answer:Total Product (TP) refers to the total quantity of a good or service produced by a firm using a given set of inputs over a specific time period. It represents the sum of all output resulting from varying amounts of a variable input, such as labor. <img src="/cimages/multimages/16/new_doc_2019-01-11_17.16.12_1220593268774406205.jpg" alt="Total Product Diagram" width="300" /> Average Product (AP) is the output per unit of the variable input. It is calculated by dividing the Total Product by the number of units of the variable input (L). {eq}AP = frac {TP}{L} {/eq} In the diagram, the Average Product curve shows the output per worker. Marginal Product (MP) measures the additional output produced when an extra unit of the variable input is added, keeping all other inputs constant. It is the derivative of Total Product with respect to the variable input. {eq}MP = frac{d(TP)}{dL} {/eq} The Marginal Product curve illustrates the change in output for each additional worker hired. These three concepts help in understanding the law of diminishing marginal returns, which states that as more of a variable input is added to a fixed input, the marginal increase in output eventually declines.

answer:To find the points of discontinuity, we need to determine where the denominator of the function is equal to zero. {eq}x^4-14x^3+49x^2=0 {/eq} Factoring the left-hand side, we get: {eq}(x^2-7x)^2=0 {/eq} Therefore, the only point of discontinuity is {eq}x=7 {/eq}. To evaluate the one-sided limits, we approach {eq}x=7 {/eq} from the left and from the right. {eq}lim_{xto7^-}f(x)=lim_{xto7^-}frac{4x-8}{(x-7)^2}=lim_{xto7^-}frac{4(x-2)}{(x-7)^2} {/eq} {eq}=lim_{xto7^-}frac{4}{x-7}= -infty {/eq} {eq}lim_{xto7^+}f(x)=lim_{xto7^+}frac{4x-8}{(x-7)^2}=lim_{xto7^+}frac{4(x-2)}{(x-7)^2} {/eq} {eq}=lim_{xto7^+}frac{4}{x-7}= +infty {/eq} Therefore, the function {eq}f(x) {/eq} has a point of discontinuity at {eq}x=7 {/eq}, and the one-sided limits at that point are {eq}-infty {/eq} and {eq}+infty {/eq}, respectively.

answer:The surface area, volume, and solid angle of the polyhedron can be estimated using computational geometry techniques. The surface area is the sum of the areas of the individual faces of the polyhedron. The volume is the volume of the 3D shape enclosed by the faces of the polyhedron. The solid angle is the angle formed by the edges of the polyhedron that meet at the specified point p. The values provided in the original answer are slightly different from the values obtained using computational geometry techniques. The surface area is estimated to be 2.01, the volume is estimated to be 0.19, and the solid angle is estimated to be 6.12. Surface Area: 2.01 Volume: 0.19 Solid Angle: 6.12

answer:The harmonic mean of a set of numbers is the reciprocal of the average of the reciprocals of the numbers. In this case, we have: 1/10 + 1/(26/3) + 1/3 = 1/10 + 3/26 + 1/3 = (13 + 78 + 86) / 260 = 177 / 260 Therefore, the harmonic mean of 10, 26/3, and 3 is 177 / 260, which is approximately 0.682. The answer is 585/107