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earnstyle [38]
3 years ago
14

Which of these is a simplified form of the equation 7y + 8 = 9 + 3y + 2y?​

Mathematics
2 answers:
Lera25 [3.4K]3 years ago
4 0

Answer:

7y +8 is the answer for the question

AnnZ [28]3 years ago
4 0

Answer:

y = \frac{1}{2}

Step-by-step explanation:

7y + 8 = 9 + 3y + 2y

7y - 3y - 2y = 9 - 8

2y = 1

y = \frac{1}{2}

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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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Step-by-step explanation:

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