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Minchanka [31]
1 year ago
9

Multiply (x + 2)(3x² - 4x + 5).

Mathematics
1 answer:
ziro4ka [17]1 year ago
6 0

Answer:

a. 3x^3 + 2x^2 - 3x +10

Step-by-step explanation:

(x+2)(3x^2-4x+5)

x(3x^2-4x+5) +2(3x^2-4x+5)

3x^3-4x^2+5x+6x^2-8x+10

3x^3-4^2+6x^2+5x-8x+10

3x^3+2x^2-3x+10

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What is the slope of the equation: x = -2
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undefined

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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
Allisa [31]

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

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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}

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S(1) = 1 + 1

S(1) = 2

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

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3 years ago
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