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Firlakuza [10]
3 years ago
14

a scale on a blue print says that 1/4= 3 on the real wall. if a wall measures 5" on the blue print , what is the actual length o

f the wall in real life
Mathematics
1 answer:
Nady [450]3 years ago
7 0
We need to first simplify the ratio of blueprint to wall, of a ratio of 1 on the blue print to x in the real wall. This can be done by multiplying by the denominator, which is 4. 1/4 x 4 = 1, 3 x 4 = 12. Our new ratio is 1 to 12. If 1 = 5, then we need to multiply both sides by 5.
5 x 12 = 60.
60" on the real wall.
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What is the sum of the first 51 consecutive odd positive integers?
Angelina_Jolie [31]
We call:

a_{n} as the set of <span>the first 51 consecutive odd positive integers, so:

</span>a_{n} = \{1, 3, 5, 7, 9...\}

Where:
a_{1} = 1
a_{2} = 3
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a_{4} = 7
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<span>and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
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7-5 = 2
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Then, the common difference is 2, thus:

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<span>
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</span>a_{n} = a_{1} + (n-1)d
<span>
So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

</span>S_{k} = ( \frac{a_{1} +  a_{k}}{2}  ).k
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Therefore, we need to find:
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Given that a_{1} = 1, then:

a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1

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