The pressure on a scuba diver at sea level is 14.7 pounds per sq inch (psi). The pressure increases 0.445 psi for each foot of depth. Suppose the pressure on a diver is 41.4 psi. How deep is she?
A spring is 2 in long with no weight suspended from it. For each ounce of weight. the spring stretches 0.3 in until it reaches its maximum length of 8 in. How many weight must be added for the spring to reach its maximum length?
Jennifer lit a 12 inch candle and let it burn. She found that after each hour, the candle was 3/4 in shorter. If she let the candle burn until it was only 1 in tall, how many hours did it burn?
csc
To calculate how deep the scuba diver is, we can use the given information about pressure. We know that the pressure increases by 0.445 psi for each foot of depth. Initially, at sea level, the pressure is 14.7 psi.
Let's denote the depth of the diver as "d" (in feet). The total pressure experienced by the diver can be represented by the equation:
Total pressure = Initial pressure + (Pressure change per foot * Depth)
We can set up this equation using the given information:
41.4 psi = 14.7 psi + (0.445 psi/ft * d)
Subtracting 14.7 psi from both sides of the equation:
26.7 psi = 0.445 psi/ft * d
To isolate "d," we divide both sides of the equation by 0.445 psi/ft:
d = 26.7 psi / (0.445 psi/ft)
Evaluating the expression:
d ≈ 59.9 ft
Therefore, the diver is approximately 59.9 feet deep.
Next, let's calculate how many weights must be added for the spring to reach its maximum length.
We know that the spring initially measures 2 inches and stretches 0.3 inches for each ounce of weight until it reaches its maximum length of 8 inches.
Let's denote the weight to be added as "w" (in ounces). The total stretch of the spring can be calculated using the equation:
Total stretch = Initial length + (Stretch per ounce * Weight)
We can set up this equation using the given information:
8 inches = 2 inches + (0.3 inches/ounce * w)
Subtracting 2 inches from both sides of the equation:
6 inches = 0.3 inches/ounce * w
To isolate "w," we divide both sides of the equation by 0.3 inches/ounce:
w = 6 inches / (0.3 inches/ounce)
Evaluating the expression:
w = 20 ounces
Therefore, 20 ounces must be added for the spring to reach its maximum length.
Finally, let's determine how many hours the candle burned for, given that it decreased in height by 3/4 inch for each hour and we want to find the number of hours until it reaches a height of 1 inch.
Let's denote the number of hours the candle burned as "h." The candle initially measures 12 inches.
The height of the candle after "h" hours can be calculated using the equation:
Height after h hours = Initial height - (Height decrease per hour * Number of hours)
We can set up this equation using the given information:
1 inch = 12 inches - (3/4 inch/hour * h)
Subtracting 12 inches from both sides of the equation:
-11 inches = -(3/4 inch/hour * h)
To isolate "h," we divide both sides of the equation by -(3/4 inch/hour):
h = -11 inches / -(3/4 inch/hour)
Simplifying the expression:
h ≈ 14.7 hours
Therefore, the candle burned for approximately 14.7 hours.
To find the depth of the scuba diver, we can use the equation:
Pressure = 14.7 psi + (0.445 psi/ft) * Depth
Given that the pressure on the diver is 41.4 psi, we can set up the equation:
41.4 psi = 14.7 psi + (0.445 psi/ft) * Depth
To isolate the Depth variable, we can subtract 14.7 psi from both sides:
41.4 psi - 14.7 psi = (0.445 psi/ft) * Depth
26.7 psi = (0.445 psi/ft) * Depth
Now, we can solve for Depth by dividing both sides of the equation by 0.445 psi/ft:
Depth = 26.7 psi / (0.445 psi/ft)
Simplifying the units, we get:
Depth = 60 ft
Therefore, the diver is located at a depth of 60 feet.
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To find the number of weights needed for the spring to reach its maximum length, we can use the following formula:
Change in Length = (Weight * Stretch per weight) + Original Length
Given that the original length is 2 inches and the maximum length is 8 inches, we can set up the equation:
Change in Length = (Weight * 0.3 inches/ounce) + 2 inches
We can subtract 2 inches from both sides to isolate the Change in Length:
Change in Length - 2 inches = Weight * 0.3 inches/ounce
Now we can solve for Weight by dividing both sides by 0.3 inches/ounce:
Weight = (Change in Length - 2 inches) / 0.3 inches/ounce
Given that the maximum length is 8 inches, the Change in Length would be 8 - 2 = 6 inches.
Substituting this value into the equation:
Weight = (6 inches) / 0.3 inches/ounce
Simplifying the units, we get:
Weight = 20 ounces
Therefore, 20 ounces of weight must be added for the spring to reach its maximum length.
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To find the number of hours it took for the candle to burn from 12 inches to 1 inch, we need to determine the number of 3/4 inch intervals.
We can set up the equation:
(12 inches - 1 inch) / (3/4 inch/hour) = Number of Hours
Simplifying the units and performing the calculation, we have:
11 inches / (3/4 inch/hour) = Number of Hours
To divide by a fraction, we can multiply by its reciprocal:
11 inches * (4/3 inch/hour) = Number of Hours
The inches cancel out, leaving us with:
44/3 hours = Number of Hours
Using decimal approximation, we find:
44/3 ≈ 14.67 hours
Therefore, it took approximately 14.67 hours for the candle to burn from 12 inches to 1 inch.