Find parametric equations for the path of a particle that moves along the circle x2 + (y − 3)2 = 16 in the manner described. Enter your answer as a comma-separated list of equations. Let x and y be in terms of t. a) once around clockwise, starting at (4, 3). 0 ≤ t ≤ 2?. b) four times around counterclockwise, starting at (4, 3). 0 ≤ t ≤ 8?. c) Halfway around counterclockwise, starting at (0, 7). 0 ≤ t ≤ ?.

Q: Find parametric equations and a parameter interval for the motion of a particle in the xy-plane that…

A:

Q: In each part, find an equation of the sphere with center (5, -6, –3) and satisfying the given…

A:

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: osen y

A: Is it sen y =x

Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

Q: Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

A:

Q: Find the distance of point A(1,0,2) to the plane 3x+y+z=9?

A: Here we have to find the distance from the point A(1,0,2) to the plane 3x+y+z-9=0

Q: In each part, find an equation of the sphere with center (5, –8, –2) and satisfying the given…

A: Given  Centre of sphere is =(5,-8,-2)

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: I Find the Parametric equ. sor he line f intersect of Pae Plan 3X- 6y -22 =15 and 2x+Y 2Z%=5? X-3…

A: 3x-6y-2z=152x+y-2z=5a→=3, -6, -2b→=2,  1, -2a→×b→=ijk3-6-221-2a→×b→=(12+2) i^-(-6+4) j^+(3+12)…

Q: Find parametric equations for the complete parabola x = y2. Answersare not unique.

A:

Q: Show that the parabolas $r=c /(1+\cos \theta)$ and $r=d /(1-\cos \theta)$ intersect at right angles.

A:

Q: In each part, find an equation of the sphere with center (2, –3, –3) and satisfying the given…

A:

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1:2x – y…

A:

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: Line of intersection

Q: In each part, find an equation of the sphere with center (1, – 7, –8) and satisfying the given…

A:

Q: Sketch the xy-trace of the sphere whose equation is (x−3)2 +(y−2)2 +(z+4)2 =52.

A: We can find the xy trace by setting z = 0 in the original equation.

Q: Find a parmetric equation that describes the entire set of points (x,y) such that 4x2-9y2=36

A: The given curve can be represented in a different manner as shown on the whiteboard.

Q: Q2: A cube of edge 24mm is resting on the top of a frustum of cone of base diameter 60mm and top…

A: We are asked to draw the isometric view of the solid.

Q: Find a parameterization of the line formed by the intersection of the following planes: 1:2x-y+3z 1…

A:

Q: Find parametric equations for the path of a particle that moves along the circle æ² + (y – 1)² = 4…

A: As per our guidelines we are supposed to solve only one question. For the first question follow the…

Q: Without eliminating the parameter t, find a Cartesian equation for the lin curve C, defined by the…

A:

Q: Let S be the quadric with equation 36x² – 4y? – 9z2 – 36x = 0 - - (a) Classify the graph of S. (b)…

A:

Q: find the distance from the point to the plane. (0, 1, 1), 4y + 3z = -12

A: we have to find the distance of the point (0,1,1) from the plane 4y+3z=-12.   as we know that the…

Q: Which of the following point is the closest point on the sphere z² + y² + z² = 4 from the point…

A: Given Equation of Sphere X2+y2+z2=4 And point (3, 1, -1)

Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

A:

Q: Determine the location of a point (x, y, z) that satisfies the condition z = −5

A: The condition is z = −5

Q: In each part, find an equation of the sphere with center (−3, 5,−4) and satisfying the given…

A: Consider the given: a) Tangent to the xy−plane:x−−32+y−52+z−−42=−42x+32+y−52+z+42=16

Q: Find the distance between the skew lines with parametric equations  x = 1 + t, y = 3 + 6t, z = 2t,…

A:

Q: Find the parametric and symmetric equation for the satisfying the given condition. 1. Through the…

A:

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

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: Given the planes 3.x – 6y – 2z = 15 and 2x + y – 2z = 5 anser the following. (b) Find parametric…

A: I have solved using an intersection point and direction ratios

Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x –…

A: Cross product of normals of planes is normal to the required line of intersection

Q: In each part, find an equation of the sphere with center (5, –8, –4) and satisfying the given…

A:

Q: . (a) Show that as (x, y)→ (0, 0) along any straight line y = mx, or along any parabola y = kx², the…

A: Given : f(x) = x³y/(2x^6+y²)  To find : To prove that limit exist along parabola

Q: Find Parametric efuatins for the lines - The line through (1-2-2) Paralle tothe(Z)-axis.

A:

Q: Sketch the xy-trace of the sphere whose equation is (x+3)2 +(y−1)2 +(z−3)2 =18.

A:

Q: What kind of conic section is given by the quadratic form ? -11x,? + 84x,x2 + 24x2? = 156 Transform…

A: Given quadratic form is-11x12+84x1x2+24x22=156The above conic is determined and transformed to…

Q: Determine the set of points satisfying the condition described by |z – 3| + |z + 3| = 10 Then…

A:

Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x -…

A:

Q: Verify algabraically whether the parametric equation x(t) = 10-2.5t, y(t) = 1.5t and the rectangular…

A:

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: 2)as per our guideline we have to write one question at a time kindly repost remaining questions

Q: Find parametric equations for the path of a particle that moves along the circle x 2  + (y - 1)2…

A: A particle that moves along the circle .

Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: Find the points PCo10,0),Q Ce,2,0) and RCOl- thal- 2I to the line: the Line in the Plane of passes…

A:

Q: Find a set of parametric equations for the rectangular equation that s y = 2x – 3, t = 0 at the…

A: let x = t + a put all the given points to find out the value if a x = 4 and t = 0 4 = 0 + a a = 4 so…

Q: For Exercises 35-42, use the results of Exercises 27–30 and use the parameter t to write parametric…

A: we have to find the parametric equation of the given curve by using the parameter t. the given curve…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.