What is the best estimate for the quotient 5,397 divided by 62
2 answers:
Answer:
The best estimate is 90.
Step-by-step explanation:
Given : Quotient 5,397 divided by 62 .
To find : The best estimate of the given situation.
Solution : We solve this by approximating the term and then divide to get solution.
Approximation is rounding off the number
→ When the ones digit is greater than 5 (5, 6, 7, 8, or 9) then it round the number up.
→ When the ones digit is less than 5 ( 0, 1, 2, 3, or 4) then it round the number down.
Approximation of 5397 to hundredth is 5400
Approximation of 62 to tenth is 60
Now, divide 5400 by 60
Therefore, The best estimate is 90.
We can also cross check by actual division of 5397 by 62.
When we approximate 87.04 it round off to 90.
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Answer:
72 feet from the shorter pole
Step-by-step explanation:
The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.
The shorter pole height as a fraction of the total pole height is ...
18/(18+24) = 3/7
so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:
d/168 = 3/7
d = 168·(3/7) = 72
The wire should be anchored 72 feet from the 18 ft pole.
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<em>Comment on the problem</em>
This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.
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Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:
L = √(18²+x²) + √(24² +(168-x)²)
and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.
