1. (Section 15.6) Consider surface S: 4x² + y² + 4z² = 100. (a) Draw a well-labeled graph of surface S. (b) Find the equation for the tangent plane to S at point P(3,0,-4) ax+by+cz = d format.

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A: The given surface x216-y29+z2=-1. We have to sketch the graph of the surface.

Q: (6) Let -1 3 1 y = 2 and uj = -1 u2 -1 -2 Find the closest point to y in span{u1,u2}. What is the…

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Q: Without using a graphing utility, sketch the surface with equation x2 + y2 − z2 = 0.

A: Surface with the equation

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: Sketch or describe the surfaces in R³ of the equation presented x² + y} – 2x = 0

A: The equation is x2+y2-2x=0

Q: Find a parametric description of the line segment with endpoints P(-1,3) to Q(3,-2)

A: The line segments with endpoints P(-1,3) to Q(3,-2)

Q: 9) Sketch the graph of the equation y² +2²=1 and correctly identify the surface.

A: Given: The equation is y2-x24+z2=1. To sketch: The graph of the given equation. To identify the…

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,…

A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…

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Q: Find a parametric equation for the line through the point (6,5, - 3) and perpendicular to the plane…

A: Given plane is, 7x+4y+4z=15 Since, the line is perpendicular to the plane then the normal vector…

Q: Can you please help me question 1? parts a, b, c and d please.

A: Step 1:Step 2:Step 3:

Q: Sketch the curve (x2 + y2 )3 =4x2y2 by converting to polar coordinate system

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Q: Let S be the quadric with equation 36x² –4y² –9z² – 36x = 0. Sketch a graph of the surface with…

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Q: 6. Sketch the graphs of the following equations and identify the surface: (a) x² - 16y² = 4:² (b)…

A: (a) The equation x²- 16y²= 4z² is the equation of an hyperboloid of one sheet. To visualize the…