1.)The following formula can be used to convert from degrees Fahrenheit, F, to degrees Celsius, C:
C= 5/9*(F -32)
Gold is liquid for Celsius temperatures C such that 1063 degrees <= C < 2660 degrees. Find a comparable inequality for Fahrenheit temperatures.
2.) The following mathematical model: w = 125 (6400/6400 + x)^2
Describes the weight W (in pounds) of a 125 pound astronaut at an altitude of x kilometers above sea level. What is the astronaut's weight at an altitude of 9600 kilometers?
3.) You invest $7200 in two accounts paying 8% and 10% annual interest, respectively. At the end of the year, the accounts earn the same interest. How much was invested at each rate?
4.) The following function: f(x) = 2(x + 10) , where x>=0
Can be used to convert dress sizes x in the United States to dress sizes f(x) in Italy. For what dress sizes in the United States will dress sizes in Italy be between (not inclusive) 32 and 46?
5.) The weekly demand model for a new video game is given by N = - p + 520. The weekly supply model for the same video game is N = 3p + 400. For these models, p is the price of the video game and N is the number of video games sold or supplied each week. Find the price at which supply and demand are equal.
1) If C = 5/9*(F - 32), we can find out the reverse conversion formula by solving the above equation in F:
9/5*C = F - 32 --> F = 9/5*C + 32
For C = 1063, we will have:
F = 9/5*1063 + 32 = 1945.4
and for C = 2660:
F = 9/5*2660 + 32 = 4820
Hence, the answer is: gold is liquid between 1945.4 deg F and 4820 deg F.
2) We have the weight as a function of the altitude taken in km. This is based on a famous formula of Newton in Physics.
By replacing (x) in the formula with the actual altitude, we can find out the actual weight of the astronaut. For x = 9600 km, we will have:
w = 125*(6400/(6400+9600))^2= 20 lb
3) Let's denote (x) the amount invested in the first account ...
This solution is comprised of a detailed explanation to find a comparable inequality for Fahrenheit temperatures and etc.