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Homework Help for Mathematics
Mathematics is an exact and deductive science that studies abstract entities such as numbers, geometrical figures, symbols ans their relation.
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A utility function is a function that attaches a measure to the satisfaction or utility a consumer gets from the consumption of products per unit time. Suppose U (x, y, z)= xyz is the utility function for 3 products, A, B, and C, with x, y, and z representing the number of units of 3 different products, respectively. The prices of these three products are pa, pe, and pc, in dollars, given by: PA=1 Pa = 2 Pc =1 Find the values of x, y, and that will maximize U (x, y, z)= xyz, subject to the condition that you must purchase $600 worth of products. In other words, P.X+ Pey+ Pez=600, with x, y, and z>0.
4. (a) Define what it means for a function T:R" → R to be a linear transformation. [2 marks] 4. (b) Let T:R2 + R2 be defined by T Show that T is not a linear transformation. (4 marks) 4. (c) Let A = 21. and T : R2 + Rº be the linear transformation defined by T'(x) = Ax for every x € R2 Sketch, as accurately as possible, a graph of the image under T of the square with vertices (0,0), (1.0), (1,1),(0,1). [4 marks]
23. The Lord motor company pro- duces 40% of its cars at plant A and the remainder at plant B. Of all cars produced at plant A, 20% do not have a spare tire, while 30% of the cars produced at B do not have a spare tire. A Lord car is purchased, and it happens to have a spare tire. What is the probability that the car was pro- duced at plant A? (A) .7 (B) .8 (C) 32/74 (D) 1/2 (E) 42/74 (F) none of the above
4. For the function 22 - 1 f(0) = 72-4 determine all of the following if they are present: (i) critical points (where f'(x) = 0 or f'(x) does not exist), local maxima and minima, intervals where f(x) is increasing or decreasing; (ii) inflection points and intervals where f(2) is concave upward or downward; (iii) asymptotes (horizontal, vertical). Sketch the graph of y = f(c), giving the (x,y) coordinates for all of the points of interest above. Please make your sketch big enough to see clearly all features of interest. 6(3.x2 + 4) You may use, without demonstrating it, the fact that f"(x) = ? (x2 – 4)3
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