# Desmos Portrait 2018 How did you figure what equations to use?

I started this assignment with a list of different functions I could use or may needed for the self portrait, through it involved a lot of trial and error. On the graph or “portrait” contains linear (y=x), quadrant (y=x2), and circle (r2=y2+x2) functions along with using greater, less than or equal to (<,>,=) to limit certain lines, as was said it took some playing around to figure out what numbers to use as coefficients and constants. There were some moments where I would come to a road block, in one way for example – making the function that involved shading an area, so I had asked for help and it had me understand better the use of <,> or =. However, as a result I decided not to use that function. What did this assignment help you understand about functions?

This assignment allowed me to use and practice different functions, work on graphing numbers and memorize the outcomes of each function. Overall, using Desmos is more than just place the numbers for input (x) and output (y), it includes planning what should be used, balancing each function and a lot of problem solving. # Surface Area of a Sphere In todays activity was to use the peelings of a spherical orange to determine the formula to find the surface area. First we had to cut it in half, trace the circumference as many times as needed, then peel the half oranges and fill as many circle fully with peelings. As a result, 4 circles were filled giving me the conclusion that >>
Area of Sphere could = 4 x (pi) x diameter.

However, this is what I assume.

# Garibaldi Lake Garibaldi is a lake you may recognize from many well known photos of Canada. The lake is glacier water dammed on one side by lava formation (aka The Barrier), along with feeding Rubble Creek and it is located north of Squamish and south of Whistler, BC.

Estimate how much water the Barrier contains behind it in the lake?

To get a general idea of how much water the lake consists of requires to find the approximate volume of the lake. There are many ways to find volume and since Garibaldi Lake isn’t exactly a circle or has a flat lake bed, its needed to assume the lake as a shape like a triangular or rectangular prism because the surface can be rectangular and have it triangular for the floor inclines as you go deeper.

The formula for volume of a prism is >>  V= base area height – or depth in our case.

The known area of Garibaldi lake is 9.94 km square and the average depth of the lake is 119 m. To complete the equation, first kilometres has to change to metres and since 1 km = 1,000 m, 9.94 has to be multiplied by 1,000 in which = 9,940 m.

Since the units are now the same, they can be multiplied>>

9,940 m = area      119 m = height/depth

V = (9,940) x (119)

1,182,860 m cubed

Therefore, 1,182,860 m cubed is the estimate for how much glarier water Lake Garibaldi has.

If the Barrier faulted, what do you think would happen? Consider; how much water would escape, and what kind of power is the escaping water equivalent to?

For how much water may escape, consider the depth of the barrier. The Barrier was form 9,000 years ago from lava flow from Mount Price, it has the length of 2.4 km and the height of 243 m, along with allowing for Rubble Creek to outflow from Garibaldi Lake. The max. depth of the lake is 258 m, which leaves around 15 m difference.

To determine how much water might escape, its needed to calculate how much would remain. We already know the volume of the lake = 1,182,860 m cubed. Therefore >>

max depth – 1,182,860 m per 258 m

258 m/15 m = 1,182,860 m/x

= 15 x 1,182,860/258

= 17,742,900/258

68,771 m cubed

then>>

1,182,860 m – 68,771 m = 1,118, 089 m cubed

From this, around 1,118,089 m cubed would escape while 68,771 would remain in the lake.

For what would happen if the water could escape, it would most likely flood over Squamish, having the flow 120 metres high he estimates, according to Dr. Quane from Quest University, it would be catastrophic.

The provincial government deemed the area below the lake to be unsafe for human habitation in 1981 due to its instability in volcanic and tectonic activity or heavy rainfall.

“Geologically, the chances of this happening are almost certain”, he said “But the probability of it happening in our lifetime is really low”

Resources

Garibaldi Lake a ticking time bomb?

The Barrier

Garibaldi Lake: Everything tourists (and you) need to know before you go