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.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

83-45=38

38 was the other number

hope your goes well, here's a turkey

-thekoolkid1o1