A fireman is holding one end of a rope at the top of a building that is 100 ft high. The rope weighs 1 lb/ft and is 200 ft long. Note that 100 ft of the rope is just lying on the ground freely. What is the total amount of work done in pulling all of the rope up to the top of the building? Hint: The total amount of work is the sum of two definite integrals - one for the first 100 ft of the rope, and another one for the last 100 ft of the rope. Note that for the last 100 ft of the rope, each differential segment has to traverse a distance of 100 ft.

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!

coin flip

non-answer:

choosing

sorry if this isnt what you're looking for i dont really understand the question

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step-by-step explanation:

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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