Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22 = 4 and y? + 2z2 = 4 ?

Q: Explain why the curve of intersection of the surfaces x + 3y? – 2z2 + 2y = 4 and 2x? + 6y? – 4z2 –…

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Q: The slope of the surface z = xy² in the x-direction at the point (2, 3) is _____, and the slope of…

A: Given:z=xy2   x-directionat the point 2, 3 y-directionat the point 2,3

Q: calculate the length of the curve y=2cosh (x/2) for 0 < x < 2

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Q: Sketch the region in the xy-plane defined by the equation or inequalities. (a) -1sys3 (b) |지 < 4 and…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: Sketch the surfaces 1. 9x2 + y2 + z2 = 9  2. 4x2 + 9y2 + 4z2 = 36

A: Using graphing calculator to graph them. 9x^2 + y^2 + z^2 = 9

Q: 2 The length of the curve y = 312 between x = 0 and x = 1 is 3 %3D %3D

A: Answer is 4√2/3 unit.

Q: Find the points on the surfaces z = V² + y? and z = 2 – x/2 having the shortest distance to the…

A: We know that the two given surfaces will intersect at some curve whose equation can be obtained by…

Q: Find the length of the curve y 2ln(x) from x 1 to x =4. %3D

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Q: The length of the latus rectum of the curve x² – 12y = 0 is -12 -3 Option Option 2 12| 3.

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Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

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Q: Evaluate the length of the curve x = 5 - y+1,0<y<3

A: Given, x=5-y+1 ,     0≤y≤3

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y x2 for -2 < x<…

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Q: The intersection between the surface x + y + z = - 1 and the circle x2 + y2 = 1,z = 0 is

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Q: solve for the point on the graph y=√3x+ 2 that is closest to (3,0). What is the minimal distance…

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Q: 4- Find the length of the curves in Exercises. 1. y = (1/3)(x² + 2)³/2 from x = 0 to x = 3 3. x =…

A: for a function of the form y=f(x) length of the curve from x=a to x=b is: L=∫ab(f'(x))2+1dx and for…

Q: Determine equation of tnagent line to the common curve of 2 surfaces w/ equations: z = x? + y – 2xy…

A: follow next step

Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

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Q: Describe the level surfaces for f (x, y, z) = y+10-√√x² + z² and sketch them for several (at least…

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Q: 4- Find the length of the curves in Exercises . 1. y = (1/3)(x² + 2)³/2 _from x = 0 to x = 3 3. x =…

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Q: Find the length of the curve. ¹) x = ¹ y 3/2 - y 1/2 from x = 1/2 from 4) 3 5) x x= 16 to x = 25 =…

A: If a function y=f(x) is defined on interval [a,b] the length of the curve is given as - Length (L)=…

Q: Find the total length of the loop of the curve 6y² = x(x – 2)² between x = 0 and x = 2. %3D

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Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: The first car A moves in the northern direction at a speed u(mph), and the second car B moves to the…

A: The first car A moves in northern direction i.e. towards positive y-axis and the second car B moves…

Q: Find the exact lengthy curve x=y4/4 + 1/8y2, where 1 is less than or equal too y is less then or…

A: The formula is L = ∫ab 1 + dxdy2dy

Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: What is the shortest distance from the surface xy +12x +z^2 =144 to the origin?

A: To find the shortest distance from surface xy +12x +z2 =144  to origin.

Q: Find the minimum distance from the point (-6, -6, 0) to the surface z = O√√559 O 3√61 09 O√773 O√69…

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Q: The equation of the line tangent to the intersection of two surfaces 2 = a2 and z 25- y? at the…

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Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

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Q: Compute the length of the curve x = 2y3 + 1/(24y) from y = 1 to y = 3.

A: Given: x=2y3+124y1≤y≤3

Q: Find the areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

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Q: FIND THE LENGTH OF THE CURVE 9y = x(x – 3)´ from X = 1 to x = 4 %3D 10

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Q: What is the maximum vertical distance between the line y = x + 42 and the parabola y = x for -6 s xs…

A: Consider the equation y=x+42 and y=x2; -6≤x≤7. Substitute y=x+42 in y=x2.…

Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

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Q: Find the exact length of the curve x=y4/4 + 1/8y2 where 1 is less than or equal too y is less than…

A: Given that           x = y4/4  + 1/8y2 , 1&lt;= y &lt;= 2 Here we have to find the exact length of…

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for -1 <x<…

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Q: is the condition such that the straight lines joining the origin to the other two points of…

A: Given: Curves equation   ax2+2hxy+by2+2gx=0a'x2+2h'xy+b'y2+2g'x=0

Q: 7. Find the angle of intersection between the curves y = x + x-8 and y = x

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Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

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Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

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Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.

Q: Find the area of one side of the “winding wall” standing orthogo-nally on the curve y = x2, 0 &lt;=x…

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Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: 5. Find the length of the curve y = 2(2+ x)², 1<x<8 %3D

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Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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Q: 4- Find the length of the curves in Exercises. 1. y = (1/3)(x² + 2)³/2 _from x= 0 to x = 3 3. x =…

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find