SLUIG. UU Question Help X 14.5.72 Find the radius of curvature of the following curve at...
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the graph of y = sin | 2x | in the xy-plane.) An equation for the circle of curvature is (Type an equation. Type an exact answer, using π as needed.) X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the...
Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) = (3t+2, 5t - 7,67 +12) T= 000 (Type exact answers, using radicals as needed.) JUNIL Score: 0 of 2 pts 42 of 60 (58 complete) HW Score: 72.17%, 7 X 14.4.40 Ques Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter. r(t) = (7+2,8%. 31), for 1sts Select the...
Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= - 8 cos 0-6 sin 0 Write the Cartesian equation. Describe the curve. Select the correct choice below and, if necessary, fill in any answer box O A. The curve is a circle centered at the point with radius (Type exact answers, using radicals as needed.) B. The curve is a vertical line with x-intercept at the point (Type exact answers, using radicals as needed.) O C. The...
Find the slope of a line tangent to the curve of the given equation at the given point. Sketch the curve and the tangent line. y=x? -5; (4,11) The slope is (Simplify your answer.) Enter your answer in the answer box and then click Check Answer. 1 part remaining Clear All
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...
Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at this point x=16 cost, y = 4 sint,t= The equation represents the line tangent to the curve at t= (Type an exact answer, using radicals as needed.) d²y The value of dx2 (Type an exact answer, using radicals as needed.) att =
14.4.23 For the following trajectory, find the speed associated with the trajectory and then find the length of the trajectory on the given interval. r(t) = (31°, -1, 6r%), for Osts 4 The speed associated with the trajectory is 32/46 (Type an exact answer, using radicals as needed.) The length of the trajectory on the given interval is units (Type an exact answer, using radicals as needed.) 3 Enter your answer in the answer box and then click Check Answer...
d²y Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at this point dx x= 16 cost. y = 4 sint, t = 7 л 2 The equation represents the line tangent to the curve att (Type an exact answer, using radicals as needed.) dy The value of att is dx? (Type an exact answer, using radicals as needed.) 70 4
The total curvature of the portion of a smooth curve that runs from s so to s can be found by integrating k from so to s,. If the $1 curve has some other parameter, say t, then the total curvature is K K ds-dtK|v dt, where to and ty correspond to so So and s1 a. Find the total curvature of the portion of the helix r(t) = (3 cos t)i + (3 sin tj-tk, 0 sts 4m b...
A circle has the equation x² + y2 - x - 4y + 4 = 0. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph. (a) The center of the circle is (Type an ordered pair, using integers or fractions.) The radius of the circle is (Type an integer or a fraction.) (b) Use the graphing tool to graph the circle. Click to enlarge graph...