Establish the identity.6 csc2? - 2 cot2? = 4 csc2? + 2

What will be an ideal response?


6 csc2? - 2 cot2? = 4 csc2? + 2 csc2? - 2 cot2? = 4 csc2? + 2 (csc2? - cot2?) = 4 csc2? + 2

Mathematics

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Find the particular solution to the given differential equation that satisfies the given conditions.D2y - 6 Dy + 9y = 0; Dy = 2 and y = 5 when x = 0

A. y = (5 - 13x)e3x  B. y = (5 + 13x)e3x  C. y = (5 - 13x)e-3x  D. y = (c1 + c2x)e3x 

Mathematics

Factor the polynomial completely, given that the binomial is a factor.x + 6, x3 + 17x2 + 90x + 144

A. (x + 6)(x2 + 24) B. (x + 6)(x2 - 11x + 24) C. (x + 6)(x2 + 11x + 24) D. (x + 6)(x + 3)(x + 8)

Mathematics

Under ideal laboratory conditions, the rate of growth of bacteria in a culture is proportional to the size of the culture at any time t. Suppose that 4,000 bacteria are present initially in the culture and 5,000 are present 1 hr later. How many bacteria will be in the culture at the end of 4 hr? ? Round the answer to the nearest thousand. ? __________ bacteria

Fill in the blank(s) with the appropriate word(s).

Mathematics

Provide an appropriate response.The demand function for a manufacturer's product is p = f(q) = 600 - 2q, where p is the price (in dollars) per unit when q units are demanded (per week). Find the level of production that maximizes the manufacturer's total revenue and determine this revenue.

Fill in the blank(s) with the appropriate word(s).

Mathematics