Answer:
The values of x for which the model is 0 ≤ x ≤ 3
Step-by-step explanation:
The given function for the volume of the shipping box is given as follows;
V = 2·x³ - 19·x² + 39·x
The function will make sense when V ≥ 0, which is given as follows
When V = 0, x = 0
Which gives;
0 = 2·x³ - 19·x² + 39·x
0 = 2·x² - 19·x + 39
0 = x² - 9.5·x + 19.5
From an hint obtained by plotting the function, we have;
0 = (x - 3)·(x - 6.5)
We check for the local maximum as follows;
dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0
6·x² - 38·x + 39 = 0
x² - 19/3·x + 6.5 = 0
x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2
∴ x = 1.288, or 5.045
At x = 1.288, we have;
V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99
V ≈ 22.99 in.³
When x = 5.045, we have;
V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023
Therefore;
V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5
The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.
Answer: 
Step-by-step explanation:
Given
It takes 20 min and 30 min for a person and his friend to paint a wall individually i.e.
In 1 min they cover 
part and 
part of wall respectively.
If the work together, 1 minute work is
Time required will be reciprocal of it
The range of a function is the set of possible values that can be obtained from the dependent variable. The range of the function is: 
Given that:
Let the number of months be t. So, the function C(t) is calculated as follows:
The range is calculated as follows:
The smallest possible value of t is 0 i.e. when no monthly subscription is done.
So, we have:
And the highest is 
i.e. for a large value of t
So, we have:
Hence, the range of the function is:
Read more about range of functions at:
brainly.com/question/13824428
Answer:
23
Step-by-step explanation:
Taking an algebraic approach
let the number be n, then (n - 17) is 17 subtracted from number and
- 2(n - 17) = - 12 ( divide both sides by - 2 )
n - 17 = 6 ( add 17 to both sides )
n = 23
Thus Julio's number was 23
