We are given the description of an enclosure that has fencing on 3 sides and can use 3,056 yards of fencing. We are to find the dimensions that will maximize the area contained within the fence. A rectangle formed along a straight portion of a river. The rectangle is formed by the river (a long side), a long side of fence labeled y, and two short sides of fence labeled x. Let y represent the length of fence that is opposite the river and x represent the length of each length of fence perpendicular to the river. As there are 3,056 yards of fencing available, the sum of the lengths of the sides of the enclosure results in

The sum of the lengths of the sides is 2292 yards and the sum of the lengths of the triangle is 3056 yards

Explanation:

Since y represents the length of fence that is opposite (parallel) to the river and x represent the length of fence perpendicular to the river.

Therefore since we can use 3,056 yards of fencing

Side perpendicular to the river = x and,

Side opposite to the river = y = 3056 - 2x

The area of the rectangle formed (A) = Perpendicular side × Parallel side

∴ A = x(3056 - 2x) = 3056x - 2x²

A = 3056x - 2x²

To maximize the area, A' (dA/dx) = 0

∴ A' = 3056 - 4x = 0

3056 - 4x = 0

4x = 3056

x = 764 yards

y =  3056 - 2x = 3056 - 2(764) = 1528 yards.

Side perpendicular to the river = 764 yards and,

Side opposite to the river = 1528 yards

The sum of the lengths of the sides = 764 + 1528 = 2292 yard and the sum of the lengths of the triangle = 764 + 764 + 1528 = 3056 yards

explanation: in any substance/object, the particles inside it (atoms/molecules) constantly move in random directions and with random speeds (this motion is called brownian motion). as a result, the particles have some kinetic energy (which is proportional to the temperature of the substance).

explanation:

have a great day!

most voltage drop calculators want the distance between the source and destination. then internally, they double it so both the source and return wires are calculated. but you need to know which distance the calculator uses so you're not half of what you should be or double what you should be.

most circuit breakers will not take a #6 directly, so the electrician will have to splice on a smaller pigtail. you also have to upsize the grounding wire when you upsized the ungrounded (hot) wire (see note in 250.122). this will preclude using most cable assemblies, as a cable with #6 copper will most likely only have a #10 grounding conductor. you need a #6 grounding conductor if the circuit is 20a. a #8 cable is no better, as it will have a #10 grounding conductor too. but most 20a breakers will take a #8 directly.

in your related post, you didn't say what type of load this is. if it is a light or heater, voltage drop won't be a big issue. if this is a motor, the current needs are huge at startup and the voltage drop can pose a problem. if this is a motor, knowing if the motor is under much load during startup will answer the voltage drop effect (a saw is easier to start than a compressor).