The enrollment of a school was 1200. Since then, it has increased at a rate of 35 students per year. Write an equation to represent the enrollment of the school each year after 2000. Identify your variables

The general equation to represent the enrollment of the school each year after 2000  = 1200 +35 n    

where n = number of years after 2000.

Step-by-step explanation:

Here, according to the question:

The initial number of students enrolled in the school = 1200 students

The number of students increased each year  = 35 students

Now if the initial year is 2000, then the number of student in the first year

= Initial enrollment  +  ( n  x Number of students increasing each year )

where n : The total number of years after 2000

So, the number of students in first year after 2000 for n = 1 is

1200 + ( 1 x 35)  = 1235

The number of students in second year after 2000 for n = 2  is

1200 + ( 2 x 35)  = 1270

The number of students in third year after 2000 for n = 3 is

1200 + ( 3 x 35)  = 1305

Hence, the general equation to represent the enrollment of the school each year after 2000  = 1200 +35 n    where n = number of years after 2000.

Therefore Y = 1200+35 (T-2000)

T is variable.

Step-by-step explanation:

Variable : A variable represent many numbers.

Given that the enrollment of a school was  1200.

The increase rate per year is 35.

T = the year after 2000.

Since the increase rate per year is 35.

Therefore the number student increase =  35 (T-2000)

Let Y represent total number of student on T year.

Therefore Y = 1200+35 (T-2000)

Where T is a year after 2000.

Here T is variable.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

144.50

step-by-step explanation:

21.5 x 13.4=288.10 divide by 2