If a =5, 0, −1,find a vector b such that compab = 2.b = _______.
1 answer:
Response:
Step-by-step breakdown:
According to the question,
The provided vector is
Additionally
Generally
Here represents the magnitude of a, expressed mathematically as
=>
b is a vector that we can assume has the following characteristics
Thus
=>
=>
Consequently, the vector can be mathematically expressed as
This implies that vector b includes multiple values as it consists of variables.
This indicates that if
Then
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Answer:
The variable x lies within the interval of all positive real numbers less than 5 cm.
Detailed solution:
Problem statement:
Determine the volume of the open-topped box as a function of the side length x (in centimeters) of the square cutouts.
Refer to the provided diagram for clarity.
Define:
x → length in centimeters of each square cutout side
The volume of the box with open top can be written as:
Given this, we have:
By substitution:
Determine the domain of x:
Because:
Therefore:
Domain is the interval (0,5)
That means all real numbers strictly greater than zero and less than 5 cm are valid for x.
Hence, the volume V as a function of x is:
