Answer:
2,400 foot-pounds
Step-by-step explanation:
Say at any instant x is length of Rope
Work done in lifting rope by dx amount will be:
dw = -(2.5x + 10)dx
w = -(40)∫(2.5x+10)dx
w = (2.5(40)^2) / 2 + 10(40)
w = 2000 + 400
w = 2,400 foot-pounds
ANSWER:
examples of limiting factors are, food, water and sunlight
It can be helpful to use technology (a spreadsheet program or graphing calculator) to help you with iterated functions. What you are doing is evaluating the function using its output as new input.
(A) Whenever the magnitude of the slope of a function is less than 1, it will iterate toward the point where it intersects the line y = x. Here the magnitude o the slope is 1/2, so the final value in this case will approach
.. x = y = (-1/2)x +3
.. 3/2x = 3 . . . . . . . . add x/2
.. x = 2 . . . . . . . . . . . multiply by 2/3
You can see several iterations in the table in the figure here.
(B) The values get closer to 2 in each case.
_____
Iteration of this function is like drawing a spiral on the graph. Start with some point on the function curve, such as (0, 3). Draw a horizontal line to the line y=x. this gives you x=3. Now draw a vertical line to the function curve. This will give you the point (3, f(3)) = (3, 1.5). Draw a horizontal line to y = x, repeating as many times as you like. You will see the points get closer and closer to (2, 2) with each loop around the spiral.
If the slope of the function is greater than 1, the "spiral" will diverge instead of converging.
There is a rather-hard-to-remember formula for the lateral area of a cone. I'd suggest you look that up on the 'net. Here you have a right circular cone with radius 24/2, or 12 units and slant height 36 units. If you're unable to find the formula on your own, come back and I'll give you some hints.
Answer:
-1/4
Step-by-step explanation:
Multiplicative inverse is another word for reciprocal
It is the number you multiply by to get 1
-4 * x = 1
Divide each side by -4
x = 1/-4
x = -1/4