For each of the described curves, decide if the curve would be more easily given by...
For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a) A circle with radius 4 and center (3, 2). (b) A circle centered at the origin with radius 1.
need help Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
2. Consider the circle of radius 9 centered at the origin in the ry-plane. It can be described by the equation 2 +y2 81. The sphere of radius 9 centered at the origin can be created by rotating the curve y v81- about the a-axis. (a) The volume of the sphere can be calulated using a definite integral. Set up that definite integral, but do not solve it. (b) Complete the calculation of the integral. 2. Consider the circle of...
Write the equation of the square root function described. The function value, f(x), is an ordered pair,(x,f(x) , on a circle of radius 5 with its center at the origin of a coordinate system. (Hint: The equation for a circle of radius r and its center at (0,0) x^2+y^2=r^2) and what value of r is the known surface area of a sphere, given by the function S(r)=4πr^2, numerically equal to the known volume of the sphere given by the function...
Any help would be appreciated! 6. (3 pts.) Let R be the region colored in black in the figure below. The two curves bounding R are the circle 12 + y2-= 1 and the curve described in polar coordinates by the equation r-2 sin(20). Set up but do NOT evaluate a (sum of) double integral(s) in polar coordinates to find the area of R. We were unable to transcribe this image 6. (3 pts.) Let R be the region colored...
[G] Find the parametric equations for the curves described below. Then write the corresponding vector-valued function that represents the given curve. Be sure to include an appropriate interval for the parameter. *Make sure you give both the parametric equations and vector- valued function and don't forget the interval for the parameter either. (G.1) The line segment from (-3,4,7) to (6,4,0). (G.2) The segment of the curve with equation y = (x + 4 from (12,4) to (-3,1). (G.3) The lower...
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
Sketch the described surfaces. Give a parametrization of each. (Be sure to include bounds of parameters as necessary): (a) A cone with its point at (1, 3, 4) and its base a circle of radius 6 on the plane z = 7, centered at (1, 3, 7) (b) A cylinder of radius 3/2 centered at the y-axis, with a base on the plane y = 0 and height going on to y = +. (c) The plane 2x+3y+z=10 restricted to...
3. (Polar Coondinates: Areca of a Region). For each of the following regions, bounded by curves given in polar coordinates: sketch the bounding curves, shade the corresponding region. find its area, and then round the answer to five decimal places 1-cos Use the WolframAlpha website to obtain sketches of the required curws say, in order to plot the required part of the third curve in (t), enter the command polar plot r7/(1-cos(theta)), theta pi/4 to pi/2) at the website 3....
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...