The curvature of vector-valued functions theoretical Someone, please help! 2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos t, a sin t), show that the curvature is n(t) = (b) Recall that the tangent line to a curve at a point can be thought of as the best approx- imation of the curve by a line at that point. Similarly, we can...
Hello, Please Help. Part A Part B Part C Find T, Ñ and B for the curve F(t) = (cos(34), sin(3t), 3t) at the point t = 0. Write exact values or round each number to two decimal places T(0) =( > Preview Preview Preview N(0) = { Preview Preview Preview B(O) = ( C. Find the length of the curve F(t) = (4 ln(t), 9, 12t) for 1 st < 4. Answer: (Write the exact value or round to...
3. (12 points) Consider the curve C defined by r(t) = (4 sint, -4 cost,0) with t€ (0,2) (a) Compute the length of the curve C. (b) Parametrize fit) with respect to are length measured from t = 0. (c) Determine the curvature of C.
3. (12 points) Consider the curve C defined by r(t) = (4 sint, -4 cost,0) with t € (0,2) (a) Compute the length of the curve C. (b) Parametrize f(t) with respect to arc length measured from t=0. (c) Determine the curvature of C.
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
2. a) Show that the (signed) curvature for a curve in polar coordinates (r, 0) is given by where ro denotes do Hint: derive the formulas r-r(0)cosa, y-r(θ)sin θ with respect to θ b) Compute the signed curvature for the cardioid r(0) 1-sin θ Sketch the curve with a suitable plotting tool. 2. a) Show that the (signed) curvature for a curve in polar coordinates (r, 0) is given by where ro denotes do Hint: derive the formulas r-r(0)cosa, y-r(θ)sin...
for the curve r(t) find an equation for the indicated plane at the given value of t 56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D) z -9 (3t sint+3 cos t)i + (3t cos t-3 sin t)j+ 4k; normal plane at t 1.5r.. A) y=-3 57) r(t) 57) B) y 3 C)x-y+z-3 D) x+y+z=-3 56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D)...
12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the plot of the curve? IV 20 50 (a) Compute the arc length of the curve from t = 0 to t = 3. (b) Find the unit tangent vector T(t). (c) Compute the curvature of the curve at any value of t. 12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the...
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
t) (2,t, e') 1. Consider the space curve r and B Tx N (a) Find T N= r°T T' (b) Compute the curvature K(t) of r(t) t) (2,t, e') 1. Consider the space curve r and B Tx N (a) Find T N= r°T T' (b) Compute the curvature K(t) of r(t)