How do I find the area inside the cardioid #r=1costheta#?What I did I converted the equation $x^2y^22ax=0$ to polar form $r=2acos\theta$ and $z=\frac{x^2y^2}{2a}$ to $z = \frac{r^2}{2a}$ thus got the double integral as $$\int_{\pi/2}^{\pi/2} \int_{0}^{2acos\theta}\frac{r^2}{2a}\cdot r\cdot dr\cdot d\theta$$ which I calculated to be $\frac{3\pi a^3}{4}$3x−x2 − x2 2!
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X^2+y^2=2ax graph-Substitute (x−1)2 − 1 ( x 1) 2 1 for x2 −2x x 2 2 x in the equation x2 − 2xy2 = 0 x 2 2 x y 2 = 0 Move −1 1 to the right side of the equation by adding 1 1 to both sides Add 0 0 and 1 1 This is the form of a circle Use this form to determine the center and radius of the circleGraph y^2=2x Rewrite the equation as Divide each term by and simplify Tap for more steps Divide each term in by Cancel the common factor of Tap for more steps Cancel the common factor Divide by Move the negative in front of the fraction Find the
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F) DS= ?S F Ds= This problem has been solved!Area enclosed by curve y 2 = 2ax – x 2 and y 2 = ax is shown by shaded part in the following graph Solving both equations, x = 0, a Required Area = area OPMO = Area OMPQO Area POQPSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
X 2 y 2 − 2 a x − 2 b y a 2 = 0 All equations of the form ax^ {2}bxc=0 can be solved using the quadratic formula \frac {b±\sqrt {b^ {2}4ac}} {2a} The quadratic formula gives two solutions, one when ± is addition and one when it is subtractionOr (x2)^2 (y3)^2–4–9–3=0 or (x2)^2 (y3)^2= (4)^2 , thus center O is (2,3) and radius (r) is 4 units 1st part Center of the concentric circle is (2,3) and radius of this circle=2r=2×4 =8 units Equation of this circle is (x2)^2 (y3)^2 = (8)^2 or x^2y^24x6y51 =0 Answer5 CassinianOvals Cartesian Equation (x2 y2)2 ¡2a2(x2 ¡y2)¡a4 c4 =01 105 05 PSfrag replacements x y ¡a a Facts (a) The Cassinian ovals are the locus of
Graph x^2y^22x=0 Find the standard form of the hyperbola Tap for more steps Complete the square for Tap for more steps Use the form , to find the values of , , and Consider the vertex form of a parabola Substitute the values of and into the formula Simplify the right sideExample Find the volume of the solid region E between y = 4−x2−z2 and y = x2z2 1 Soln E is described by x2 z2 ≤ y ≤ 4− x2 − z2 over a disk D in the xzplane whose radius is given by the intersection of the two surfaces y = 4− x2 − z2 and y = x2 z2Relation to Rectangular Coordinates • x = rcosθ, y = rsinθ ⇒ x2 y2 = r2, tanθ = y x • r = p x2 y2, θ = tan−1 y x Circles in Polar Coordinates Circles in Polar Coordinates In rectangular coordinates In polar coordinates
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Dx = " 3x2 2 − x3 2 # 1 x=0 = 1 Note that Methods 1 and 2 give the same answer If they don't it means something is wrong 011 Example Evaluate ZZ D (4x2)dA where D is the region enclosed by the curves y = x2 and y = 2x Solution Again we will carry out the integration both ways, x first then yTom Lucas, Bristol Wednesday, " It would be nice to be able to draw lines between the table points in the Graph Plotter rather than just the points Emmitt, Wesley College Monday, " Would be great if we could adjust the graph via grabbing it and placing it where we want too thus adjusting the coordinates and the equationY= x^2 2x Solved by pluggable solver SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons For these solutions to exist, the discriminant should not be a negative number First, we need to compute the discriminant Discriminant d=4 is greater than zero
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F(x) = 2x^2 6x F(x) = 2x 3 F(x) = x^2 3x 54 F(x) = x^2 3x 18 Honestly have no idea where to Calculous the figure shows the graph of F', the derivative of a function f the domain of the function f is the set of all X such that 3 or equal to x Algebra 2Very simply x^2 y^2 12y _____ 45 = 0 x^2 y^2 12y 36 45 = 36 Complete the square within brackets x^2 (y 6)^2 45 = 36 Represent the completed square as a product of identical factors x^2 (y 6)^2 = 81 Add 45 tWhere Ris the region that lies to the left of the yaxis between the circles x2 y2 = 1 and x2 y2 = 4 Solution This region Rcan be described in polar coordinates as the set of all points
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x2 y2 − 2ax b√x2 y2 = r b −2acos(θ) = 0 x2 y2 − 2ax − b√x2 y2 = r −b −2acos(θ) = 0 So, in polar coordinates reduces to (r b − 2acos(θ))(r −b −2acos(θ)) = 0 wich are two versions of the same cardioid Attached a plot showing in red rHow do I find the area inside a cardioid?$\begingroup$ The best way to achieve this kind of problems is sketching a graph Do you now how to plot a circle, a parabolla and the function $\left\lfloor \sin^2\frac{x}{4}\cos\frac{x}{4} \right\rfloor$?
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SOLUTIONS TO ASSIGNMENT #10, Math 253 1 Compute the total mass of the solid which is inside the sphere x2 y2 z2 = a2 and outside the sphere x2y2z2 = b2 if the density is given by ˆ(x;y;z)= c p x 2 y z Here a;b;care positive constants and 0Find the coordinates of the foci, the ends of major and minor axis, the ends of latus rectum then sketch the graph of y^2/169 x^2/144 =1 (i need the anwers to that i will have an idea on how to solve the remaining ) Pre Cal write the equations of the parabola, the directrix, and the axis of symmetry vertex (4,2) focus (4,6) if someoneAll equations of the form a x 2 b x c = 0 can be solved using the quadratic formula 2 a − b ± b 2 − 4 a c The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction \left (14a^ {2}\right)x^ {2}2axy^ {2}4a^ {2}y^ {2}=0 ( 1 − 4 a 2) x 2
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The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction This equation is in standard form ax^ {2}bxc=0 Substitute 1 for a, 2y for b, and x^ {2}y^ {2}2ax for c in the quadratic formula, \frac {b±\sqrt {b^ {2}4ac}} {2a}X^2 y^2 = 2ax is the general equation of a circle with centre at (a,0) and radius of a Its centre lies on x axis and the circle touches the y axis at origin 27K views · 164E Exercises for Section 164 For the following exercises, evaluate the line integrals by applying Green's theorem 1 ∫C2xydx (x y)dy, where C is the path from (0, 0) to (1, 1) along the graph of y = x3 and from (1, 1) to (0, 0) along the graph of y = x oriented in the counterclockwise direction 2 ∫C2xydx (x y)dy, where C
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How do you graph the lemniscate #r^2=36cos2theta#?Use Stoke's Theorem to evaluate the line integral ∮ C (xz)dx (x−y)dy xdz The curve C is the ellipse defined by the equation x2 4 y2 9 = 1, z = 1 (Figure 2 ) Solution Figure 2 Let the surface S be the part of the plane z = 1 bounded by the ellipse Obviously thatFind the area included between the parabolas y 2 = 4ax and x 2 = 4by
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What is the graph of the Cartesian equation #(x^2 y^2 2ax)^2 = b^2(x^2 y^2)#?In Exercises 27– 34, convert the rectangular equation to polar form and sketch its graph x 2 2ax y 2 = 0 π/2 x 2 2ax a 2 a 2 y 2 = 0 (x 2 2ax a 2) a 2 y 2 = 0 (xa) 2 y 2 = a 2 Circle r = a, center is M(a ,0) x = r cos θ 0 y = r sin θ 1a 2a x 2 y 2 2ax If the circles x^2 y^2 2ax cy a = 0 and x^2 y^2 – 3ax dy – 1 = 0 intersect in two distinct point P and Q asked in Mathematics by aditi (
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I think the last function is a bit hard, so you probably will need a program that graphsExample Show the graph of r = 2a cos θ is a circle of radius a centered at (a, 0) Some simple algebra gives r 2 = 2ar cos θ = 2ax ⇒ x 2 y 2 = 2ax ⇒ (x−a) 2 y 2 = a 2 This is a circle or radius a centered at (a, 0)Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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0}, (oriented As A Graph) ?S = {(x, Y) X2 Y2 = 1} F = Zi Xj (2zx 3xy)k S Curl(F) DS= S (?The graph y = x 1/3 illustrates the first possibility here the difference quotient at a = 0 is equal to h 1/3 /h = h −2/3, which becomes very large as h approaches 0 This curve has a tangent line at the origin that is vertical The graph y = x 2/3 illustrates another possibility this graph has a What is the graph of the Cartesian equation #y = 075 x^(2/3) sqrt(1 x^2)#?
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreAssignment 7 Solutions Math 9 { Fall 08 1 (Sec 154, exercise 8) Use polar coordinates to evaluate the double integral ZZ R (x y)dA; Verify Stokes theorem for F =(y^2 x^2 x^2)i (z^2 x^2 y^2)j (x^2 y^2 z^2)k over the portion of the surface x^2 y^2 2ax az = 0 While evaluating the integral we get hard to evaluate integrals What can we do to simplify this?
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where the center is ( a, b) and the radius c If you expand, x 2 y 2 − 2 a x − 2 b x ≤ c 2 − a 2 − b 2 When the center is the origin, x 2 y 2 ≤ c 2 You observe that the coefficients of x 2 and y 2 are equal, and this remains true even if you multiply theIn this video explaining triple integration exampleFirst set the limits and after integrate This is very simple and good example#easymathseasytricks #defi Figure 1573 Setting up a triple integral in cylindrical coordinates over a cylindrical region Solution First, identify that the equation for the sphere is r2 z2 = 16 We can see that the limits for z are from 0 to z = √16 − r2 Then the limits for r are from 0 to r = 2sinθ
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Find the Center and Radius x^2y^22x=0 Complete the square for Tap for more steps Use the form , to find the values of , , and Consider the vertex form of a parabola Substitute the values of and into the formula Simplify the right side Tap for more steps Cancel the common factor of0}, (oriented as a graph)?S = {(x, yConvert the rectangular equation x 2 y 2 − 2ax = 0 to polar form and sketch its graph check_circle
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