check the attach files.. 9) A force of 20 pounds stretches a spring from its natural length of 5 inches to a length of 10 inches. How much work is done stretching the spring from 8 inches to 12 inches? 10) Find the centroid of the region bounded by the graphs of y = - x - 1 and y = x 2 - 1.

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Hi teachers, Could you please solve these questions for me. Regards,

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Could someone please provide their work so i can follow and understand how to do these 4 problems. Thank you

Calculus volume questions. Just need to do question #10,11,15-18 ,only need to set up the integral and sketch. Thank you!!!

Suppose f is a continuous function on [-2, 2] such that f(-2) = 1, f(2) = -1 . Which of the properties below follow without further restriction on f by applying the Intermediate Value Theorem? A. f(c) = 0 for some c in (-2, 2); B. f2(c) = 14for some c in (-2, 2); C. the graph of f(x) + x crosses the x-axison (-2, 2). 1. C only 2. A only 3. B and C only 4. A and C only 5. A and B only

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I need the second question answered, see attached file, please show me how you got the answers.

(1+x 4 )dy/dx-4x 3 y=(x 5 +x)arctan(x 2 ) y(1)=3.14

I need help with question number 7 which is the last question both part a and b . thank you in advance for your help :) . I would appreciate an explanation as well.

I need help with my assignment. Engineering Mathematics One (ENGE501): Differential and Integral Calculus (MATH501)

Find an equation in-coordinates for the conic section that satisfies the given conditions. Parabola; focus: (-8, -8) ; vertex: (-8, 0)

Hello! I am trying to solve this problem, but I have no clue how to do it. I think it involves derivatives, but I am unsure. Smartshop Electronics company has a weekly production cost of z widgets that is given by C(z) = 0.000004z 3 - 0.03z 2 + 100z + 75,000 *** z is in the interval [0, 10,000]. The demand function for this product is given by p(z) = -0.005z + 200. What is the: a: marginal cost for Smartshop Electronics b: marginal revenue for Smartshop Electronics c: marginal profit for Smartshop Electronics when 2,000 & 7,000 TV widgets are made

I need help coming up with discussion postings on the information below. All i need is 3 explanations of the below questions. Each answer only has to be a few sentences long, nothing super in-depth. This week, we will look at second-order differential equations. Here are some questions we will address. Please post answers to these questions in this area. How is a second-order differential equation different from a first-order one? What clues does the notation give us? How is a homogeneous differential equation different from a nonhomogeneous differential equation? What steps should we follow to solve a homogeneous differential equation? What steps should we follow to solve a nonhomogeneous differential equation? How do we ensure that each term in the solution to a differential equation is unique?