Answer:
0 ≤ t ≤ 5.
Step-by-step explanation:
In the function  ,
,  is the independent variable. The domain of
 is the independent variable. The domain of  is the set of all values of
 is the set of all values of  that this function can accept.
 that this function can accept. 
In this case,  is defined in a real-life context. Hence, consider the real-life constraints on the two variables. Both time and volume should be non-negative. In other words,
 is defined in a real-life context. Hence, consider the real-life constraints on the two variables. Both time and volume should be non-negative. In other words, 
 . .
 . .
The first condition is an inequality about  , which is indeed the independent variable.
, which is indeed the independent variable. 
However, the second condition is about  , the dependent variable of this function. It has to be rewritten as a condition about
, the dependent variable of this function. It has to be rewritten as a condition about  .
.
![\begin{aligned} f(t) &\ge 0 &&\text{Assumption} \cr 80000 - 16000\, t& \ge 0 && \text{Definition of} ~ f \cr 80000 & \ge 16000\, t && \begin{aligned}&\text{Add $16000\, t$} \\[-0.5em] & \text{to both sides of the inequality}\end{aligned} \cr 5 &\ge t &&\begin{aligned}&\text{Divide both sides of} \\[-0.5em] & \text{the inequality by $16000$}\end{aligned} \cr t &\le 5 && \text{Flip the inequality}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20f%28t%29%20%26%5Cge%200%20%26%26%5Ctext%7BAssumption%7D%20%5Ccr%2080000%20-%2016000%5C%2C%20t%26%20%5Cge%200%20%26%26%20%5Ctext%7BDefinition%20of%7D%20~%20f%20%5Ccr%2080000%20%26%20%5Cge%2016000%5C%2C%20t%20%26%26%20%5Cbegin%7Baligned%7D%26%5Ctext%7BAdd%20%2416000%5C%2C%20t%24%7D%20%5C%5C%5B-0.5em%5D%20%26%20%5Ctext%7Bto%20both%20sides%20of%20the%20inequality%7D%5Cend%7Baligned%7D%20%5Ccr%205%20%26%5Cge%20t%20%26%26%5Cbegin%7Baligned%7D%26%5Ctext%7BDivide%20both%20sides%20of%7D%20%5C%5C%5B-0.5em%5D%20%26%20%5Ctext%7Bthe%20inequality%20by%20%2416000%24%7D%5Cend%7Baligned%7D%20%5Ccr%20t%20%26%5Cle%205%20%26%26%20%5Ctext%7BFlip%20the%20inequality%7D%5Cend%7Baligned%7D) .
.
Hence, t ≤ 5.
Combine the two inequalities to obtain the domain:
0 ≤ t ≤ 5.
 
        
             
        
        
        
Answer:
x=13,y=0
Step-by-step explanation:
We are given a system of equations

For equation 1,square all terms to reduce it
√x²+√y²=169
x+y=13
Make x the subject as required by the question to use substitution method
x=13-y
Plug x=13-y into eqn 2
3(13-y)+2y=39
39-3y+2y=39
39-y=39
y=39-39=0
Plug y=0 into equation 1
x+0=13
x=0
 
        
             
        
        
        
Answer:
1/10
Step-by-step explanation:
 
        
             
        
        
        
Answer:
28,993
Step-by-step explanation:
Subtract 8,500 from 37,493
The answer is 28,993
Hope this helped :)
 
        
                    
             
        
        
        
Tan inverse 28/19 is the answer