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Ksju [112]
2 years ago
5

In a theater, there are 15 chairs in the first row, each row has 3 more chairs than the previous row, and there are 15 rows. how

many chairs are there in the theater?
SAT
1 answer:
Nimfa-mama [501]2 years ago
5 0

The 1st row has 15 chairs.

The 2nd row has 15 + 3 = 18 chairs.

The 3rd row has 18 + 3 = 15 + 2•3 = 21 chairs.

The 4th row has 21 + 3 = 15 + 3•3 = 24 chairs.

The pattern continues, so that the n-th row has 15 + (n - 1)•3 = 3n + 12 chairs.

If there are 15 rows, then the total number of chairs is

\displaystyle \sum_{n=1}^{15} (3n + 12) = 3 \sum_{n=1}^{15} n + 12 \sum_{n=1}^{15} 1 = 3\cdot\frac{15\cdot16}2 + 12\cdot15 = \boxed{540}

where we use the formulas

\displaystyle \sum_{n=1}^N 1 = N

\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2

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By making the determinant equal to or smaller than zero, we will see that there are 15 values of n such that the inequality has no real solution.

<h3>Solving the inequality:</h3>

Here we have the inequality:

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Now, we can write the quadratic equation:

y = x^2 + nx + 15.

If the determinant of this quadratic equation is negative or 0, then we have a single root or we don't have roots, and because the leading coefficient is positive, that would mean that the function never becomes negative. Then for these cases, the inequality has no real solutions.

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If you want to learn more about inequalities, you can read:

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The poster is missing and so i have attached it.

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The intentions and message the poster is trying to communicate is very direct because it tells us that  if the workers waste time, the production rate of ships and destroyers will definitely decrease and as such the war will continue and it will take a far longer time to win the war.

The persuasive technique used in this poster is that it shows the glittering generalities about the viewer and from the images fear over a possible outcome.

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