problem-solvinga-measuring-wheel-is-used-to-calculate-the-length-of-a-path-the-diameter-of-the-wheel

Name: problem solvinga measuring wheel is used to calculate the length of a path the diameter of the wheel
Uploaded: 2020-03-09
Duration: 46 s
Channel: Numerade
Description: PROBLEM SOLVINGA measuring wheel is used to calculate the length of a path. The diameter of the wheel is 8 inches. The wheel makes 87 complete revolutions along the length of the path. To the nearest foot, how long is the path? (See Example 3.)

Question

PROBLEM SOLVINGA measuring wheel is used to calculate the length of a path. The diameter of the wheel is 8 inches. The wheel makes 87 complete revolutions along the length of the path. To the nearest foot, how long is the path? (See Example 3.)

Ali Soave · Accepted Answer

Let&#x27;s first find the circumference of the wheel so we know circumference is equal to pi times diameter. The day matters eat, so the circumference is equal to eight pi. And then it says that it takes 87 complete revolutions of the wheel to follow the length of this path, so each circum. If each revolution of the wheel is once your conference or a pie, we can take that amount and multiply it times 87 we get about 2100 86 0.31 inches. So the length of the path you know, there&#x27;s foot if we divide this by 12 since this is the inches is about 182 feet.

Julie Silva · Answer

in this problem forgiven the half pipe, which they tell us is in the shape of a semi circle. In other words, it&#x27;s half of a circle and we&#x27;re told that the radius is eight feet. They want us to find the length of the ram. Well, the remain would be representative of half of the circumference because we&#x27;re talking about a circle. Well, how do we find circumference? While the formula for circumference would be C equals two pi r. But that would be if we had, ah, full circle. But in this case, we only have half the circle. So when we need half of the circumference, So to find the ark length we&#x27;re going to do arc length in this particular case is gonna be half off the circumference. So have two pi r. Well, 1/2 times two is equal to one. So it&#x27;ll just be pi Times are well, in this case, our radius is eight. So we&#x27;ll have pi times eight and now we simply need to multiply. Well, if you have the pie button on your calculator, you should use that. And if you don&#x27;t, then you can use 3.14 for pie. I do have the pipeline, and so I&#x27;m going to use that. So I find that I get 25.13274123 So now I&#x27;m going around to the nearest hole number. So I&#x27;m gonna look at the first place after the decimal, which is a one to determine whether that five should get rounded up or stay the same. Well, because that first, please, after the dust, Eliza one, we&#x27;re knocking around that five up, and it will stay the same. So what we found is that the arc length of the ramp would be equal to 25. Now we need our units. And again, we&#x27;re talking about a distance, so we&#x27;ll just be feet.

Supratim Roy · Answer

Hi, everyone. So, in this problem, we have a bicycle tire off diameter 20 forage. Okay, so we&#x27;ve been asked that How much distance does it travel when it makes eight revolutions? Okay, so let us ah, examine what happens when a bicycle air dribbles one revolution. Okay, so if ah, this is a born which is in contact with the ground. Okay. So to make it a complete revolution that will will rotate, and he&#x27;s appointed again come into contact to the ground. So that means the situation will be like that. So this will be again here, and this contact point will be here. Okay, So that means the part of the wheel which has touched the ground is all of which circum parents for one revolution. Okay, so this length is actually no circumference C off this circle. Okay, so this is goodbye. Okay, so we even asked that how many? How much distance doesn&#x27;t doesn&#x27;t cover for eight rural revolution. So if we I am the distance for one revelation, which is the circumstance off this circle, we can multiply, eat with eight, and thus find a total distance covered. Okay, so let me delete this one? No. First of all, we have their diameter, which was equal to, uh, Deez 24 in just. Okay, So the formula for second currencies C equals to buy. Now, you know that the diameter is actually equal to twice the radius off circle so we can replace. Two are with the D in this formula, and it will be be multiplied by by. Okay, So the diameter was Ah, 24 inch. And it is I. So this is the distance that has been covered with one revolution? No, the distance covered for total eight revelation and be so let me date here. Solutions would be, um, eight multiplied by this seldom parents, which is it goes toe eight multiplied by 24 and multiplied by 3.14 in just. Okay, so after calculating you will get the answer is 600 to born 88 in just so this is the distress covered in inches. But we have been asked to find the distance in feet. Okay, So if you ah, look upon the conversion off able, you&#x27;ll find that one inch equals zero. Morning, Zito eight, 33 field. Okay, So 600 two orange 88 INGE would be cool. Toe 600 to 188 multiplied with 0.8 double three fruit. Okay, so that is, if you kill college, the value would be 50 point 219 friend. So, rounding this off 200 space of decimal, we will get if d point to do so. This is the distance 50 point dodo feet, which will be covered by the rotating will in eight revolutions. Okay, so they&#x27;re sold. Thank you.

Audrey Faison · Answer

move a on an architect&#x27;s blueprints. One inch corresponds to four feet. Final length of the wall represented by a line that is three and 78 inches long on the blueprint. So, um, we want to figure out the feet and what I&#x27;m gonna dio is so it&#x27;s three and 70 inches long. Actually, just gonna turn this into a mixed number real quick. So three times a is 24 24 plus seven, this 31. So it&#x27;s 31 over eight. Now, we&#x27;re gonna use cross multiplication. So one times X is one ex, which is just X and then we have four over one Tim&#x27;s 31 over eight. Um, this can reduce. So we have 31 over to so X equals 31 over to now. I&#x27;m just gonna convert it back into a mixed number. So this is 31 divided by two. Um, two can go into 31 time 11 divided by two. Go in there five times and again five times. So it&#x27;s 15.5 feet and that&#x27;s it.

Katelyn Chen · Answer

for this question. We know the diameter is three feet. Listener circumference is equal to D times pi just case sequel to three type I. And so we know that the total travel was 20,619 feet, so we can divide that by three pie. To get us to to get us X is equal to 2400 revolutions.

Maurizia De Palma · Answer

question tells us that there&#x27;s some kids who cut across the lawn and were asked to figure out the total amount of feet that they save by cutting across the salon and said, Ah, walking around the perimeter. So we&#x27;re going to start this off are using the Pythagorean theorem. And what will notice is that this is our high pot news or our C squared. And then these two values here are the legs so we can plug in X or A and X plus 10 for B and then 40 Percy. And you just have to remember that Expose 10 is the same thing as this. So we have to foil that in order to get that answer. So we get X squared Waas X squared plus 20 x plus 100 and 40 squared gives us 1600. And now we can combine our like terms here. So we have two x squared most 20 X plus 100 equals 1600. And since this has a two in front of the X squared and all of these numbers are divisible by two, we can divide every term too. When we do that, we get X squared plus 10 x minus or sorry plus 50 equals 1600. And now we want to solve this quadratic. So we want our right hand side t equals zero, so we&#x27;ll subtract 1600 from both sides. We&#x27;re sorry. This should actually be 800 So we&#x27;ll subtract 800 from both sides. And when we do, you get X squared plus 10 x minus 750 equals zero. And now we&#x27;re going to use the quadratic formula. So I will write that on the side. Oh, eastward menace for a C over to a And now I will label what the A, B and C terms are in this equation. And now we just have to plug those values into that formula. So X equals negative B, which is minus 10 in this case, plus or minus the square root of B squared, which is 10 squared minus four times a just one time. See, which is minus 750 all over, two times a, which is one, and we can simplify what we have underneath our radical sign. And when we do that, we get minus 10 plus or minus 10 squared. It was this 100. We have two negatives here, so we&#x27;ll get a positive answer. And 750 times four gives us 3000. This is all over too. And now we can add 103,000 together and we&#x27;ll get 3100 over to. And our trick with this 3100 to simplify it is we want to think of a perfect square that goes into that. And luckily, 100 does. So we can rewrite this of minus 10 plus or minus 100 times 31. Number two and the square root of 100 is 10 so we can pull that turn out. And I&#x27;m also going to break this up into two separate fractions. So we get minus 10 over to plus or minus 10 Route 31 over two and minus 10 over to will simplify to minus five. And we can divine both of these turn by two. And when you do that, you get one when we get five and we can ignore our negative answer because we can&#x27;t have a negative length in this case. Eso When you simplify this, we get negative. Five plus five Route 31 you can use a calculator to simplify this. But this is approximately 23 feet, and now we have to go back to our triangle and we see that we have a side length of X. We have a side length of X plus 10. So we have X. We have. Let&#x27;s see, we have X Plus X plus 10. So we&#x27;ll plug 23 for X. And when we add all of this together we get 56. And now we have to subtract our high Ponte news, which is 40. So 56 minus 40 gives us 16. So that tells us by cutting across the lawn, they save 15 or 16 feet.

Problem

PROBLEM SOLVING You ride your bicycle 40 meters. …

Problem 13 Medium Difficulty

PROBLEM SOLVINGA measuring wheel is used to calculate the length of a path. The diameter of the wheel is 8 inches. The wheel makes 87 complete revolutions along the length of the path. To the nearest foot, how long is the path? (See Example 3.)

Answer

182 $\mathrm{ft}$

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