14. (5 points) Find a polar equation for the curve represented by ? + y2 =...
please include the graph 12. la) Use a graphing utility to graph the curve represented by the following polar equation: r(θ)-1-cos(θ) over the interval 0 ses 2. (b) Find the arc length of this curve over the interval with your notation, show orientation arrows on your curve, and show your steps clearly.) (b) are length of this curve over the interval 0 0 S 2,- 12. la) Use a graphing utility to graph the curve represented by the following polar...
Problem 6 [5 points] |(y ( y-dan- 0.708 Set up an equation with a double Integral in polar coordinates to find a such that the volume inside the hemisphere z 16-x-yi and outside the cylinder x2 + y2 = a 2 is one-half the volume of the hemisphere. Do not solve it. Problem 6 [5 points] |(y ( y-dan- 0.708 Set up an equation with a double Integral in polar coordinates to find a such that the volume inside the...
3. (6 points) Consider the curve y = 2 - 2.22 restricted to the first quadrant. (a) Set up a definite integral that gives the length of this curve. Do NOT evaluate the integral (b) Set up a definite integral that gives the surface area of the solid generated by rotating the curve about the x-axis. Do NOT evaluate the integral.
only answer if you can write it neat so I understand. thanks. 5) Find the average value of the function from-110-S 0) Set up the necessary integral to find the length of the curve over the given interval. Do not evaluate the 22 M'- integral exactly. Find the arc length of the curve 3 Com x-x-3
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane. 4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
Find a polar equation of the form r = f(@), where r > 0, for the curve represented by the Cartesian equation x2 + y2 = 9. Note: Since is not a symbol on your keyboard, use t in place of 0 in your answer. =
4. Consider the area of the region that lies inside the curve given in polar form) by r = 6 sin(@) and outside the cardioid given by r=2+2 sin(0). (a) (3pts) Set up but do not evaluate an integral(s) which represents the area of this region. (b) (3.5pts) Evaluate this integral to determine the exact area of this region. (Hint: you will need to use a trig, identity)
please help me and show all the steps and make sure it's correct [10pts.) 5. Find dy and the equation of the tangent line at the point (x,y)=(-2, 0) on the curve r = 21-sin(@)). Include a graph of the polar curve with the orienation indicated. dx [10 pts.) 6. Graph the polar equations r = 5 cos(30) and r = 3cos() for --/2S15 /2. Label any key points needed to find the area that lies in the common interior...
8. (a) Use a graphing utility to graph the curve represented by the following polar equation: r(e)-2cos(3) over the interval 0s0<t. b) Find the area of one petal of this curve. (c) Shade the interior of the petal whose area you are computing. (Be careful with your notation show orientation arrous on your curve, and show your steps clearly.) (b) area of one petal of this curve- 8. (a) Use a graphing utility to graph the curve represented by the...
Please show all steps. Thank you, need to verify what I'm doing wrong. 1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, and in the first octant (z, y, z 0)、z, y and z are measured in meters and the density over B is given by the function p(z, y, z)-(12 + y2 + ?)-1 kg/m3 (a) Set up and write the triple integral that gives the mass...