The perimeter of an ellipse is given by P = 4a V1-k-sin-8 de where, k = Using the Simpson's rule, calculate the perimeter of the following ellipses: (x/4)+(y/7)=1 while considering n-6. Oa 35.20335 b.35 20314 O. 35 03054 O4 23 01251

Q: Which of the following is simply connected? a) the horizontal strip Imz <1 b) the annulus 1</z <2 c)…

A: This is a problem of topology.

Q: Graph the curve 8y2 = x2 (1 − x2 ). Use a computer algebra system to find the surface area of the…

A:

Q: Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V…

A: Consider the given:  Express volume in terms of “h”, “r” and “w”.…

Q: snip

A: Except for degenerate cases, the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 defines an ellipse if ____.

Q: Find the area of the surface formed by revolving the ellipse about the z-axis (an ellipsoid) y² + a²…

A:

Q: 7. The parametric equation of an ellipse is given by x = a cost, y=bsint; 0<t<2n. Determine the area…

A:

Q: Find the area of the resulting surface if an arc of a parabola y = x? from (1,1) to (2,4) is rotated…

A: Given curve is y=x2

Q: 3. Prove that the equation of the normal to the rectangular hyperbola xy = c² at the point P (ct,)…

A:

Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

A:

Q: Given the equation of an ellips in parametric form x = acost, y = bsint semi axes of the ellipse, t…

A: We have been given the parametric form of an ellipse x = acost, y == bsint where a, b are semi-axes…

Q: te the line integral c 3 == 1 from A=(2, 0) to (0, -1) Jax + 2xyay where is the arc on the ellipse

A:

Q: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

A:

Q: 2 Find pxV 1+ 3x² dr, where P is the ellipse parametrized as follows: r(t) = , 0<t< 2n

A:

Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

A:

Q: 35. Calculate || 9x*+4y* dx dy, where D is the interior of the ellipse (G) + (4)' =

A: Given:

Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

A:

Q: Given the equation of an ellipse in parametric form:x=acost,y=bsint,where a, b are semi-axes of the…

A: Equation of ellipse in parametric form is Differentiating with respect to t, we get Now,

Q: Consider the curve in the xy plane defined by the equation 4y? – 22 – 8y – 6x = 21 Show that this…

A:

Q: 3. Evaluate (sin r +y cos r)dr + (sin r + z cos y)dy + sin ydz), where C'is the ellipse 36.r + 4y =…

A:

Q: For which point y on the ellipsoid æ² + 2y² + 4z² =1 (shown below) is %3D the quantity x+ y+ z as…

A: Lagrange's Multiplier:- To find:- Extreme values of f(x, y, z)…

Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

A:

Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = &lt;t, t2&gt;That implies,

Q: Show that the arclength of the graph of y=sinx on the interval [0, 2n] is equal to the circumference…

A:

Q: 1. Using the data 2 12 8 9 X = 9. 8 10 1) Find the 95% confidence ellipse for µ = [µ1, µ2],…

A: Using the data  x = 2128969810 Find the 95% confidence ellipse for μ = [μ1,μ2], calculate the axes…

Q: Use Green's theorem to find the area between ellipse 16 = 1 and circle x2 + y2 = 25.

A:

Q: Find the area of the region enclosed by the parametric equation x = t³ - 7t y = 6t²

A:

Q: (c) . sin (92? +4y?) dA D where D is the region in the first quadrant bounded by the ellipse 9a?…

A:

Q: The area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: Area of ellipse initially  = Ai  = πab    Now, lengths of axis are changed,   They are  [ 2(1.0099)a…

Q: 3. Find the exact area of the surface obtained by rotating the curve described by the parametric…

A:

Q: What is the size of the largest segment parallel to the y axis inside the ellipsoid

A:

Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

A:

Q: Need some help with Greens Theorem and ellipse plz, thanks

A: It is required to calculate the value of the integral using green’s theorem:

Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

A:

Q: Find the area of the surface formed by rotating the curve with the equation x ^ (2) - (y ^ (2)) /…

A:

Q: (d) Find the area of the surface generated by revolving the curve y = 2a, 0 < x < 3, about the…

A: Part (D) To find the area of the surface generated by revolving the curve, y=2x,0≤x≤3, about the…

Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

A:

Q: 3. he tangent to the ellipse I at the point P: V2 4. 3. 3w q(w) = 2w+ V2 %3D 3 q(w) = 3w V2w - V2 3…

A: Ellipse tangent

Q: The arc of the parabola y = x? from (1, 1) to (2, 4) is rotated about the y-axis. Draw the surface…

A: Given: Equation of parabola : y= x2  Arc of parabola passes through (1,1) and (2,4).

Q: 17. Evaluate F · dš if F(x, y) = (y*, 2xy*) and & is the ellipse x? + 2y? = 2 (with counterclockwise…

A:

Q: Find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter…

A:

Q: Find a parametrization of the osculating circle for the parabola y= X sequar when x=1

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

Q: Show that the arclength of the graph of y = sin x on the interval [0, 27] is equal to the circum-…

A: The length of the smooth curve ζ : [ 0 , 2π] →ℝ2  is given by I(ξ) = ∫02π ξ'(t)  dt

Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: I am having trouble solving this.

A: To find the area of the overlap between the interior of the ellipses given below.

Q: Give a parameterization for the ellipse 9 a? + 36 y? = 324 that begins at the point (6,0) and…

A:

Q: 4. Find the area of ​​the surface of the revolution formed by rotating the part of the 4x^2 + y^2= 4…

A:

Q: Find the surface area of the ellipsoid obtained by rotating the ellipse (=) = 1 about the x-axis.

A:

Q: Find the area of the region enclosed by the parametric equation x = t³ - 8t y = 4t²

A: This is a loop formed find graph  And then find limits of t

Q: Consider the ellipse + = 1. n/2 Show that the circumference of the ellipse is given by C 2 V4 cos? t…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: Find the area of the surface obtained by rotating the curve y² = 4x + 4 0<x<8 about the x-axis?

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.