Find the moment of inertia of the area in the first quadrant bounded by the curves y = 9 – x² and y = 3x – x2 about the y-axis -

Q: Find the moment of inertia: x = y +1; y = 1; y = 2; x = 0 about x-axis.

A:

Q: Show that the inflection points of the curve y=sinxxy=sin⁡x/x lie on the curve y2(x4+4)=4.

A: Given: To prove that the inflection points of the curve y=sinx/x lie on the curve y2(x4+4)=4.

Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

A:

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: Find the curve y if dy = x2 +5, dx + 5, curve passes through (0, 25)***

A:

Q: Sketch one loop of the curve 9y² = x(3x)² Find the area of the surface of revolution generated by…

A:

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: What is the moment of inertia of this area about the line y = -10 ?

A:

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: Verify that i, is an eigenvalue of A and that x, is a corresponding eigenvector. 8 -1 8 1 = 8, x, =…

A: Here the given matrix is                                          A=8-18061007 And the given…

Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

Q: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.