A rectangle is bounded by the x-axis and the semicircle y = √ 49 -x² (see figure). What length and width should the rectangle have so that its area is a maximum? (smaller value) (larger value) 20 15- y 10- y = sqrt(49-x^2) 5- -10 -5 0 5 10 -5

A rectangle is inscribed in a right triangle. The base of the triangle is 6 inches and height of 3 inches. Determine the dimensions of the rectangle so that its area is maximum.

A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y=81-x^2. What are the dimensions of the rectangle with the maximum area? What is the area?  In terms of shorter and longer dimensions of rectangle.

A farmer wants to fence a rectangular piece of landand divide that into three rectangles. He has 480 metersof fencing available. Use calculus to find the dimensions of the land that has maximum area. Also, give the maximum area.

A rectangle can be drawn in the first quadrant bounded by the curve y=8-x^3, the x-axis, and the y-axis. Determine the dimensions (length and width) of the largest rectangle that can be drawn.

A field bordering a straight stream is to be enclosed. The side bordering the stream is not to be fenced. If 1000 yards of fencing material is to be used, what are the dimensions of the largest rectangular field that can be fenced? What is the maximum area?

A farmer wishes to fence a Rectangular plot of land with one side or in a long road the cost per foot of the fence along the road is $10 per foot what is the cost of prefer the fencing on the other side is only five dollars a foot as it's not a study the former can spend $6000 on fencing what are dimensions of the rectangle that has a maximum area