Find the dimensions of the rectangle of maximum area that can be drawn within a semicircle of radius 3, if one side of the rectangle lies along the diameter of the semicircle.

Q: The intersection of the sphere (x-3)^2 + (x+2)^2 + (z-1)^2 = 49 with each of the coordinate planes…

A:

Q: find the center and radius of the circle x^2 + y^3 - 2x + 6y - 7=0

A: The given equation of the circle is x2+y2-2x+6y-7=0.

Q: Use the method of Lagrange Multipliers to find the area of the largest rectangle with edges parallel…

A: The rectangle inscribed the ellipse x218+y232=1. Let sides of rectangle be 2x and  2y.  Draw the…

Q: Need help with this calculus question, please do all. Thanks.

A: We are given a 3rd degree polynomial, of which we need to integrate from -2 to 2. Also, we are…

Q: Find the equation of a circle in standard form. center at (-4,3) and tangent to the x-axis O…

A:

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y =1- x².…

A:

Q: the area of the ellipse 9x^2 + 8y^2 = 72 answer: 26.7

A: To Find: Area of the ellipse  9x2+8y2=72

Q: What is the equation for a sphere centered at the point (4,-3,-7) with a radius of 5.

A: The general equation for a sphere in three dimensions is given by (x - h)^2 + (y - k)^2 + (z - l)^2…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 25 -…

A: