Do you mind helping me please?
You have resubmitted this question perhaps because the answer wasn't what you expected. I've answered again because nothing seems to have changed. Maybe I misinterpreted the definition of c(x)? But it is no clearer than it was before. "50 squared(x2)" I read as "50x^2", 50 times x squared. Isn't this right?
A. Domain is 0≤x≤100 because x is a percentage, and 0%-100% is the only range for percentage. But a value of x=0 would make the cost c(x) negative, which wouldn't make sense. [However, if c(x) is to be positive, then there must be a minimum value for x that makes c(x) zero, implying that there is no cost for removing less than the minimum percentage of pollutants. The paragraph below shows that c(10.95)=0, so x=10.95% is the minimum value.
If c(x)=50x^2-100x-4900, and c(x)=0, x^2-2x-98=0, x^2-2x=98; completing the square: add 1 to each side: x^2-2x+1=99, so (x-1)^2=99 and minimum x=1+√99=1+3√11=10.95 approx, making the domain 1+3√11≤x≤100 so that 0≤c(x)≤485100 (pesos). For removing less than 10.95% of pollutants there is no cost.]
B. If c(x)=50x^2-100x-4900, then putting x=50, 70, 90 and 99.5 into the function we get:
c(50)=115100 pesos; c(70)=233100 pesos; c(90)=391100 pesos; c(99.5)=480162.5 pesos.
[These amounts may look large but the peso is a small amount of money and a Phillipine peso, for example, is worth about 2 American pennies. So the maximum cost is around $10000 US.] Read More: ...