Answer:
a) 18 students per teacher
b) 9 students per tutor
c) 7 tutors
Step-by-step explanation:
An arts academy requires there to be 6 teachers for every 108 students and 5 tutors for every 45 students.
a) How many students does the academy have per teacher?
6 teachers = 108 students
1 teacher = x
Cross Multiply.
6x = 108
x = 108/6
x = 18 students per teacher
b) Per tutor?
5 tutor = 45 students
1 tutor = x
Cross Multiply
5x = 45
x = 45/5
x = 9 students
= 9 students per tutor
c) How many tutors does the academy need if it has 63 students?
45 students = 5 tutors
63 students = x
Cross Multiply
45x = 63 × 5
x = 63 × 5/45
x = 7 tutors
Here's the equation for one year:
0.06(6500) + 6500
But because it is 25 years:
25(0.06(6500)) + 6500
1.5(6500) + 6500
We can make it simpler:
2.5(6500)
The total amount is $16350
F(-1)= 4*7(-1) = 4*-7 = -28
F(2)= 4*7(2) = 4*14 = 56
Answer:
110 pages
Step-by-step explanation:
Let number of pages read on 1st day = x
-> No. of pages read on 2nd day = 2x
& No. of pages read on 3rd day = x - 6
Total no of pages read = 458
-> x + 2x + x - 6 = 458
-> 4x - 6 = 458
-> 4x = 458 + 6
-> 4x = 464
-> x = 464/4
-> x = 116
No of pages read on third day = x - 6 = 116 - 6 = 110
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).
