Amit's school is an unusual school. it has 1677 students in grades 3-6.there are twice as many fifth graders as sixth graders and three times as many forth graders as fifth graders. finally, there are five times as many third graders as fourth graders. how many fifth graders are in amit's school?

Step-by-step explanation:

Let

x-----> number of students in third grade

y----> number of students in  fourth grade

z---> number of students in  fifth grade

r----> number of students in  sixth  grade

we know that

-----> equation A

 ----> -----> equation B

-----> equation C

----> equation D

Substitute equation C in equation D

-----> equation E

Substitute equation B, equation C, equation E in equation A and solve for z

step-by-step explanation:

through just a quick inspection, one can see that the graph of this cubing function starts in quadrant iii and ends in quadrant i.   when x = 0, y = 3, so the y-intercept is (0, 3).

if graphs are part of the problem statement, share them.   .

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt