Given a triangle whose dimensions are changing. Its base is…

Given a triangle whose dimensions are changing. Its base is increasing at a rate of 3 in/s while its height is decreasing at a rate of 2 in/s. Find the rate at which the area is changing when the base is 20 in and the height is 30 in. State your final answer as a complete sentence. Show your work on your paper (5 points).  

Let  a) Find the linear approximation L(x) for the given fun…

Let  a) Find the linear approximation L(x) for the given function that can be used to approximate the values of g(x) near x=0. Show your steps. b) Use linear approximation from part (a) to estimate the value of g(-0.1). c) Find the difference of your linear approximation to the actual value of g(-0.1). Round to at least 5 decimal places.    Show your work on your paper (5 points).

Baker is single and earned $226,300 of salary as an employee…

Baker is single and earned $226,300 of salary as an employee in 2025. How much should his employer have withheld from his paycheck for FICA taxes? Social Security is 6.2% on first $176,100, Medicare is 1.45%, Additional Medicare is .9% over $200,000.  Note: Round your answer to the nearest whole dollar amount.

Suppose, hypothetically, that the function in the previous p…

Suppose, hypothetically, that the function in the previous problem (logarithmic differentiation problem) models the amount of bacteria in a container after t hours. Find the rate at which the number of bacteria is changing after 7 hours. State your answer in a complete sentence. Type your answer here. There is no need to show your work.