Find the area of the following surface using a parametric description of the surface.   The cap of the sphere x2 +y2+z2=25 for 2≤z≤5

Q: Evaluate sin³ x cos²x dx.

A:

Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

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Q: The graph of x2+y2+z2-14y=0 is a sphere. what are the center and radius of the sphere?

A: Given    Equation of sphere  x2+y2+z2-14y=0To calculate:-     Center  and  radius  of the sphere.

Q: Identify and sketch the surface 9x² + y² − 2z² — 18x - 4y - 12z - 9 = 0. - Explain the position and…

A: The given surface is: 9x2+y2-2z2-18x-4y-12z-9=0. The given equation can be written as:…

Q: Find the center of the sphere x² + y? + z? + 4x – 8z + 19 =

A: To find the center of the equation from the given equation.

Q: Consider the equation 4x² - 3y² + 12z² = -12. Describe the traces of this surface on the xy-plane,…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: Identify and sketch the surface r+y +- 2r +2 = 0.

A: Answer

Q: In which variable(s) should you complete the square to identify the surfacex = y2 + 2y + z2 - 4z +…

A: We have to determine which variable should we complete the square to identify the surface…