To find the values of a and b, we can use the given information about the function f(x) and its derivatives at x = 0.
First, we know that the value of f(0) is 1, which means that when we plug x = 0 into the function, we get f(0) = 20 + a0 + b*0^2 - 0 + 2 = 1. Solving this equation for b, we get b = -1.
Next, we know that the derivative of the function f(x) at x = 0 is ƒ'(0) = 1. The derivative of a polynomial function is given by ƒ'(x) = 2x + ax + bx^2 - 1. Plugging in x = 0, we get ƒ'(0) = 20 + a0 + (-1)*0^2 - 1 = 1. Solving for a, we get a = 1.
Therefore, the values of a and b are a = 1 and b = -1. The sum of these values is a + b = 1 + (-1) = 0.
D) Social Roles. These are roles that Shellie's manager position entails that directly involve managing and working with people, which makes them her social roles. Shellie surely has other functions at the office, such as reviewing paychecks and resumes, and perhaps compiling expense reports. The examples listed above are social roles because they require her to work directly with the people in her office.
The volume of the triangular prism with the given height and base dimensions to the nearest hundredth is 310.38cm³.
<h3>What is a triangular prism?</h3>
A triangular prism is simply a three-dimensional solid with three rectangular sides and two triangular bases.
The volume of an equilateral triangular prism is expressed as;
V = (√3/4) × a² × h
Given the data in the question;
We substitute our values into the equation above.
V = (√3/4) × a² × h
V = (√3/4) × (8cm)² × 11.2cm
V = (√3/4) × 64cm² × 11.2cm
V = 310.38cm³
Therefore, the volume of the triangular prism with the given height and base dimensions to the nearest hundredth is 310.38cm³.
Learn more about triangular prism here: brainly.com/question/24046619
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