5. In the standard (x, y) coordinate plane, the midpoint of LM is at (4, –4) and L is at (1,3). What is the y-coordinate of M ?

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A:

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A: We have to choose the correct answer

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Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

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A: see below the answer and calculation

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A: We have to solve

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A:

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A:

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A: Let the 2 points in the line segment be,

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A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

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A: answer is in next step . please give a like !!

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A: Use line integral

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A:

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A: first we shall find equation of line then find distance from line of that point

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A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

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A:

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A: The length of the curve is given by:

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A:

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

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A: Given that level curve of a function z=f(x,y) consists of straight lines.

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A: Using the parametric equation of the curve C.

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Q: 2. Find for x? +x+ y? +2 3xy the lines that are tangent and normal to the curve at point (3,2).

A:

Q: 6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented…

A: region of integration is part of circle, x2+y2=7, lying in 3rd quadrant, thus, limits of x,y are -7…

Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: | 6. Let y = 3 and u = . Compute the distance from y to the line through u 1 2 and the origin.

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A: Let I is the value of given Line Integral.

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Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

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Q: and V is the dosed by the Planes x=0, y=O, ニこ

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Q: Evaluate (x-y+z-2)ds where C is the straight-line segment x=t, y= (1-t), z=1, from (0,1,1) to…

A:

Q: 11. Find the distance between the point (1,0,-1) and the line x = 5 – t, y = 3 t, z = 1 + 2 t.

A: 11) The direction ratio of the lines  = -1,3,2 The direction ration of the point (1,0,-1) and the…

Q: 3. Find the length of the curve y = x - In a, 1< x < 4.

A: Note: According to bartleby we have to answer only first question please upload the question…

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Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance