Topic: Triple Integrals in Spherical Coordinates Sketch the solid described by the given inequalities: 1<=rho<=2, 0<=phi<=pi/2, pi/2<=theta<=3pi/2 Can you solve this with steps?
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Topic: Triple Integrals in Spherical Coordinates
Sketch the solid described by the given inequalities:
1<=rho<=2, 0<=phi<=pi/2, pi/2<=theta<=3pi/2
Can you solve this with steps?
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- Triple Integrals using polar coordinates (cylindrical) - calc 3 questiona) Use Polar-style integration to find the area contained within one petal of the Polar rose with equation r=5sin8theta.For convenience, use the First petal fully graphed on the interval [0, 2Pi]. b) When graphed over the [0, 2Pi] interval, how many petals does r=5sin8theta have in its’ graph? How much area, total, do they contain? (use your a) answer to help get this one) c) The Polar Rose in a) and b) above is bounded (encircled!) by the graph of the circle r = 5. What is the area of the region that is Inside this circle but Outside of the Rose? (don’t integrate to get this answer, there’s no need – use b)'s answer to help get it)Volumes in spherical coordinates Use integration in sphericalcoordinates to find the volume of the following solid. The solid rose petal of revolution D = {(ρ, φ, θ): 0 ≤ ρ ≤ 4 sin 2φ,0 ≤ φ ≤ π/2, 0 ≤ θ ≤ 2π}
- 2. Consider the polar curves r = 4 - 2cosθ and r = 2 + 2cosθ. In this problem, we want to find the area of A, B, and C pictured below. (c) B is the area inside both r = 2 + 2cosθ and r = 4 - 2cosθ. Find the area of B. (Hint: What happens at the angle where the two polar curves intersect? Your answer should involve a sum of two polar integrals.)as engineer design a cooling tower in the shape of hyperboloid of one sheet. The horizontal cross sections of the cooling tower are circular with 10m.The cooling tower is 40m tall with maximum cross-sectional radius of 15m. (A) Construct a mathematical equations for this cooling tower. (B) If x=a cos(u) cosh(v) ,y=b sin(u) cosh(v) and z= csinh(v), show that (x,y,z)lies on your equation in Q1(A). (C) A colleague at the same institution want to construct the cooling tower using an hyperbolic cylinder, give reasons for your result in Q1(A) as the best model for the design of cooling tower.Polar curves C2: r = 4cosθ and C3 : r = 4sinθ. Solve for the slope of the tangent line at the non-pole point on C2 which intersects C3 . Set up an integral giving the area of the region inside both C2 and C3 .
- Topic: Integrals - Areas of a Plane Regions Using Definite Integrals Prove that the answer to this problem is equal to 15 by showing your solution.Using the concept of triple integral in spherical coordinates theta rho and r solve the problem by drawing a GRAPH. ALSO PLEASE WRITE THE SOLUTION WITH THE GRAPH AND SEND as the math numbers become overlapped in the solution . Thank you .Fast pls solve this question correctly in 5 min pls I will give u like for sure Anu Integrate f (x, y) = y over the top half of the circle (x − 1)2 + y2 = 1 in two ways a) In rectangular coordinates. b) In polar coordinates
- 2. Consider the polar curves r = 4 - 2cosθ and r = 2 + 2cosθ. In this problem, we want to find the area of A, B, and C pictured below. (a) Find the angles where the two polar curves intersect. (b) A is the area inside r = 2 + 2cosθ, but outside r = 4 - 2cosθ. Set up and evaluate a polar integral to find the area of A.UPVOTE WILL BE GIVEN! PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. DO NOT COPY ANSWERS IN CHEGG AND BARTLEBY. BOX THE FINAL ANSWER. Use CYLINDRICAL COORDINATES to evaluate an iterated triple integral equal to the given equation.Point -masses mi are located on the x-axis as shown. Find the moment M of the system about the origin and the center of mass x̄