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Igoryamba
3 years ago
14

A stadium has a total of 18,000 seats. Of these, 9,500 are field seats, and the rest are grandstand seats. Complete an equation

that could be used to find s, the number of grandstand seats.
Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
6 0

Answer:

Wow, thanks for all the points!

Step-by-step explanation:

Heres your equation:

18,000 - 9,500 = <em>s.</em>

Theres your equation, have a nice day/afternoon/evening/night.

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Find a positive number for which the sum of it and its reciprocal is the smallest​ (least) possible. Let x be the number and let
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Answer:

S(x) = x + \frac{1}{x} --- Objective function

Interval = \{x:x=1\}

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

x + \frac{1}{x}

Hence, the objective function is:

S(x) = x + \frac{1}{x}

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

S'(x) = 1 - \frac{1}{x^2}

Equate S'(x) to 0 in order to solve for x

0 = 1 - \frac{1}{x^2}

Subtract 1 from both sides

0 -1 = 1 -1 - \frac{1}{x^2}

-1 = - \frac{1}{x^2}

Multiply both sides by -1

1 = \frac{1}{x^2}

Cross Multiply

x^2 * 1 = 1

x^2  = 1

Take positive square root of both sides because x is positive

\sqrt{x^2} = \sqrt{1

x = 1

Representing x using interval notation, we have

Interval = \{x:x=1\}

To get the smallest sum, we substitute 1 for x in S(x) = x + \frac{1}{x}

S(1) = 1 + \frac{1}{1}

S(1) = 1 + 1

S(1) = 2

<em>Hence, the smallest sum is 2</em>

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