Exercises Find parametric equations for the line tangent to the curve of in- tersection of the surfaces at the given point. 1. Surfaces: r + y + 2z = 4, I=1 Point: (1,1,1) 2. Surfaces: ryz = 1, r + 2y + 3z? = 6 Point: (1,1, 1) 3. Surfaces: r? + 2y + 2z = 4, y =1 Point: (1,1, 1/2) 4. Surfaces: r+ y? +z = 2, y = 1 Point: 5. Surfaces: + 3ry +y + 4ry (1, 1. 3) 2 = 0, 1 + y + 2 = 11 Point: 6. Surfaces: r + y = 4. 2+ y -z = 0 Point: (2, 2. 4) 7+ y - z = 0 Point: (v2, 2, 4)

Q: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

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Q: Find parametric equation for the lines .. The line through (0, -7, 0) perpendicular to the plane x +…

A: A parametric equation of a line can be written if a point on the line is given and a vector parallel…

Q: Find the parametric equations of a vertical line through point (0,9). Assume v = 0 corresponds to…

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Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 42² = 4…

A: To find: Parametric equation of the Intersections of the curves  4x2+y2+4z2=4 and y2=x2+2z2.

Q: III. Find a set of parametric equations for the curve of intersection of the cylinder (x-1)² + ² x²…

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Q: 31. (a) Show that the parametric equations x = x, + (x2 – x1)t y = yı + (y2 – yı)t where 0 <t< 1,…

A: Given data: The first parametric equation is x=x1+(x2-x1)t. The second parametric equation is…

Q: Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric…

A: Solve for tan t and sec t from the given equations.

Q: Find parametric equations for the line through the point (0, 2, 3) that is perpendicular to the line…

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Q: Let P be the point with Cartesian coordinates (6,9), and C be the plane curve with parametric…

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Q: Find parametric equations and a parameter interval for the motion of a particle that starts at (a,…

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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…

Q: Find the cartesian equation for the curve that the points of the parametric equations x(1) = In t,…

A: (a) Given the two parametric equation:- x(t) = lnt............(1) y(t) = ln(2t)............(2) Now…

Q: a) Find parametric equation for the line of intersection of T1 : x + 2y – z +1 = 0 and TT2 : 2x – y…

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Q: Find parametric equations for the tadgent line to the curve with the given parametric equations at…

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Q: a) Find the parametric equations for the line tangent to the curve of intersection of surfaces at…

A: To find the parametric equation of the line tangent to the…

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² +: 4 the…

A: We will use trigonometric identity  sin2t+cos2t=1 and parametric form of standard ellipse to find…

Q: Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve.…

A: To sketch the parametric curve and eliminate the parameter , to find the Cartesian equation of the…

Q: Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric…

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Q: a)Find the equation of the tangent line to the curve and find a set of parametric equations for the…

A: To find the tangent equation of the line to the curve of intersection of both the given surfaces at…

Q: find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Exercises Find parametric equations for the line tangent to the curve of in- tersection of the…

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Q: Consider the following parametric equations. x = -t +3 y = 4t – 3 te (-00, 00) a) Find four unique…

A: The given parametric equations are: x=-t+3y=4t-3t∈(-∞,∞) (a) We need to find four unique points on…

Q: Find parametric equations for the line described below. The line through the point P(2, 5, 0) and…

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Q: Given two points P(6,3, 1) and Q(5,0,0), find the parametric equations for a smooth curve, C:x = 5+…

A: C : x = 5 + z        y  = 3z^2

Q: A line with parametric equations x = 10 + 2s, y = 5 + s, z = 2, seR, intersects a sphere with the…

A: The solution of given problem as follows :

Q: Find parametric equations for the line through the point (0, 2, 2) that is parallel to the plane x +…

A: Here we have to find the parametric equation of the line through the point 0,2,2 that is parallel to…

Q: Find a set of parametric equations for the line passing through the point (2, 0, 4) that is parallel…

A: To find a set of parametric equations for the line passing through the point 2, 0, 4 that is…

Q: nd a set of parametric equations for the line passing through the point (1, 0, 9) that is parallel…

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Q: What is the parametric equation for the line through the point (1,2,3) parallel to the y- axis? (a)…

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Q: Find parametric equations for the line through the point  (0, 2, 2)  that is perpendicular to the…

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Q: 24) Consider line L of parametric equations x =t, y = 2t, z = 3, t E R. a. Find parametric equations…

A: The given line is: x=t, y=2t, z=3 and t∈R Now, consider the angle θ between two intersecting plane,…

Q: Find the distance between the point (2, 3, 2) and the line given by the set of parametric equations…

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Q: A- The level surfaces f(x, y, z) = x² + y² + z² 11 = 0 and the plane g(x, y, z)= x+y+ Z- - 5 = = 0…

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Q: O Given two points P(6,3,1) and Q(5, 0,0), find the parametric equations for a smooth curve, C:x =…

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Q: Find parametric equations for the line tangent to the curve of the intersection of the surfaces x +…

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Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A: Given parametric equations, x=et,y=e3t+4 To find y.

Q: What is the parametric equation for the line through the point (1,2, 3) paralkel to the y- axis? (a)…

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Q: I Let C be the line segment from A(0,-3) to B(-4, 1). a) Sketch the graph of C, and find parametric…

A: The parametric equation of a line includes a real parameter t. It is of the form  x=xt,y=yt A line…

Q: Find the parametric equations for the line of intersection of the planes x+y+z= 3 and 2:z-3y = 6.…

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Q: (a) Find parametric equations for the line through (5, 2, 4) that is perpendicular to the plane x -…

A: answer is in next step.

Q: What is the rectangular form of the parametric equations? z(t)=t-3, y(t) = 2t2-1, where t is on the…

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Q: Consider the surface defined by the equation z2 = 2x² + 4x - 6y? - 2y+ 1. %3D Find a set of…

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Q: Find the area of the surface obtained by rotating the curve of the following parametric equations…

A: We need to find surface area.

Q: It can be shown that the parametric equations x = x1 + (x2 – x1)t, y = y1 +(y2 – yı)t, where 0 <t 1,…

A: Given: Parametric equation of line segment joining the points P1x1,y1 and P2x2,y2 is given as…

Q: Determine any differences between the curves of the parametric equations. (a) x = t y = 9t + 8 (b) x…

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Q: It can be shown that the parametric equations I = x1 + (x2 – r1)t, y = Y1 + (y2 – Y1)t, where 0 < t…

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Q: Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line…

A: Topic - equation of line

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.