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Find the coefficient of (a^6)(b^2) in the expression (a^2 - 2^b)^9.

Approximate the function  f(x) = 3lnx^4    about the point where x = a = 1 as a 3rd order Taylor series

"State the domain and range for a given function. State the domain and range for   then find f -1(X) and state its domain and range.Verify the inverse relationship using composition. "

"Bloomington Brewery produces beer and ale. Beer sells for $5 per barrel, and ale sells for $2 per barrel. Producing a barrel of beer requires 5 pounds of corn and 2 pounds of hops. Producing a barrel of ale requires 2 pounds of corn and 1 pound of hops. The brewery has 60 pounds of corn and...

"The total monthly cost for a small manufacture of swimwear is given by the equation C(x) = 10,000+4X – 0.001X2"

Find the vertex of the parabola y = x2‐4x+3.

"The owners of a large farm have decided to begin converting the land to soybean production. The annual soybean harvest, H, in bushels, is a product of Y, the yield per acre (bushels per acre), times A, the number of acres of soybeans planted. If Y and A as functions of t, the time in years...

"The total monthly cost for a small manufacture of swimwear is given by the equation C(x) = 10,000+4X – 0.001X2"

Estimate the indicated derivative by any method.

Consider the fuction as representing the value of an ounce of silver in Indian rupees as a function of the time t in days. Find the average rates of chage of R(t) over the time intervals [t, t+h], where t is as indicated and h = 1, 0.1, and 0.01 days. Hence, estimated the instantaneous rate of change of R at time t.

The graph of function is shown together with the tangent line at a point P. Estimate the derivative of f at the coeersponding x value.

Find the pH of an acidic substance of your choice. Using this pH, show how to find the hydrogen ion concentration, [H+], of the substance using the formula. Discuss the meaning of pH and [H+], the pH scale and why your chosen substance is acidic. Use scientific notation or enough decimal places so...

A six-sided die is rolled. What is the probability that an even number or a number less than 3 is rolled? Show work.

"A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory.  A random sample of 100 greeting cards indicates a mean value  of $2.55 and a standard deviation of $0.44. a. Assuming  a normal  distribution, construct a 95% confidence...