the combined area of two squares is 45 square cm. each side one square is twice as long as a side of the other Square. what is t
1 answer:
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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.
Answer:
30% students
Step-by-step explanation:
Let x be the number of total students of a school.
63% are girls then total number of girls = (0.63)x
37% are boys then total number of boys = ( 0.37)x
Now 23% of girls wear contacts then total number of girls
= (0.63x) × 0.23
= (0.1449x)
And 42% of boys wear contacts then total number of boys wearing contacts
= (0.37x) ( 0.42)
= (0.1554)x
Total students wears contacts = ( 0.1449x) + (0.1554x)
= (0.3003x)
Percentage of students wear contacts = × 100
= × 100
= 30%
All 30% students wear contacts.