plve the following related rates and optimization problems. We want to build a greenhouse that has a half-cylinder roof of radius r and height r mounted horizontally on top of four rectangular walls of height h as shown in the figure. We have 200n m² of plastic sheet to be used in the construction of this structure. Find the value of r for the greenhouse with the largest possible volume we can build.

Q: 1. The side of a cube decreases at a rate of 2.5m/s. Find the rate at which the surfacearea…

A:

Q: 4. A cylindrical tank with a given volume V (V is a constant) is to be made without a lid. The…

A: Given:  A cylindrical tank with a given volume V V is a constant is to be made without a lid. The…

Q: A visitor is staying in a tent that is 7 kilometers east of the closest point on a shoreline to an…

A: We have to solve given Questions.

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 450…

A: Let z be the cost function. The volume of the cylinder must be 450 cubic centimeters.

Q: Two light sources of intensities I1 and I2 are L units apart. Find the point on the line segment…

A:

Q: A trough is 5 meters long and 1 meter high. The vertical cross-section of the trough parallel to an…

A: To find the work required to empty the trough, you can use the principles of calculus and fluid…

Q: 6) The marginal cost of producing z units of a product is modeled by 28 – 0.02x. dz It costs $40 to…

A: We use separable differential equation

Q: A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material…

A: we have to find the dimensions and then minimize production cost

Q: Write an equation to compute the volume V of the cube using the length of an edge x. V= cm

A: We have to write an equation to compute the volume V of the cube using the length of an edge x.