Consider the level surface 3x?y + 14z° = 3, the angle in degrees that the z-axis makes with the tangent plane at P(1,-3.67,1)

Q: Find the equation of the tangent plane Pr to the surface S: x2 + y? +z² = 9 at (2, –1, 2)

A: The equation of the tangent plane to the surface f(x, y, z)=0 at a, b, c is defined as: fxa, b,…

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find an equation of the plane tangent to the following surface at the given points. zexy; (1,0,1)…

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Q: The horizontal tangent plane of the surface z = 2x² – xy – y² + 6x – 6y – 2 is given by the equation…

A: Consider the given equation. z=2x2-xy-y2+6x-6y-2 Find the derivative with respect to x and y.…

Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? + z? = 25 at the point…

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Q: Find the point(s) on the surface z = 3 − x2 − y2 + 6y, at which the tangent plane is horizontal.

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Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

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Q: find an equation for the plane that is tangent tothe given surface at the given point. z = ln (x2 +…

A: The given function is It can be written as as the given function has both variables x and y.

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y?, (6,…

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Q: Find the angle of inclination 0 of the tangent plane to the surface at the given point. x² + y² =…

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Q: 3. Find the equation of the tangent plane and normal to the surface z =x? +y? + 4 at point (1, -1,…

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Q: Given the surface x²y + y° z+ z?x = 38. Find the normal line and the tangent plane to the given…

A: A detailed solution is given below.

Q: Find an equation of the tangent plane to the surface defined by the equation zf(x, y) + 2³ = 3 at…

A: The given surface is:zf(x, y)+z3=3The point is (-1, 2, 3)

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = √(y - x),…

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Q: Find the angle of inclination of the tangent plane to the surface 2xy − z3 = 0, at the given point…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y?,…

A: Solving tangent equation

Q: Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in…

A: Let's find.

Q: Given a surface, ƒ(x,y,z)=15, explain what you would do to find the equation of the tangent plane at…

A: Nothing

Q: Find the angle of inclination 6 of the tangent plane to the surface at the given point. x2 + y2 =…

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Q: Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: The line joining P1,0 and Q0,1 is     x-11-0=y-00-1=t(say)⇒x=t+1,y=-t⇒dx=dt,dy=-dt

Q: At which of the points below is the tangent plane to the surface x² – 2y + z + yz = 2 vertical?…

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Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

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Q: Find the equation of the tangent plane to x² the surface z = + y? 4 - at the point (2, 3, 10) x + 6y…

A: The equation of the tangent plane to a surface f(x,y,z) is given by:

Q: Find the angle of inclination of the tangent plane to the surface at the given point. x² + y² = 5,…

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Q: At which of the points below is the tangent plane to the surface z - 2y + z?+ yz = 2 vertical?…

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Q: Find the point(s) on the surface at which the tangent plane is horizontal. z = 9 - x2 - y? + 4y (х,…

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Q: Find the equation of the tangent plane to the surface determined by z'y' + z – 25 = 0 at z = 4, y =…

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Q: ind the angle of inclination of the tangent plane to the surface at the given point. (Round your…

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Q: At which of the points below is the tangent plane to the surface - 2y² + z²+ yz = 2 vertical? Select…

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: Find the tangent plane to the surface z = 9 – x* – y? at the point (1, -3, –1).

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Q: Find the equation of the tangent plane Pr to the surface S:x2 +y? + z2 = 9 at (2,-1, 2)

A: To find :Equation of tangent plane to the surface x2+y2+z2=9 at the point (2,-1,2).

Q: . Show that the tangent plane to the surface 2yyo cz at the point P(xo,Y0, zo) is given by the 2rro…

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Q: Prove that the curve given by the equations x=R(cost+tsint),y=R(sint−tcost) is the involute of the…

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Q: How many square units is the area of the surface obtained by rotating the curve y = V4-z, 0 <I<2…

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Q: Find an equation of the tangent plane to the given surface za² + y² +1 at (1,1,3).

A: Given equation of the surface is  z=x2+y2+1 We have to find the tangent plane of the given surface…

Q: 2. At what point on z = a? + y? is the tangent plane parallel to 3.r – 4y + z = 7 ?

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Q: At which of the points below is the tangent plane to the surface r2 – 2y? + z2 + yz = 2 vertical?…

A: From the tangent plane to a surface

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In V x2 + y², (6,…

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Q: (b) Find the point that makes the tangent plane to the surface z = x- xy +y-2x + 4y horizontal.

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Q: Find the equation of the tangent plane to the given surface at the point (0,-1,2). y = 2x2 – z2 O y…

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Q: Find the equation of the tangent plane to the surface x?+ Qy?-322=3' at (2-1,1) x²+ 2y 2-322=3'at…

A: Equation of a tangent plane

Q: Show that the tangent plane to the surface x 2 a 2 + y 2 b 2 = cz at the point P(x0, y0, z0) is…

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Q: Find the equation of the tangent plane to the surface determined by a'y + z- 55 = 0 at a = 4, y = 3.…

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Q: Find the equation of tangent plane to the surface x? + 2y? + 3z2 = 21 which is parallel to the plane…

A: equation of the tangent surface of  F= x2+ 2y2+ 3z2= 21   which is also parallel to the plane…

Q: Find the angle of inclination of the tangent plane to the surface 3x2 + 2y2 − z = 15, at the given…

A: We have given surface 3x2+2y2-z=15 at point (2, 2, 5)   We have to find the angle of inclination…

Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? +z? = 25 at the point…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.