The population, y, of a small town can be represented using a quadratic model. the maximum population, 6,000 people, occurred 20 years after record keeping began. five years later, the population was 5,950. if x represents the number of years after record keeping began, which equation represents the given scenario? y = 2(x – 20)2 + 6,000 y = –2/9(x – 20)2 + 6,000 y = –2(x – 20)2 + 6,000 y =2/9 (x – 20)2 + 6,000

y = -2(x - 20)² + 6000

Step-by-step explanation:

Given: The maximum population, 6,000 people, occurred 20 years after record keeping began. Five years later, the population was 5,950

To Find: If x represents the number of years after record keeping began, which equation represents the given scenario?

Solution:

Vertex = (20,6000) and the parabola opens downward.  

So, Equation is:  

y = A (x - 20)² + 6000    --1

Now, we need to find A.

It is also given that Five years later, the population was 5,950

This means in 25th year the population was 5950.

So, point (25,5950) is on the parabola. Now substitute the given point in the equation to get value of A

5950 = A (25 - 20)² + 6000  

-50 = A (5)²  

-50 = 25 A  

A = -2  

Now substitute the value of A in 1

Thus Equation becomes:   y = -2(x - 20)² + 6000

Hence Option 3 is correct .

y = -2(x - 20)² + 6000 represent the situation.

answer: $420.00

step-by-step explanation:   multiply $400.00 by 5%.

400.00*.05=20

400+20 = 420

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.