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:
Step-by-step explanation:
There are several things we need to do/know to figure this out. First we have to know that the perpendicular slope to a line is the opposite reciprocal of the slope of which it is perpendicular (did that make sense?!). In other words, we have to find the slope of the line 5x - 8y + 24 = 0 and then take the opposite reciprocal of it. Solving for y:
with a slope of 5/8. The perpendicular slope, then, is -8/5. So we have m now in y = mx + b. Now onto the second equation...
The equation for which we need the same x-intercept is 7x - 12y - 70 = 0. The x-intercept exists when y = 0, so filling in a 0 for y:
7x - 12(0) = 70 and
x = 10. Now we know x. We also know, however, that when x = 10, y = 0, so we have everything we need to sub into the linear equation and solve for b:
0 = -8/5(10) + b and
0 = -16 + b so
b = 16 and the equation we are looking for is
y = -8/5x + 16
Answer:
72 cent
Step-by-step explanation:
Answer:
90°
Step-by-step explanation:
90
Thales Theorem
ANSWER
A.

EXPLANATION
The expression given to us is,

We have to do the multiplication in standard form

We now multiply the first two numbers and simplify the last two index numbers using the laws of exponents to obtain,

We simplify to get,

Therefore the correct answer is A.