Plane R is tangent to sphere 0 at point T. How are radius OT and plane R related?

Q: The exact value of the curvature of ƒ(x)=arcsin x when x= , can be expressed as the product of a/b…

A: Given,               f(x)= arcsin xDifferentiating both sides with respect to x…

Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

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Q: Prove that the parabola y = x^2 at the points where the line has an angle of inclination "o" the…

A: Curvature of  a graph y= f(x)  k=d2ydx21+dydx232

Q: Find the lateral surface area of the cone generated by revolving the line segment y = x/2, 0 ≤ x ≤…

A: Given equation of line segment is  y = x/2, 0 ≤ x ≤ 4,

Q: Which lines or line segments or rays must be drawn or con- structed in a triangle to locate its a)…

A: (a) The orthocentre is the point where all the three altitudes of the triangle cut or intersect each…

Q: 4) Find the curvature of y = cos x at the point (÷,²). Then find the equation of the osculating…

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Q: Give a parametric description for a cylinder with radius a andheight h, including the intervals for…

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Q: bounded by the parall tus rectum. bounded by the parall axis.

A: Given as, The parabola y2=8x  latus rectum (x=2)

Q: A curve is given in polar coordinate as r=R(f). What is its curvature? Find it in terms of R,R' and…

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Q: Determine if line XY is tangent to circle Z. Please show work.

A: using pythagoas theorem

Q: Show that the surface area of a sphere with radius a equals 4ra². r(u, v)= (a sin u cos v, a sin u…

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Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

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Q: Surface at 0 = 30° and r = 10 is a.. Cylinder Cone Circle Plane

A: Solve

Q: / Using Stokes theorom, evaluate : s [czx-y)dx-yz dy-yzdz3, uhere C is the Circle x+y=1,…

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Q: Surface at θ = 40⁰ and r = 20 is a     plane    cirlce   cone

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Q: What cross-section cannot be formed by intersecting a plane with a right cylinder? Campbol OM…

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Q: Exercise 7. Show that the curvature of a circle of radius r is , and the curvature of the line is…

A: Show that the curvature of a circle of radius r is 1r and the curvature of the line is zero.

Q: Give a geometrical interpretation of torsion.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find an arc length parameterization of the circle in the plane z = 9 with radius 4 and center (1, 4,…

A: The parametrization of the circle in the plane z=9 is:                                   r(t)=⟨1, 4,…

Q: 30cm 30 cm 30 cm 100 cm 20сm 50 cm 30 cm

A: Given:- Let us assume Area of rectangle is = A1 Area of first Circle = A2 Area of second Circle = A3…

Q: Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for the…

A: We have to find the equation of tangent plane to parametric surface.

Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = &lt;u,v,uv&gt; , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central…

A: If a cylinder of radius b is cut from a sphere of radius a, then the volume of sphere depends on the…

Q: True or False: AB and AG are tangents that intersect circle M at points B and G, then AMGB is…

A: We have to state true or false .

Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

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Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: # 3 Let act) (cost, sint a is plane Siht) %3D Decide whether not ? curve

A: Given that  α(t)==(cost,sint,sint) Now take α(t)=(x(t),y(t),z(t)) Then, x(t)=cost, y(y)=sint,…

Q: The lateral (side) surface area of a cone of height h and base radius r should be πr√r2 + h2, the…

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Q: Show that the average straight-line distance to a fixed point on the surface of a sphere of radius a…

A: As per the hint we will assume the north pole (0,0,1) as the fixd point. Then in order to find the…

Q: (b) The circle of radius 2 centered at (0, 0, 0) and lying in the i. xy-plane ii. yz-plane iii.…

A: According to our company's guidelines I can only answer first question (b), since (c) is not…

Q: Find a formula for the distance from the point P(x, y, z) to thea. xy-plane. b. yz-plane. c.…

A: Distance FormulaDistance between two points x1,y1,z1 and x2,y2,z2d=x2−x12+y2−y12+z2−z12

Q: A curve is drawn on a parabolic cylinder so as to cut all the generators at the same angle. Find the…

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Q: Tangents are drawn to the concentric circles x^(2)+y^(2)=a^(2) and x^(2)+y^(2)=b^(2) at right angle…

A: We have to Show that locus of their point of intersection is a 3rd concentric circle and find its…

Q: 3) Find the radius of curvature for the parametric curve et cost, y = et sin t.

A: To find the radius of curvature. The radius of curvature is the inverse of curvature.

Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

Q: Show that the area of the plane region bounded by the curves,  x=y^2 -1,  x= 1 - y^2  is 8/3 square…

A: Given equation of cyrves, x=f(y)=y2-1,x=g(y)=1-y2

Q: Find a plane curve a(s) endowed with a unit-speed prametrization by SE (-0, 0) such that its signed…

A: The curvature of the curve αs is given by: αs=∫s0scos(θ(u))du, ∫s0ssin(θ(u))du-----(1) in which…

Q: Show that the geodesic on the surface of a right circular cylinder is a segment of a helix

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Q: Find the surface area of a sphere of radius r

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Q: The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 +…

A: Obtain the lateral surface area as follows.

Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

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Q: y = x, 0 < x <7

A: The given line  y = (7/5)x This is revolved about x axis  0≤x≤7

Q: Find the radius of curvature of 6y = x3 at the point (2,). %3D

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Q: Find parametrization of the horizontal circle of radius 4 with center (5, -2, 6). r(t) = %3D

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Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

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