A steam line will increase in length by 1.440% when heated to operating temperature. Determine the original length of the line, if it increased in length by 5.000 cm when heated. (Round your answer to 3 decimal places).
.0144L = 5.000
solve for L
Well, it seems like that steam line couldn't handle the heat and decided to stretch itself out. What a flexible little line we have here!
To figure out the original length of the line, we need to do a little bit of math. We know that the line increased in length by 1.440% and that this increase is equal to 5.000 cm. So, let's set up an equation.
1.440% of the original length = 5.000 cm
Now, we just need to isolate the original length. To do that, we'll divide both sides of the equation by 1.440%.
Original length = 5.000 cm / 1.440%
Now, since we're asked to round our answer to 3 decimal places, we get:
Original length ≈ 347.222 cm
So, it looks like the original length of the steam line is approximately 347.222 cm. Now, let's hope it doesn't decide to stretch itself out again!
To solve this problem, we can use the formula for percent increase:
Percent Increase = (Increase in Length / Original Length) * 100
We know that the percent increase is 1.440% and the increase in length is 5.000 cm. Let's assign the original length of the line as "L".
1.440% = (5.000 cm / L) * 100
Divide both sides of the equation by 100 to isolate the fraction:
0.0144 = 5.000 cm / L
Multiply both sides of the equation by L to isolate it:
0.0144L = 5.000 cm
Divide both sides of the equation by 0.0144 to solve for L:
L = 5.000 cm / 0.0144
Performing the division, we find:
L ≈ 347.222 cm
Therefore, the original length of the line is approximately 347.222 cm (rounded to 3 decimal places).
To determine the original length of the steam line, we can use the percentage increase formula:
Percentage increase = (increase in length / original length) * 100
In this case, the percentage increase is 1.440% and the increase in length is 5.000 cm. Let's set up the equation:
1.440% = (5.000 / original length) * 100
First, convert 1.440% to its decimal form by dividing it by 100:
0.0144 = (5.000 / original length)
Next, solve for the original length by multiplying both sides of the equation by original length:
0.0144 * original length = 5.000
Now, divide both sides of the equation by 0.0144 to isolate the original length:
original length = 5.000 / 0.0144
Calculating this value gives us:
original length ≈ 347.222 cm
So, the original length of the steam line is approximately 347.222 cm.