The distance traveled by a snowball thrown straight down from the top of a bluff can be calculated with the equation d=ut+12gt2, where d is the distance traveled in meters, u is the initial velocity in meters per second, t is the time in seconds, and g is the acceleration due to gravity, which is 9.8ms2. If the snowball traveled 200 meters in 5 seconds, what was its initial velocity?

15.5 m/s

Step-by-step explanation:

Using the equation, d = ut+1/2gt² where all the variables have meaning as given above, making u subject of the formula, we have

d = ut+1/2gt²

d - 1/2gt² = ut

d/t - 1/2gt²/t = u

u = d/t - 1/2gt

Since d = 200 m, t = 5 s and g = 9.8m/s², substituting the values of the variables into the equation, we have

u = d/t - 1/2gt

u = 200 m/5 s - 1/2 ×  9.8m/s² × 5 s

u = 40 m/s - 49 m/s ÷ 2

u = 40 m/s - 24.5 m/s

u = 15.5 m/s

So, the initial speed of the snowball is 15.5 m/s

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: