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dmitriy555 [2]
3 years ago
14

Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the sq

uares of the last 2 numbers.
Mathematics
1 answer:
lora16 [44]3 years ago
3 0
Let the first number of the five we are looking for equal n.

Because the numbers are consecutive, the next four can be expressed as (n+1), (n+2), (n+3) and (n+4).

Our series of 5 numbers is therefore n,(n+1),(n+2),(n+3),(n+4).

We are told the sum of the squares of the first 3 is equal to the sum of the squares of the last 2 therefore:
n² + (n+1)² + (n+2)² = (n+3)² + (n+4)²

expand all the brackets to give
n² + n² + 2n + 1 + n² + 4n + 4 = n² + 6n + 9 + n² + 8n + 16
3n²+6n+5 = 2n²+14n+25
n²-8n-20=0

factorising this gives us
(n+2)(n-10) = 0 so the solutions are n=10 and n=-2

That means that n,(n+1),(n+2),(n+3),(n+4) could be [-2, -1, 0, 1 and 2] or [10, 11, 12, 13 and 14].

Since the question asks for whole numbers, and negative numbers are not classed as whole numbers, the numbers we want must be 10, 11, 12, 13 and 14.

You can check this on a calculator by doing 10² + 11² + 12² (=365) and 13² + 14² (=365).
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Answer:

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Step-by-step explanation:

The direction vector will be perpendicular to any/all vectors between the given points. It can be found, for example, using the cross product:

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The cross product can be computed by hand or by any of a number of calculators or web tools. Here it will be ...

  d = (20, -20, 5)

These can be the coefficients of x, y, and z in the plane equation. However, the equation is better written using coefficients that are mutually prime, so we choose the direction vector to be ...

  d = (4, -4, 1)

The constant C in the plane equation

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6 0
3 years ago
Please help in Math!? What value of y makes the equation true?
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\frac{-7}{12} = \frac{y}{-36}

First, simplify \frac{y}{-36} to - \frac{y}{36} / Your problem should look like: - \frac{7}{12} = -\frac{y}{36}
Second, multiply both sides by 36. / Your problem should look like: -21=-y
Third, multiply both sides by -1. / Your problem should look like: 21 = y
Fourth, switch your sides. / Your problem should look like: y = 21

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Between July 28 and 30 of last year over 41.2 cm​ (about 16 ​inches) of rain fell in a city. The normal total monthly rainfall i
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The amount more of rain that fell in those three days than normally falls in July and August combined was 31.19 cm.

<h3>How much more rain fell in those three days?</h3>

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