The number of TV sets an appliance store sells per week is given by a function of two variables,
Would you expect
Would you expect
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Calculus & Its Applications (14th Edition)
- An airport can be cleared of fog by heating the air. The amount of heat required depends on the air temperature and the wetness of the fog. The figure below shows the heat H(T,w) required (in calories per cubic meter of fog) as a function of the temperature T (in degrees Celsius) and the water content w (in grams per cubic meter of fog). Note that this figure is not a contour diagram, but shows cross-sections of H with w fixed at 0.1, 0.2, 0.3, and 0.4. (a) Estimate HT (10,0.2): HT (10,0.2) ≈ (Be sure you can interpret this partial derivative in practical terms.) (b) Make a table of values for H(T,w) from the figure, and use it to estimate HT (T,w) for each of the following: T = 20,w = 0.2 : HT (T,w) ≈ T = 30,w = 0.2 : HT (T,w) ≈ T = 20,w = 0.3 : HT (T,w) ≈ T = 30,w = 0.3 : HT (T,w) ≈ (c) Repeat (b) to find Hw(T,w) for each of the following: T = 20,w = 0.2 : Hw(T,w) ≈ T = 30,w = 0.2 : Hw(T,w) ≈ T = 20,w = 0.3 : Hw(T,w) ≈ T = 30,w = 0.3 : Hw(T,w) ≈ (Be sure you can interpret this…arrow_forwardAn airport can be cleared of fog by heating the air. The amount of heat required depends on the air temperature and the wetness of the fog. The figure below shows the heat H(T, w) required (in calories per cubic meter of fog) as a function of the temperature T (in degrees Celsius) and the water content w (in grams per cubic meter of fog). Note that this figure is not a contour diagram, but shows cross-sections of H with w fixed at 0.1, 0.2, 0.3, and 0.4. H(T,8.4) 500 H(T,8.3) B00 H(T,8.2) 200 100 H(T,8.1) (a) Estimate HT(10,0.2): HT(10,0.2) (Be sure you can interpret this partial derivative in practical terms.) (b) Make a table of values for H(T, w) from the figure, and use it to estimate HT(T, w) for each of the following: Т%3 20, w — 0.2: Нт(Т, w) T = 30, w = 0.2 : HT(T, w) = T = 20, w = 0.3 : HT(T,w) z T = 30, w = 0.3 : HT(T, w) 2arrow_forwardFind y as a function of t if 64y" - 112у + 65у %3D 0, У(5) %3D 3, У(5) 3 6. y =arrow_forward
- If real and imaginary part of an analytic function are constants. Show that the curves given by u and v intersect orthogonally.arrow_forwardDetermine the stationary points of the function y = x2e-x and hence classify them.arrow_forward9. Determine an expression for the gradient of f =-Y x+y will use toarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,