Mathematics, 07.04.2020 21:59 george8396
N exponential spiral has parametric equationr(t) =〈etcost, etsint〉.(a) Plotr(t). Make sure your plot includeslimt→−[infinity]r(t).(b) Find the unit tangent vectorT(t)tor(t).(c) Find the length ofr(t)for−[infinity]< t≤0.(d) Letf(x, y) =−12ln(x2+y2)−arctanxy. Find∇f(x, y).(e) Compute the angle between∇f(r(t))andr′(t).
Answers: 2
![L=\int_{-\inf}^{0}\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2+(\frac{dz}{dt})^2}dt\\\\L=\int_{-inf}^0e^t\sqrt{2}=\sqrt{2}[e^{0}-e^{-inf}]=\sqrt{2}](/tpl/images/0587/5084/abd0e.png)
![|\bigtriangledown f(x,y)|=\sqrt{(\frac{-24}{x^2+y^2}-\frac{y}{1+x^2y^2})^2+(\frac{-24}{x^2+y^2}-\frac{x}{1+x^2y^2})^2}\\\\\theta=cos^{-1}[\frac{\bigtriangledown f(x,y) \cdot r'(t)}{|\bigtriangledown f(x,y)||r'(t)|}]](/tpl/images/0587/5084/9d266.png)
Another question on Mathematics
Mathematics, 21.06.2019 19:00
How do i start to solve? would appreciate a walk-thru! a bird sitting 16ft above the ground in an apple tree dislodges an apple. after how many seconds does the apple land on the ground? (assuming that no branches will interfere with it's fall)
Answers: 1
Mathematics, 21.06.2019 19:00
Find the equation of a line whose slope is 2/5 and y- intercept is 2.write your answer in the form 1) ax+by+c=02) x/a+y/b=1
Answers: 1
Mathematics, 21.06.2019 23:00
72 the length of a side of a triangle is 36. a line parallel to that side divides the triangle into two parts of equal area. find the length of the segment determined by the points of intersection between the line and the other two sides of the triangle.
Answers: 1
You know the right answer?
N exponential spiral has parametric equationr(t) =〈etcost, etsint〉.(a) Plotr(t). Make sure your plot...
Questions
Physics, 06.02.2021 17:30
Physics, 06.02.2021 17:40
English, 06.02.2021 17:40
Computers and Technology, 06.02.2021 17:40
Computers and Technology, 06.02.2021 17:40
Mathematics, 06.02.2021 17:40
English, 06.02.2021 17:40
History, 06.02.2021 17:40
Mathematics, 06.02.2021 17:40
Mathematics, 06.02.2021 17:40
English, 06.02.2021 17:40
