Please solve: Question one: F=-KMn/r^2.
Question two: Estimate a safe speed X for a car for a stopping distance of 210 feet. Use the formula: 1/9x^3+11/3x=210.
X = 11.476
Question three:The polynomial 0.0014x^3-0.08x^2+1.5x+12 models naturla gas consumption in trillions of cubic feet, where x=0 corresponds to 1960, x=1 to 1961 and so on. Inwhich year between 1970 and 1990 was natural gas consumption about 21.2 trillion cubic feet?
1975
Question four: The breaking distance D in feet required to stop a car traveling x miles per hour on dry level pavement can be approximated by D=1/9X^2. (A) Calculate the breaking distance for 20 miles per hour and 60 miles per hour. How do your answers compare? (B) If the breaking distance is 49 feet estimate the speed of the car. (C) Use a calculator to solve part (B) numerically. Do your answers agree?
(A) 400/9ft, 400ft; with the increase in speed by 3 times, the braking distance has increased 9 times. (B) 21 miles /hr
Question five: The formula P=D/1+i is used to determine what amount of principal P should be invested for one year at simple interest rate i in order to have D dollars after a year. Solve the formula for i.
Question six: The funtion f(x) 360x/100-x models the cost f(x) in millions of dollars to remove x % of a rivers pollutants. If the government commits %540 million for this project what percentage of the pollutants can be removed?
60%
Question seven: The cumulative number of car accidents from 2000 to 2010 can be modeled by the quadratice expression c=-44x^2+1672x+21120 where x=1 corresponds to 2000, x=2 corresponds to 2001 and so on until x=11 corresponds to 2010. (A) Find the number of cumulative car accidents in 2001. (B) Create a table by evaluating the quadric c=-44x^2+1672x+21120 for each x value that corresponds to the years from 2000-2010.
(A)24288
(B) Table is given below.
x / C(x)1 / 22748
2 / 24288
3 / 25740
4 / 27104
5 / 28380
6 / 29568
7 / 30668
8 / 31680
9 / 32604
10 / 33440
Question eight: The height Hin feet of a ball after T seconds is given by: H=80T-16T^2. How long did it take for the ball to hit the ground?
5secs