Think of asy. as limiting fences to where your graph can travel. If, for example, you graph y = 1/x properly, you'll see that the graph never crosses either the x- or the y-axis. As x increases, your graph will get closer and closer to the line y=0 (which happens to be the horiz. axis), but will not cross it. Similarly, as x approaches x=0, the graph gets closer and closer to the vert. axis, x=0, but will not cross it. Do you see how the asymptotes limit where the graph can go?
Vertical asy. stem only from rational functions and correspond to x-values for which the denominator = 0. As you know, we can NOT divide by zero. Instead, we draw a vertical line thru any x-value at which the rational function is not defined.
Horiz. asy. have to do with the behavior of functions as x grows increasingly large, whether pos. or neg. Go back and re-read my earlier comments on horiz. asy. As x grows incr. large, in the positive direction, the graph of y=1/x approaches, but does not touch or cross, the horiz. asy.I will stop here and encourage you to ask questions if any of this discussion is not clear.
The answer should be either 2.5 x 10^4 or 2.1 x 10^4.
But I feel 2.5 x 10^4 is a better estimate.
Hope it helped :))
Answer:
1) x=1
2) x=6
3) x=3
Step-by-step explanation:
i just did them :) good luck
Answer:
The volume of the cone is 128π mm³ ⇒ answer (C)
Step-by-step explanation:
* Lets study the cone
- Its base is a circle
- Its height the perpendicular distance from its vertex to
the center of the base
- The length of its slant height = √(h² + r²)
- The volume of the con is 1/3 the volume of the cylinder
∵ The volume of the cylinder = πr²h
∴ The volume of the cone = (1/3) πr²h
* In our problem:
- r = 4 mm
- h = 24 mm
∴ Its volume = (1/3) × π × (4)² × 24 = 128π mm³
* The volume of the cone is 128π mm³
