Problem 16 Find the dimensions of the rectangular box of maximum volume that can be inscribed inside the sphere x2 + y? + z2 = 4.

Q: Find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme values.

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Q: Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z2 +…

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Q: A mirror is shaped like a paraboloid of revolution and will be used to concentrate the rays of the…

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Q: QUESTION 3. Maximize xyz on the ellipsoid

A: I am doing first question

Q: Show that when a satellite is in elliptical orbit, its speed V is given by v² = k = k ( ² − ²) and…

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Q: Find the points on the ellipse 2x + 4y = 1 where f(x.y) = xy has its extreme values.

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Q: 9. Explain in your own words how to decide what kind of conic it is if you have the equation Ax? +…

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Q: Problem 8. Use the Lagrange Multiplier method to compute the extreme values of the function f(x, y)…

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Q: PROBLEM 2 • Obtain a DE of the family of parabolas with axis parallel to x-axis. Draw some…

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Q: 15 Problem 2: Find the area of the surface generated by revolving the curve x = 2/4- y, 0 < y< 4…

A: Given curve x=24-y ,0≤y≤154 revolving around y-axis Find the area of the surface

Q: Describe in words the level curves of the top half of the sphere x2 + y2 + z2 = 1.

A: Top half of the sphere will be a hemisphere.

Q: Find the center and the radius of the sphere. x2+y2+z2+4x-5z=0

A: Comparing with standard equations of sphere,

Q: Problem 8 udi. Consider the surface z- f(z, y) whose level curves are below (some of which are…

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Q: Question 4 The equation ( x - 2) 2 + (y2 + 5) 2 + (z - 1) 2 = 16 represents a: O parabolic cylinder…

A: As we know that equation of sphere is (x-h)2+(y-k)2+(z-g)2=r2  centered at the point (h,k,g) As per…

Q: Question 1 Determine the convexity/concavity property of the following: (ii) f(x, y) = 2x² – y?

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Q: 5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ²…

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Q: In Problems 69 and 70, find an equation of a sphere with radius rand center P0 .69. r = 1; P0 = (3,…

A: Given: 60. r=1; P0=3, 1, 170. r=2; P0=1, 2, 2 To Find: Equations of the given spheres.

Q: Find the length of a,b,c of the given hyperbola: x^2/4 - y^2/5=1

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Q: Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed…

A: Let the dimension of such a rectangle be 2x by 2y. Clearly (x, y) is point on the ellipse.

Q: Given hyperbola   (y + 1)2   −   (x − 2)2   = 1       9                4         what will its…

A: Given: An equation of the hyperbola, y+129-x-224=1.

Q: Problem 1. Find F.n dS if S is the sphere (x-1)+y+z =1 and F(x, y,z)= (x², x²y, zy³).

A: given sphere  x-12+y2+z2=1 and Fx,y,z=x3,x2y,zy2 to find ∫∫SF·n dS

Q: Given : The region is bounded by the curve y=4x-x^2, y=4 and the y-axis Problem : The intersection…

A: We have to determine the points of intersection of the given curves and find the value of a+b+c.

Q: Question 24 Fit a least-squares parabola having the form y = a + bx + cx- to the given data. 1.2 1.8…

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Q: Problem 4: For what valnes of a and o s the line y=-2x+b tangent to the parabola y=Ox° whern X=2?

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Q: Problem 8 Consider the surface z = f(x, y) whose level curves are below (some of which are labeled)…

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Q: Q.2. Show that the area of the ellipse =1 is z ab. ab

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Q: Given hyperbola   x2   −   y2   = 1   9         16       how do you determine the focal length?

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Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: Find the radius and center of the sphere described by 3x2 + 3y2 + 3z2 + 6x – 6y = 3.

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Q: Let S CR³ be the portion of the graph of the cone z2 = x² + y? which satisfies 0 s z < 1. Using…

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Q: 4x² – 25y² – 24x+250y+ v² –11x+5y-3=0 13. 14.

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Q: Question 17 Find the point on the parabola y= - x¯ whose tangent line is parallel with y= 3x-5 +4 3…

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Q: In problems 1 and 2, find any intercepts with the three coordinate axes and sketch a graph of the…

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Q: Question 12 Calculate the area of the smaller region (to the left of the parabola) bounded by…

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Q: Question 3: Use Lagrange Multipliers to find the absolute maximum value and absolute minimum value…

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Q: Problem 2: Let F be the 3-dimensional figure whose base is the region bounded by the circle a? + y =…

A: Given the region bounded by the circle x2+y2=9. The height of the cross-section is 3-x and its…

Q: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: In each of Problems 14 through 18, determine whether the given boundary value problem is…

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Q: The hyperbola with vertices at (0, 3) and (0, – 3) and foci at (0, 5) and (0, – 5) has the equation…

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Q: It has been shown that when like particles with a common charge are hurled at each other, they…

A: Let's find.

Q: An isosceles triangle with vertex at (0, -1) is to be inscribed in the ellipse x² + 4y2 = 4. Find…

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Q: Problem #1:x =- Vy (y – 3); 1 <y< 9

A: Given:  x=13yy-3; 1≤y≤9 To Find:  a To graph the given curve.b To determine the arc length of the…

Q: A flashlight is shaped like a paraboloid, so that if its light bulb is placed at the focus, the…

A: Given :  The paraboloid has a depth of 1.8 in  and the diameter on its surface is 6 in .   Schematic…

Q: Problem 1 Find the point on the sphere with radius 99 centered at (0,0, 0) that is closest to the…

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Q: Find the area of the fundamental rectangle of the hyperbola. x2 − y2 − 6x − 8y = 8

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Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: Given that a person shoots a basketball overhand from a position 8 feet above the​floor, then the…

Q: If the two spheres (x-4)^2+(y-1)^2+z^2=27 and (x-13)^2+(y-10)^2+(z+9)^2=a are externally tangent to…

A: Consider the given two spheres x-42+y-12+z2=27 and x-132+y-102+z+92=a are externally tangent to each…

Q: Problem 2 A surface in R3 is defined by the equation z2 +1 = x² + y?. Sketch the intersection…

A: Given, z2+1=x2+y2.   XY trace: Put z=0, we get x2+y2=1. It is a circle with a unit radius and…

Q: 1-cube 2-cube 3-cube 2.(a) What are the numbers of vertices (corners) for the N-cubes you drew in…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…