In the Search tab, type in Warrego Valles and zoom to ∼120 miles. Notice the general shape of th

In the Search tab, type in Warrego Valles and zoom to ∼120...

Key Concepts

Fluvial Processes

Fluvial processes involve the actions of running water, including erosion, transportation, and deposition of sediments. These processes are fundamental to shaping drainage networks and landforms, and they occur as a result of groundwater seepage, surface runoff from precipitation, or a combination of both.

Radial Drainage

Radial drainage patterns occur when streams flow outward from a central high point, such as a dome, volcano, or hill. This type of drainage reflects the influence of a dominant topographic feature that forces water to diverge in all directions, creating a spoke-like network.

Drainage Patterns

Drainage patterns are the characteristic arrangements of channels and tributaries in a drainage basin, shaped by the interplay of underlying geology, topography, and hydrologic processes. They help geomorphologists understand the dynamics of erosion, sediment transport, and landscape evolution.

Dendritic Drainage

Dendritic drainage is a common type of pattern that resembles the branches of a tree. It generally forms in areas where the underlying rock is uniform and unfractured, allowing water to carve channels in a pattern that follows the natural slope of the land without significant structural influence.

Transcript

00:01 So we're taking a piece of metal that is 12 inches long and folding it like so.

00:10 So let's say that this is x units tall, this is x units tall, and this is like y.

00:16 So i know that two x's plus y have to add up to 12 inches long for the metal.

00:24 And i don't really want to end up having both of these very.

00:30 In here i only want one so we'll solve for y and so i get y is equal to 12 minus 2x so this is 12 minus 2x and i know we're looking at the area of a cross section and so my area is by taking my length and my width and multiplying them together so i need to multiply those two quantities together so i have x times 12 minus 2x and i can can see that if i distribute that i get negative i get 12x minus 2x squared which means this is a parabola that opens downward for the area so if i was thinking up the graph i have the the graph of this parabola opening downward i can see that the y intercept is at zero and i can see that these zeros of my function when x is zero my area is zero and when x is when 12 minus 2x is equal to zero or when x is six when x is six i also have that area being zero and i know my parabola let me go in a different color we'll go with green and i know my parabola goes up like this and then comes down and i know i have symmetry along x equals three so i know that the best or the maximum area that can be enclosed here is taking place right here when x is three and i believe that's what the first question asked.

02:10 It asked, how should you fold this so that you end up having the maximum area? and that has to happen when x is three inches.

02:18 So you'd want this to be three inches.

02:21 And then two times three is six and 12 minus six is six.

02:26 This is six inches.

02:30 And then again, that would be three inches.

02:32 So that will allow the maximum flow.

02:35 So now our next question, was what should the dimensions be so that the area is at least 16 square inches? so you want the area to be at least 16 square inches.

02:54 And so we know that, let's go up here, in this maximum area that we have, that's going to take place.

03:03 Again, if i put, i can see that the cross -sectional area here happens to be an area of 18 square.

03:10 So that's the maximum you can possibly get.

03:13 And i want it to be at least 16...

Please give Ace some feedback