Suppose the total cost of producing x units of a certain commodity is c(x) = 6x4 − 30x3 − 54x2 + x + 2. determine the largest and smallest values of the marginal cost for 0 ≤ x ≤ 5.

You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function.how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions

Geometry in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.

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