Answer:
the answer is A
Step-by-step explanation:
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:
B
Step-by-step explanation:
easy
The value of the given expression (3m - n)² + 4m when m = 63 and n = 45 is equal to 20,916.
<h3>What is an expression?</h3>
An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
<u>Given the following variables:</u>
Substituting the given variables into the given expression, we have;
Expression = (3m - n)² + 4m.
Expression = (3(63) - 45)² + 4(45).
Expression = (189 - 45)² + 180
Expression = 144² + 180
Expression = 20,736 + 180
Expression = 20,916.
Read more on expressions here: brainly.com/question/28260012
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Complete Question:
Evaluate the expression when m = 63 and n = 45. (3m - n)² + 4m.
False. Only right triangles.
