solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks.

1. [-/1 Points] DETAILS SCALCET9 14.1.004. Let h(x, y) = e (a) Evaluate h(-2, 13). (b) Find and sketch the domain of h. 10 Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties. Fill . - 10 9 -3 -7 -6 -5 4 -3 -2 $ 9 10 No Solution Help WebAssign. Graphing Tool (c) Find the range of h. (Enter your answer using interval notation.) Need Help? Read It2. [-/1 Points] DETAILS SCALCET9 14.1.006. Let f( x, y, z) = In(z - v x2 + 12). (a) Evaluate f(3, -4, 7). (b) Find the domain of f. (Enter your answers as a comma-separated list of inequalities.) Need Help? Read It3. [-/1 Points] DETAILS SCALCET9 14.1.008. Find and sketch the domain of the function. MY NOTES A( x, y ) = V x - 9y ASK YOUR TEACHER PRACT y 10 y 40 40 10/ 5 20 20 5 X 5 10 -4 - 2 -X 2 4 -4 - 2 X 2 14 -10 X -5 5 -20 10 -20 -5 O - 10 -40 -40 Need Help? AO - 10 Read It4. [-/1 Points] DETAILS SCALCET9 14.1.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In this example we considered the function W = f(T, v), where W is the wind-chill index, T is the actual temperature, and v is the wind speed. A numerical representation is given in this table. (a) What is the value of f(-5, 60)? What is its meaning? We get f(-5, 60) = ,which means that if the temperature is -5C and the wind speed is 60 km/h, then the air would feel equivalent to approximately .C without wind. (b) Describe in words the meaning of the question "For what value of v is f(-10, v) = -15?" The question is asking: when the temperature is |.C, what wind speed gives a wind-chill index of .C? Answer the question. V = km/h (c) Describe in words the meaning of the question "For what value of T is f(T, 10) = -45?" The question is asking: when the wind speed is| km/h, what temperature gives a wind-chill index of .C? Answer the question. T = OC (d) What is the meaning of the function W = f(-15, v)? Describe the behavior of this function. The function W = f(-15, v) means that we fix 7 at and allow v to vary, resulting in a function of one variable. In other words, the function gives wind-chill index values for different wind speeds when the temperature is .C. From the table (look at the row corresponding to 7 = -15), the function ---Select--- V | and appears to approach a constant value as v increases. (e) What is the meaning of the function W = f(T, 80)? Describe the behavior of this function. The function W = f(T, 80) means that we fix v at and allow T to vary, again giving a function of one variable. In other words, the function gives wind-chill index values for different temperatures when the wind speed is km/h. From the table (look at the column corresponding to v = 80), the function |---Select--- V | almost linearly as T increases. Need Help? Read It Watch It5. [-/1 Points] DETAILS SCALCET9 14.1.021. MY NOTES The wave heights h in the open sea depend on the speed v of the wind and the length of time & that the wind has been blowing at that speed. Values of the function h = f(v, t) are recorded in feet in the table below. Wave height as a function of wind speed and duration Duration (hours) 5 10 15 20 30 40 50 10 2 2 2 2 2 2 2 15 4 Wind 20 5 8 8 9 speed (knots) 30 9 13 16 18 19 19 40 14 21 25 28 31 33 33 50 36 40 45 48 50 60 24 37 4 54 62 67 69 (a) What is the value of f(30, 20)? What is its meaning? According to the table, f(30, 20) = , which means that if a 30 knot wind has been blowing in the open sea for 20 hours, it will create waves with estimated heights of feet. (b) What is the meaning of the function of h = f(15, t)? Describe the behavior of this function. O we fix v and t, resulting in a constant value. O we fix v = 15 and allow t to vary, resulting in an equation of one variable. O we fix t = 15 and allow v to vary, resulting in an equation of one variable. O we allow v and t to vary, resulting in a function of two variables. (c) What is the meaning of the function h = f(v, 15)? Describe the behavior of this function. O We fix v and t, resulting in a constant value. O we fix v = 15 and allow t to vary, resulting in an equation of one variable. O we fix t = 15 and allow v to vary, resulting in an equation of one variable. We allow v and t to vary, resulting in a function of two variables. Need Help? Read It Watch It6. [-11 Points] Sketch the graph of the function. (If an answer does not exist, enter DNE. Select Update Graph to see your response piotted on the screen. Select the Submit button to grade your response.) (Write an (Write an (Write an (Write an (Write an SCALCETQ 1 4.1 .023. ftX.y}=5*x2*y2 equation for the cross section at z : 3 using x and y.) equation for the cross section at z : (I using x and y.) equation for the cross section at z = 3 using x and y.) equation for the cross section at y = 0 using X and 2.) equation for the cross section at x = 0 using y and z.) Stu dent Response Response Description Enter appropriate val in the answer blank(s) and click "Update Gm ." Need Help? 7. [-/1 Points] DETAILS SCALCET9 14.1.035. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Level curves (isothermals) are shown for the typical water temperature (in .C) in Long Lake (Minnesota) as a function of depth and time of year. Estimate the temperature in the lake on August 28 (day 240) at a depth of 10 m and on May 20 (day 140) at a depth of 5 m. 12 16 20 18 U Depth (m) 20 16 12 10+ 15+ 8. 120 160 200 240 280 Day of the year day 240 and depth 10 m OC day 140 and depth 5 m .C Need Help? Read It Watch It8. [-/1 Points] DETAILS SCALCET9 14.1.045. MY NOTES ASK YOUR TEACHER PRACTI Draw a contour map of the function showing several level curves. f( x , y ) = x2 - 12 X X Need Help? Read It9. [-/1 Points] DETAILS SCALCET9 14.1.053. MY NOTES ASK YOUR TEACHER PRAC Sketch a contour map of the function. f( x , y ) = x2 + 92 J X X O Sketch the graph of the function and compare it to the contour map. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) (Write an equation for the cross section at z = 2 using x and y.) (Write an equation for the cross section at z = 4 using x and y.) (Write an equation for the cross section at z = 9 using x and y.) (Write an equation for the cross section at y = 0 using x and z.) (Write an equation for the cross section at x = 0 using y and z.)(Write an equation for the cross section at x = 0 using y and z.) Update Student Response Response Description Graph Enter appropriate values in the answer blank(s) and click "Update Graph." 987654325 123 46 6189 y Need Help? Read It Watch It(a) Match the function with its graph (labeled A-F). OA OB OC OD OE OF (b) Match the function with its contour map (labeled I-VI). OI O II O III O IV OV O VI Give reasons for your choices. This function is ---Select--- vin y but not x, a condition satisfied only by ? v | and ? v . Also, note that traces in x = k are |---Select--- | with amplitude that ---Select--- |as x increases. Need Help? Read It Submit Answer11. [-11 Points] SCALCET914.1.063. Describe the level surfaces of the function. 9U. bl) = 5x + 72 - 22 O The level surfaces are a family of parallel planes. 0 The level surfaces are a family of ellipsoids O The level surfaces are a family of hyperboloids. O The level surfaces are a family of hyperbolic cylinders. O The level surfaces are a family of semiellipsoids. O The level surfaces are a family of hyperbolic paraboloids. Need Help