The boundary of a lamina consists of the semicircles y = sqrt(1 − x2) and y...

The boundary of a lamina consists of the semicircles

y =

sqrt(1 − x²)

and y =

sqrt(9 − x²)

together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin.

Expert Solution

if you have any doubts ask me in comments or if you satisfy with my answer please give thumbs up. Thank you.

milcah answered 2 years ago

The boundary of a lamina consists of the semicircles y = 1 − x2 and y...

The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 25 − x2 together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin. Hint: use polar coordinates

solve for x: [x * sqrt(1+x2)] + ln[x + sqrt(1+x2)] = 25

a) Let y be the solution of the equation y ′ = sqrt(1 − y^2) satisfying...

a) Let y be the solution of the equation y ′ = sqrt(1 − y^2) satisfying the condition y ( 0 ) = 0. Find the value of the function f ( x ) = sqrt(2)*y ( x ) at x = π/4. (The square root in the right hand side of the equation takes positive values and − 1 ≤ y ≤ 1) b) Let y be the solution of the equation y ′ = 5 x^4 sin ⁡(x^5) satisfying the...

((sqrtx)+1)dy/dx=(ysqrtx)/(x) + sqrt(y/x), y(2)=1

x2 y" + (x2+x) y’ +(2x-1) y = 0, Find the general solution of y1 with...

x2 y" + (x2+x) y’ +(2x-1) y = 0, Find the general solution of y1 with r1 and calculate the coefficient up to c4 and also find the general expression of the recursion formula, (recursion formula for y1) Find the general solution of y2 based on theorem 4.3.1. (Hint, set d2 = 0)

(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3),...

(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3), x2 = lnx3. find ∂f/∂x3, and df/dx3.

Suppose that a firm has the p production function f(x1; x2) = sqrt(x1) + x2^2. (a)...

Suppose that a firm has the p production function f(x1; x2) = sqrt(x1) + x2^2. (a) The marginal product of factor 1 (increases, decreases, stays constant) ------------ as the amount of factor 1 increases. The marginal product of factor 2 (increases, decreases, stays constant) ----------- as the amount of factor 2 increases. (b) This production function does not satisfy the definition of increasing returns to scale, constant returns to scale, or decreasing returns to scale. How can this be? (c)Find...

Solve the IVP by applying the Laplace transform:y''+y=sqrt(2)*sin[sqrt(2)t]; y(0)=10, y'(0)=0

solve the given boundary value problem. y"+6y=24x, y(0)=0, y(1)+y'(1)=0

Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y <...

Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y < 3} , u(x,y) = 5 (if y=1) and = 7 (when y=3) S = {(x,y): 1 < x2 + y2 < 4}, u(x,y)= 5 (on outer circle) and = 7 (on inner circle) I have these two problems to solve, and I'm not sure where to start. Any help would be appreciated. Thanks!

Question