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:
x minus z equals two times y
Step-by-step explanation:
x minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times yx minus z equals two times y
Answer:
6 2/3 minutes
Step-by-step explanation:
Their rates in "jobs per hour" are ...
(60 min/h)/(15 min/job) = 4 jobs/h
and
(60 min/h)/(12 min/job) = 5 jobs/h
So, their combined rate is ...
(4 jobs/h) + (5 jobs/h) = 9 jobs/h
The time required (in minutes) is ...
(60 min/h)/(9 jobs/h) = (60/9) min = 6 2/3 min
Working together, it will take them 6 2/3 minutes.
Answer: The larger rug is 4 times larger
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
The small circular rug covers an area of approximately 67 square feet. This means that
67 = πr²
r² = 67/π = 67/3.14 = 21.34
r = √21.34 = 4.62
If a large size rug has twice the dimensions of a small rug, it means that the radius of the larger rug would be
2 × 4.62 = 9.24
The area of the larger rug would be
3.14 × 9.24² = 268.06ft²
Therefore
268.06/67 = 4
The larger rug is 4 times larger