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4 years ago

Problem solving need help

Mathematics

1 answer:

snow_lady [41]4 years ago

8 0

(69+75) ÷ 2 + 3(5.5)
Parentheses first
144/2 + 3(5.5)
Mulitply/divide from left to right
72+16.5
Add/subtract from left to right
88.5

The cost would be $88.50

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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

Using first principle, this gives:

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

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

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

$S(1) = 1 + 1$

$S(1) = 2$

Hence, the smallest sum is 2

3 0

4 years ago

the product of two integers is positive.is the quotient of those same integers positive, negative,or impossible to predict? expl

KiRa [710]

Answer:

Step-by-step explanation:

pi is irrational. That was proven long ago. Unfortunately the proof is harder to understand than the proof that the square root of 2 is irrational, which is accessible to most high school students.

To prove that p is irrational you need to understand calculus, up through integration. Even then, the proof is rather intense and takes careful attention.

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Ilia_Sergeevich [38]

4x+40-3x-2-x
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The answer will be 38

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umka21 [38]

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4 years ago

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kicyunya [14]

Answer:

Step-by-step explanation:

Given m and n are parallel:

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subtract 138 from both sides

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2 years ago