answer:To convert the given equation, 11x + 6y = 18, into its slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, follow these steps: 1. Subtract 11x from both sides: 6y = -11x + 18 2. Divide both sides by 6 to solve for y: y = -11/6x + 18/6 3. Simplify the right side: y = -11/6x + 3 Thus, the slope-intercept form of the equation is y = -11/6x + 3.

answer:The eigenvalues of the matrix are: lambda = {2.438, 5.115 - 4.957 i, 5.115 + 4.957 i}

answer:The interior angles of the polygon are estimated to be {1.27, 0.65, 1.22} radians. The area of the polygon is 0.22 square units, and its perimeter is 2.25 units. Based on the given vertices, the polygon is classified as 'Convex'.

answer:To find the first-order Taylor expansion of the composition f(g(x)) about x = 4, we can use the chain rule. The chain rule states that if f is a function of g, then the derivative of f(g(x)) with respect to x is equal to f'(g(x))g'(x). In this case, f(x) = sin(x^4) and g(x) = e^x. So, f'(x) = 4x^3 cos(x^4) and g'(x) = e^x. Evaluating these derivatives at x = 4, we get f'(4) = 256 cos(256) and g'(4) = e^4. Therefore, the first-order Taylor expansion of f(g(x)) about x = 4 is: f(g(4)) + f'(g(4))(x-4) = sin(e^4) + 256 e^4 cos(256) (x-4) = e^4 sin(256) + (x-4) left(e^4 sin(256) + 256 e^4 cos(256)right) The answer is e^4 sin(256) + (x-4) left(e^4 sin(256) + 256 e^4 cos(256)right)