9. If α is a curve with K > 0 and τ both constant, show that α is a circular helix
please prove Q9.... 9. If α is a curve with K > 0 and τ both constant, show that α is a circular helix
Prove that a unit speed curve with k and tour constant is a helix circular. unit speed 3(10pts). Prove that with is and constant curve a T circular helix. unit speed 3(10pts). Prove that with is and constant curve a T circular helix.
please solve Q7.... 7. Let ㏄ 1 → R, be a cylindrical helix with unit vector u. For to E 1, the curve is called a cross-sectional curve of the cylinder on which α lies Prove (a) γ lies in the plane through o(to) orthogonal to u. (b) The curvature of γ is dsin't, where κ is the curvature of α. 7. Let ㏄ 1 → R, be a cylindrical helix with unit vector u. For to E 1, the...
Differential Geometry (4) Show that the helix α(t) = (2 cos(3t), 2sin(3t), 3t) lies on a circular cylinder, and find the arc-length of the helix. Determine β(s), the Reparametrized the helix by using the arc-length as the parameter.
Consider the production function given by Q = l^α + k^α where α > 0. At what values of α does the production technology exhibit increasing, decreasing, or constant returns to scale? Prove your answer!
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a E R3 with R3 be smooth with = 1 and curvature k and torsion r, both Assume there exists a unit Ta constant = COS a. circular helix is an example of such curve a) Show that b) Show that N -a 0. c) Show that k/T =constant ttan a 2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a...
please answer all the 4 parts of this question 2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be a point on the helix (a) Find the Frenet frame (T, N, B) at the point P (b) Find equations for the tangent and normal line at P (c) Find equations for the normal plane and the osculating plane at P (d) What is the curvature at...
2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α 0 and for every 0 < i k one has that α, κ α, > , αϊ-1 3. Find a linear system with real coefficients for which the span of 2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α...
(2%) Indicate which secondary structure or structures (α -helix, β -pleated, random coil) will the following peptide adopt in an aqueous solution at pH 7 (2%) The unfolding of the alpha helix of a polypeptide to a randomly coiled conformation is accompanied by a large decrease in a property called specific rotation, a measure of a solution’s capacity to rotate circularly polarized light. Polyglutamate, a polypeptide made up of only L-Glu residues, has the alpha helical conformation at pH 3....
prove that J2(x)=sum from k=0 to infinity [ (-1)^k/2^9@k+2)*k!(k+2)! ]*x^(2k+2) is a solution of the Bessel differential equation of order 2: x^2y'' + xy' + (x^2-4)y=0 (-1)4 9- Using the ratio test, one can easily show that the series +2converges for all e R. Prove that (-1)X h(x) = E, 22k +2k!(k + 2)! 22+2 is a solution of the Bessel differential equation of order 2: In(x) is called the Bessel function of the first Remark. In general the function...