Consider the spiral given parametrically by z(t) = 6e 0.4 sin (2) y(t) = 6e 0.4t...
Please answer all three, (:
Consider the spiral given parametrically by -0.3 sin (4t) = 6e -0.3t 6e Уб) cos (4) on the interval 0 s 1s 8 6 2 -2 -4 -6 4 5 -5 -4 -3 -2 -1 1 2 3 6 X 0 t 8 Fill in the expression which would complete the integral determining the arc length of this spiral C on dt sqrt(579.24 exp-0.3t)) Incorrect. Tries 5/8 Previous Tries Submit Answer Determine the arc length...
(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t).
(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t).
8.) (13 pts.) Assume that curve C is given parametrically by F(t) = ($(t)) i + (g(t)) ; + (h(t)) k for t20. Let s = s(t) be the arc length of curve C from t = 0 to t. Assume that the unit tangent vector is given by 1 S T(t) = T(t(s)) = + V5+ sa 5 + s2 Find the curvature of C when the arc length is s = 2. v6+ 2 75 5 + 32
please help! I cannot figure
this out.
The graph below is of the curve defined parametrically by: x-sin t and y- sin 2t -0 5 0.5 -1 (a) SET UP THE INTEGRAL TO FIND THE AREA OF THE REGION ENCLOSED BY THE CURVE AND EVALUATE (b) SET UP THE INTEGRAL TO FIND THE LENGTH OF THE CURVE TRAVERSED EXACTLY ONCE. DO NOT EVALUATE. SIMPLIFY TO JUST BEFORE MAKING A SUBSTITUION. (c) SET UP THE INTEGRAL TO FIND THE TOTAL DISTANCE...
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos (1z) – 5z sin (1x)) Do not put the constant "+c" for the potential in your answer below. f (x, y, z) = -12x*cos(2y)+5z*sin(z) Submit Answer Incorrect. Tries 1/8 Previous Tries Now calculate F. dr where C is the path † (t) = ( 4 cos t, 4 sin t, 3t) for 0 <tst. The line integral equals 0
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t) − cos(4t), where t denotes an angle between 0 and 2π. (a) Sketch a graph of this parametric curve. (b) Write an integral representing the arc length of this curve. (c) Using Riemann sums and n = 8, estimate the arc length of this curve. (d) Write an expression for the exact area of the region enclosed by this curve.
1. Consider the curve i(t) = (t sin(t) + cos(t))i + (sin(t) – t)j + tk. (a) Find the length of the curve for 0 <t<5. (b) Is the curve parameterized by arc length? Justify your answer. (C) If possible, find the arc length function, s.
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos (1z) – 5z sin (1z)) Do not put the constant "+c" for the potential in your answer below. f(x, y, z) = Submit Answer Tries 0/8 Now calculate 18.di where C is the path ř (t) = (4 cos t, 4 sin t, 3t) for 0 <tsa. The line integral equals
Question 17 Calculate the arc length of the curve r(t) = (cos: t)+ (sin t)k on the interval 0 <ts. Question 18 Find the curvature of the curve F(t) = (3t)i + (2+2)ż whent = -1. No new data to save. Last checked a
for b.
y= sin(x^2-3x+1)
og t par Set up, but do not evaluate, the integral required to compute the arc length of the curve cotr. y= 217from 0<x< /2. mense metied to compute Set up, but do not evaluate, the integral required to compute the surface area of the solid obtained by rotating the curve y=sin(x2 3x + 1), 0<x< 1 about the z-axis.