A conveyor is used to lift paper to a shredder. The most efficient operating angle of elevation for the conveyor is 35.4°. The paper is to be elevated 13.0 m. What length of conveyor is needed?
I did
sin 35.4 =13/x
x=13/sin35.4
x= 22.44160629
I got two questions:
1) is this answer correct?
2) the question is asking for significant figures. how can I do it?
yes, correct
Notice that all the given data consists of 3 digits, so
22.4 m
thank you Reiny
1) Yes, your answer of 22.4416 (rounded to four decimal places) is correct based on the information provided and your calculation.
2) To consider significant figures, you need to take into account the number of significant figures in the given values. In this case, the value "13.0 m" has three significant figures, so your answer should also be expressed with three significant figures. Thus, the final answer should be rounded to 22.4 m.
To determine if your answer is correct, we can perform the calculation and check if the results match.
x = 13 / sin(35.4)
x = 13 / 0.577
x ≈ 22.515
So, your rounded answer of 22.4416 is close enough. However, it seems there was a slight rounding error in the last digit.
Now, let's address the issue of significant figures. Significant figures are a way to express the precision of a number and are typically used to avoid presenting numbers with excessive precision.
In this case, both 13.0 m and 35.4° have three significant figures. To maintain consistency, our answer should also have three significant figures.
Given that 22.515 has five significant figures, you can round it to the appropriate number of significant figures by keeping the first three digits and rounding the third digit:
x ≈ 22.5 m
Therefore, the length of conveyor needed would be approximately 22.5 meters with three significant figures.