We have to find maximum value for a sinusoidal function.

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Q: y? Assume you are given the surface S with equation p2 9. 1.

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A: Consider the provided question,  minimize and maximize, fx,y,z=x2+y2+z2                        ....1…

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A: General equation of sphere  (x-h)2+(y-k)2+(z-p)2 = r2  center (h,k,p)  radius = r

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A: Use equation of ellipse to compare then find point of tangency

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Q: Q1/ (A) If w= (x?+yz+Z?). Find m such that W = Wxx + Wyy + Wzz=0 Ans. n= -//2 %3D (B) Use Lagrange…

A: (A) Let w=x2+y2+z2m ⇒wx=∂∂xx2+y2+z2m⇒wx=mx2+y2+z2m-1∂∂xx2+y2+z2⇒wx=mx2+y2+z2m-12x Now find wxx.…

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Q: No. of integral points lying inside the parabola y² = 8x and circle x? + y? = 16 are %3D (A) 15 (B)…

A: To find  The number of integral points lying inside the parabola y^2=8x and the circle x^2+y^2=16.

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A: A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the…

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A: Given:     f(x,y,z) = 4x2 + z2      Point: ( 1 , 2 , 3 )

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Q: The diagram below shows a rigid motion. Solve for x and y. 2y 97° 2x + 6

A: here we have AB=2y BC=4 PQ=2x+6 QR=x

Q: Find two values of d such that the line 2x + y = d is tangent to the ellipse 4x2 + y? = 36. Find the…

A: follow next step

Q: H.W: Find the center of mass- a thin Plate af deusity S=3 bouuded the by lines X- o, y=x iad the…

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Q: Q6) (Lagrange Multipliers) to the origin Find minimum distance from the surface r? – y – 2? =1

A: The solution is given below in the next step:

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Q: Maximise -x2 + 0.6x - y² + 0.4y using only points within the sphere z² + y² < 1 .What is the value…

A: Solution: Let the given function is fx,y=-x2+0.6x-y2+0.4y    ......(1) Domain is x2+y2≤1

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Q: Q#2. The temperature (in degrees Celsius) at a point (x, y) on a metal plate in the xy- 5ху 1+x² +y²…

A: differentiate the given function partially w.r.t x ∂ /∂ x (5xy1+x2+y2 ) Treat y as a constant Take…

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Q: 3. Refer to the equationf(x) =acos 5+c +dto answer the the question. Changing the parameter changes…

A: The given function is: f(x)=acos2πb(x+c)+d

Q: What is the maximum value for a sinusoidal function having a midline y = 3 and a minimum at -1? (A)…

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Q: Let f(x, y) = x? + 4y. Find the extreme values of f on the ellipse x? + 2y? = 1.

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Q: Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse x² 1² +…

A: The solution is given below

Q: Use the method of Lagrange multipliers to solve the following applied problem. Find the minimum and…

A: Let O be the origin and Px,y be any point on the ellipse, x2+xy+2y2=1. Then, OP=x-02+y-02=x2+y2. To…

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