Ratios and fractions are interchangeable (for the most part). A fraction is a type of ratio. And we've all worked with fractions before, so that's what we'll do here.
I can say that the ratio 3:1 is the same as the fraction 3 / 1. Using that fraction, it is fairly easy to find equivalent fractions.
3 / 1 = 6 / 2 = 9 / 3 = 30 / 10
...And so on
Another example, 5:6 = 5 / 6.
5 / 6 = 10 / 12 = 15 / 18 = 30 / 36
To find equivalent fractions, all you need to do is multiply both the numerator and denominator by the same number. As long as that number is the same (and your multiplication is correct), then the new fraction will be equivalent to the original.
Hope this helps!
This is a pretty mathematical question, so I will answer it in pieces as I get the time to work it out. To find the time it takes to fall, you start with Newton's second law, ma=m[d2r/dt2]=-GMm/r2=dv/dt and integrate it once to get v=dr/dt=√[2GM(R-r)/(Rr)] where, for your question, R is the distance from the center of the earth to the point from which it was dropped, r is where it is at the time t(r), G is the universal gravitation constant, and M is the mass of the earth. (The mass m of the ship does not matter.) (You can more easily get v(r) from energy conservation.) Next integrate v(r)=dr/dt to get t(r)=-2.69x105{0.5tan-1((2x-1)/(2√[x(1-x)]-√[x(1-x)]-π/4} where x=r/R; this is not a simple integral to perform, but you can find good integrators on the web, for example Wolfram Alpha. Once you have gotten the indefinite integral you are not finished, you need to find the integration constant which will put the ship at rest at x=r/R=1; that is where the π/4 comes from. Putting in your numbers, I find t=4.22x105 s=117 hr=4.89 days. The figure shows the graph of t(x).
Answer:
The correct is choice B.
Step-by-step explanation:
π/6 is an angle located in the first quadrant. Consequently, the equivalent angle for which it references should also be located in this same quadrant and is obtained by adding 2π to π/6 which becomes 13π/6
Cause AB = CD so
answer is D.
arc AB = arc CD
Answer:
x=4/3
Step-by-step explanation:
3x=5-1
3x=4
x=4/3
