5 equally spaced holes on an 80mm pitch circle diameter. Calculate their co-ordinates relative to axes Ox and Oy in (a) polar form, (b) Cartesian form. calculate the shortest distance between the centres of two adjacent holes.

Q: The propellers for a toy boat are manufactured by stamping out a rose with n petals and then bending…

A:

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

A:

Q: Use the parametric equations of an ellipse, æ = 2 cos(0), y = 5 sin(0), 0 < 0 < 27, to find the area…

A: Given :  x=2cos(θ), y=5sin(θ),  0≤θ≤2π The area under the curve can be written as:…

Q: snip

A: Polar system is a two-dimensional system . "r" is the distance of the point from the origin .  θ is…

Q: Graph the surface whose spherical equation is p = 1– sino.

A: We use maple software to graph the given surface.

Q: Two points in the xy plane have Cartesian coordinates (2.00, -4.00) m and (-3.00, 3.00) m. Determine…

A: Distance between two points is given as:…

Q: express in polar coords with: Cりり me point whose Ty-Coords are a.r>o and OsoL2

A: Introduction: The polar coordinates r,θ of rectangular coordinates (x,y) in two-dimensional…

Q: Write a polar equation for the conic with the given characteristics. e = 1.6; directrix: y = 4 6.4…

A: Given :  Eccentricity,   e=1.6       and  Directrix,         y=4

Q: Use the parametric equations of an ellipse, x=4cos(theta), y=3sin(theta), 0 less than or equal to…

A:

Q: Under what conditions can you find the length of a curver = ƒ(θ), a ≤ θ ≤ b, in the polar coordinate…

A: step 1 :           Conditions to find the length of the curver = f(θ) , ∝ ≤ θ ≤ B* The curve r =f(θ)…

Q: Cannot solve

A: To convert rectangular equation into polar equation put x = r cosθ and y = r sinθ then rearrange the…

Q: Find parametric equations and a parameter interval for the motion of a particle starting at the…

A: Given,

Q: 2. What can you infer from the axioms and illustrations of the three-line and four-line geometries

A: Sol

Q: Ма Find the polar coordinates of the point whose rectangular coordinates are (-V3,3) and then show…

A: The given coordinate is  (x, y) = (-3,3)

Q: Find the distance between the two points (2, 0.5), (7, 1.2) in polar coordinates.

A: Here, we have given two points in the cartesian coordinate system (x, y). So,…

Q: i) Find the solution of Vu O in spherical co-ordinates.

A: The given Laplace's equation is,∇2u=0Now this equation can  be written as in the spherical…

Q: Give two pairs of parametric equations that generate a circle centeredat the origin with radius 6.

A: Given- A ciecle centered at origin and radius 6. To find- the two pairs of parametric equations.…

Q: Find parametric equations for a circle of radius 2, centered at (3, 5).

A: Solution:Given    radius of the circle=r=2centre of the circle(h,k)=(3,5)To find the parametric…

Q: Find the slope of the tangent line to the graphof the polar equation 1 TU r = at Ø 1-sino 6

A:

Q: 23) convertthe Polar Coordinate (3,315) to rectaugular coondinate

A:

Q: Find two pairs of polar coordinates, with 030< 2n, for the point with the given rectangular…

A: For  the given rectangular coordinates  (x, y) = (1,-3) Polar coordinated for smaller and larger r…

Q: 9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere…

A: Given :  The equation ρ = 2 a sin ϕ  cosθ  .   To determine: The equation ρ = 2 a sin ϕ  cosθ  in…

Q: Write the equation for the sphere of radius 1 centered at the prigin in the each of the following…

A: The general equation of a sphere in cartesian coordinates is: x-a2+y-b2+z-c2 = r2 Here, r is the…

Q: compute the length of the polar curve.  The cardioid r = 1 − cos θ in Figure 16

A: compute the length of the polar curve.  The cardioid r = 1 − cos θ

Q: find the equation of the cicles in standard form given the following conditions  a) center= (0,0) ;…

A:

Q: Identify the surface whose equation in spherical coordinates is given by p= 8 cos o

A:

Q: What is the minimum angle of rotation (in degrees) that will carry the six-sided star onto itself: I…

A: It is a 6 sided star that means it will redivided into 3 parts:⇒ we divide 360°( full rotation ) by…

Q: Express the 2D Cartesian  point P(5,10) in Polar coordinates

A:

Q: the polar coordinates to find the volume of a sphere of radius 1. -

A: Given;  Sphere of radius 1.

Q: Find the polar equation of a hyperbola with eccentricity 2, and directrix y = 5. Select the correct…

A: We have to find the polar equation of the hyperbola with eccentricity 2 and directrix y=5.

Q: Derive the formula for the distance between points P1(p1,q1,z1) and P2(p2,q2,z2) given in spherical…

A:

Q: What is the polar equation of a circle of radius Va? + b centered at (a, b)?

A: General equation of a circle is given by - x-h2+y-k2 = r2              ..............(1)where,h, k =…

Q: A satellite orbits the Earth with an elliptical orbit modeled by the maximum distance between the…

A:

Q: Find the polar coovdinates rectanguar coordinak es the point whose (x,y)= LI,}) are

A:

Q: A circle is specified in parametric form by x=7+3cosθ y=−8+3sinθ What are the coordinates of the…

A: Given : A circle is specified in parametric form by  x=7+3 cosθy=-8+3 sinθ To Find : What are the…

Q: 1. Use the parametric equations of an ellipse, x = a cos 0, y = b sin 0, 0 < 0< 27, to find the area…

A:

Q: find parametric equations for the given curve. Circle of radius 4 with center (3, 9)

A:

Q: Find the Cartesian coordinates of the point (6, 4. VIT) given in cylindrical coordinates

A: First we have to determine (r,∅,z) then calculate respective Cartesian co-ordinates

Q: Describe in polar coordinates the region in the first quadrant between the circles of radius 1 and…

A: The Polar equation of a circle of radius 1 and having center at the origin is: r = 1

Q: The propellers for a toy boat are manufactured by stamping out a rose with n petals and then bending…

A:

Q: 1. Convert the Cartesian coordinate (12,5) to polarcoordinate.

A: Given the cartesian co-ordinate(x,y)=(12,5)

Q: 11 write the rectanqular coordinate equation x2+y²= coordmates and sleetch the graph, in polarr

A: Given the equation x2 + y2 = x in the rectangular coordinates and we have to convert into polar…

Q: Find the formula for the distance between the points P1(a1,b1,c1) and P2(a2,b2,c2) given in…

A: First write the given coordinates in spherical coordinates. a1=r cosθsinϕb1=r…

Q: 11.) Find a rectangular equation for the Surface whose Spherical equation is a sin ($) Sin (e)

A:

Q: 11. Find the rectangu lar coordin ates of a point whose polar coordinates are (4, 180).

A: Here we convert the rectangular coordinates into polar coordinates.

Q: Qz: sketeh in polar %3D

A:

Q: The rotation about the origin at an angle e=180° is defined by (ху)-(ху) (ху)-(ух) O (x.y)->(x,-y)…

A: The rotation about the origin at an angle 180° is defined by :-

Q: Identify the surface whose equation in spherical coordinates is given by p= 6 cos

A:

Q: [3] Determine the area of the triangle determined by the polar point (18, 240").

A: