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To find:
a. Find and , and interpret the meaning of each.
![Check Mark](/static/check-mark.png)
Answer to Problem 28AYU
Solution:
a. The amount of rain fall , The area of the opening of rain gauge is .
Explanation of Solution
Given:
Let the
Calculation:
a. If denotes the position vector of a vector , then the vector is expressed as,
Thus the vector is ,
Now the area of the vector is,
Therefore the vector is ,
Therefore the amount of rain fall ,
The area of the opening of rain gauge is .
To find:
b. Compute and interpret its meaning.
![Check Mark](/static/check-mark.png)
Answer to Problem 28AYU
Solution:
b. The volume of rain collected in the gauge is .
Explanation of Solution
Given:
Let the vector represent the amount of rainfall, in inches, and let the vector A represent the area, in square inches, . The volume of rain collected in the gauge, in cubic inches, is given by , even when the rain falls in a slanted direction or the gauge is not perfectly vertical.
Calculation:
b.
The volume of rain collected in the gauge is .
To find:
c. If the gauge is to collect the maximum volume of rain, what must be true about and ?
![Check Mark](/static/check-mark.png)
Answer to Problem 28AYU
Solution:
c. The vectors and neither parallel nor orthogonal.
Explanation of Solution
Given:
Let the vector represent the amount of rainfall, in inches, and let the vector A represent the area, in square inches, . The volume of rain collected in the gauge, in cubic inches, is given by , even when the rain falls in a slanted direction or the gauge is not perfectly vertical.
Calculation:
c.
. Therefore the vectors and neither parallel nor orthogonal.
Chapter 9 Solutions
Precalculus
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