For all problems below, show your work and explain your answers. 1. Below is a topographical map of the southern section of Mount Rainier. It will help to print a copy of this map to do this problem, or mark it on a tablet. (a) The Kautz Glacier route is marked by the left-most red/orange line, starting near Glacier Vista at the bottom right side of the map. What is the steepest part of the Kautz Glacier Route? Circle and label it on the map, use the latitude/longitude to give approximate coordinates. Then describe how you know it's the steepest part of the route. (b) The Kautz Glacier route is marked by the left-most red/orange line, starting near Glacier Vista at the bottom right side of the map. What is the least-steep part of the route? Circle and label it on the map, use the latitude/longitude to give approximate coordinate. Then describe how you know it's the least steep part of the route. (c) Identify a ridge feature. Circle and label it on the map, use the latitude/longitude to give approximate coordinate. Then describe how you know it's a ridge. It doesn't have to be a very big ridge. (d) Identify a gully feature. Circle and label it on the map, use the latitude/longitude to give approximate coordinate. Then describe how you know it's a gully. It doesn't have to be a very big gully. (e) Find Panorama Point McClure Rock. Their elevations are given in both meters and feet (Panorama Point's is to the left of the words). Below the topographical map is a Google Earth image with the approximate horizontal distance between Panorama Point and McClure Rock. Use this information to estimate the directional derivative of the elevation at Panorama Point in the direction of McClure Rock. Show & explain your work. (Pay attention to Units!) 46 $1 Columbia Crest 14411 ft 4393 m Point Success 14158 4315m 600 Mount Rainier 4650 4930 Wapowety 8410 11 2563 Camp Hazard 11600 3536 m 10000- 8400 9400 ft 12865 m EMMONS GLACIER VAR Gibraltar Rock 12660- 3859 m Disappointment Cleaver INGRAHAM HEADWALA VAR -9606 Cowlitz Emmons Glacier 11434 3485 m A Cadaver Ingraham Flat 11000 ft 3353 m Cathedral Cap Cap FUHRER FINGER KAUTZ GLACIER HOUTE SCALE: 1:24000 7620 2323 my 6831 2002-m Camp Muir 10089 3072m 10200 UN 10188 ft 3105 m 8400 Glacier 46 48 30 7400- -9600- Little Tahoma Peak 1196 3395 Ingraham Cowlitz Muir Snowfield 8600 Creek Cathedral Anvil Rock 9584 t 2921 m 6200- PEBBLE CREEK TRAN 46 50 31 Glacier Rocks 8384 2555 m Glacier 7769 It 2374 m Paradise McClure Rock 7385 1 2251 in -46 49 3 Glaciers 46 48 30 |||||| CONTOUR INTERVAL 40 FEET Ingraham Glacier Disappointment Cleaver Route Ingraham Headwall (Direct) Variation Emmons Glacier Variation Kautz Glacier Route Fuhrer Finger Route A Possible camp site Guide Hut Trail Ranger Hut N MN 21.5% -5800 12144 30 Glacier Vista 63361 1931 m 21744 6900 2103 Paradise Glacie Caves Panorama Point 6400 SKYLINE TRINE To Paradise 12143.30 INGRAHAM GLACIER. DISAPPOINTMENT CLEAVER ROUTE A FUHRER FINGER ROUTE KAUTZ GLACIER ROUTE NAVIGATION: Climbers must be prepared to navigate in white-out conditions with little or no visibility. Mistakes in navigation on Mt. Rainier during storms and white-outs have resulted in lost climbers and hikers and occasional fatalities. To decrease the possibility of this happening to your party, obtain training from experienced profes- sionals and practice your navigation skills prior to attempting Mt. Rainier. Also, obtain the handout (provided at the Paradise Ranger Station) containing compass bearings to and from Camp Muir. Essential equipment for navigating includes: compass, topographic map, and an altimeter that is accurate to within 10 feet. The above 7.5 minute topographic map is based on a USGS 1:24,000 scale (1"-2,000') quadrangle map with a 40' contour interval. Be aware that magnetic anomalies exist (due to the mountain's volcanic activity) on Mt. Rainier that can create false compass readings. McClure Rock Distance 808.93 m 5 Done ma Point McClure Rock 841.14 m Distance 808.93 m 5 Done 2. Consider the function f(x, y) = xex-y (a) What is the domain of this function? (b) Find the partial derivatives of this function. (c) Find the critical points of this function. (Hint: this is when the first ordre partial derivatives are zero. So set the partial derivatives in x and y equal to zero and solve.) (d) Find all possible secondderivatives for this function, and verify Clairaut's Theorem for it.