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- Show that the intrinsic equations of a helix on a cone of revolution are : K= 1/as and torsion=1/bs where a,b are constant step by step with all detConsider the problem of fitting a planez = ax + by + c to data: Please answer question a.The 8-m-long cable is anchored to the ground at A.If x = 4 m and y = 2 m, determine the coordinate z to thehighest point of attachment along the column.
- Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central cylinder of radius b has been removed, where 0 < b < a, only depends on the height of the band that results. In particular, this implies that such a band of radius 2 m and height 1 m has the same volume as such a band of radius 6,400 km (the radius of the earth) and height 1 m.If UV bisects XY at point W, which statement must be true?Give an arclength parametrization of the line which is the intersection of the tangent planes of z=x^2+y^3 at points (1, -1, 0) and (1, 2, 9)?
- On a bicycle you have two pulleys. Even though they have proper names let's call them the pedal gear (pulley of radius 2 inches) and the wheel gear (pulley or radius 1/2 inch) and assume the gear chain connecting them is taut. A) If the 2 inch pedal gear is caused to rotate at 15 revolutions per minute, determine the revolutions per minute of the 1/2 inch wheel gear. B)If the wheel gear iss attached to the center of a rear bicycle wheel of radius 13 inches, what is the linear velocity of the rear wheel (assume the above numbers)The planet is spherical with a radius of 1 unit in length. Suppose that in a coordinate system whose origin is at the center of the planet, the magnetic field strength is given by I(x,y,z)=4xz+4yz+7. What is the strength of the magnetic field where the radio telescope will be positioned? will be positioned in the place where the planet's magnetic field is as weak as possiblewhy wouldnt both be independent of the geometry S, as for the elliptic you can create a three point model and for the Euclidena you can create a four point model?
- Determine the force being experienced by a 2-microcoulomb charge at (-2,4,6) m due to another point charge 3 mC located at (2,0,-1) m. Assume the charges are in vacuum.AD perpendicular to OF is not given , please prove also thisYou are now allowed to assume that the half-planes determined by the line with the equation ax+by +c = 0 correspond to the points (x, y) so that ax + by + c < 0 and ax + by + c > 0, respectively. Usingthis, show that axiom B4(i) holds. (Hint. Suppose (q, r) and (s, t) are on the same side of the given lineand that (s, t) and (u, v) are on the same side of the given line. en construct the parametrized linethrough (q, r) and (u, v). Consider the mappingλ γ7→ a(q − qλ + uλ) + b(r − rλ + vλ) + c and note that it is continuous and either increasing or decreasing. Use this fact to show that, for everyλ, γ(λ) > 0 or γ(λ) < 0, depending on which half-plane the points are on.)