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Answer :
Sure! Let's solve the problem step by step.
The formula provided to find the flow rate [tex]\( f \)[/tex] is:
[tex]\[ f = 120 \sqrt{p} \][/tex]
where:
- [tex]\( f \)[/tex] is the flow rate in gallons per minute.
- [tex]\( p \)[/tex] is the nozzle pressure in pounds per square inch.
We are given that the nozzle pressure [tex]\( p \)[/tex] is 169 pounds per square inch. We need to find the flow rate [tex]\( f \)[/tex].
Step-by-Step Solution:
1. Identify the given value:
- Nozzle pressure, [tex]\( p = 169 \)[/tex] pounds per square inch.
2. Substitute the given value into the formula:
[tex]\[ f = 120 \sqrt{169} \][/tex]
3. Calculate the square root of 169:
[tex]\[ \sqrt{169} = 13 \][/tex]
4. Multiply 120 by the square root of 169:
[tex]\[ f = 120 \times 13 \][/tex]
5. Perform the multiplication:
[tex]\[ f = 1560 \][/tex]
So, the flow rate [tex]\( f \)[/tex] when the nozzle pressure is 169 pounds per square inch is:
[tex]\[ \boxed{1560 \text{ gallons per minute}} \][/tex]
The formula provided to find the flow rate [tex]\( f \)[/tex] is:
[tex]\[ f = 120 \sqrt{p} \][/tex]
where:
- [tex]\( f \)[/tex] is the flow rate in gallons per minute.
- [tex]\( p \)[/tex] is the nozzle pressure in pounds per square inch.
We are given that the nozzle pressure [tex]\( p \)[/tex] is 169 pounds per square inch. We need to find the flow rate [tex]\( f \)[/tex].
Step-by-Step Solution:
1. Identify the given value:
- Nozzle pressure, [tex]\( p = 169 \)[/tex] pounds per square inch.
2. Substitute the given value into the formula:
[tex]\[ f = 120 \sqrt{169} \][/tex]
3. Calculate the square root of 169:
[tex]\[ \sqrt{169} = 13 \][/tex]
4. Multiply 120 by the square root of 169:
[tex]\[ f = 120 \times 13 \][/tex]
5. Perform the multiplication:
[tex]\[ f = 1560 \][/tex]
So, the flow rate [tex]\( f \)[/tex] when the nozzle pressure is 169 pounds per square inch is:
[tex]\[ \boxed{1560 \text{ gallons per minute}} \][/tex]
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