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3 years ago

9

a rectangular box has a volume of 105 cubic centimeter the width of the rectangular box is X centimeters the length is 2x - 3 cm

and the height is 3 cm

2 answers:

TiliK225 [7]3 years ago

7 0

Answer is five okgffddbj

agasfer [191]3 years ago

5 0

Volume = Length x Width x Height

105 = 3x(2x - 3)

105 = 6x² - 9x

6x² - 9x - 105 = 0

2x² - 3x - 35 = 0
<span>
(x - 5)(2x + 7) = 0
</span>
x = 5 0r x = -7/2 (rejected, because it is negative)

Answer: x = 5

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2 years ago

Find the product of all real values of r for which 1/2x=r-x/7

Dahasolnce [82]

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$r = \±\sqrt{14$

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Step-by-step explanation:

Given

$\frac{1}{2x} = \frac{r - x}{7}$

Required

Find all product of real values that satisfy the equation

$\frac{1}{2x} = \frac{r - x}{7}$

Cross multiply:

$2x(r - x) = 7 * 1$

$2xr - 2x^2 = 7$

Subtract 7 from both sides

$2xr - 2x^2 -7= 7 -7$

$2xr - 2x^2 -7= 0$

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$- 2x^2+ 2xr -7= 0$

Multiply through by -1

$2x^2 - 2xr +7= 0$

The above represents a quadratic equation and as such could take either of the following conditions.

(1) No real roots:

This possibility does not apply in this case as such, would not be considered.

(2) One real root

This is true if

$b^2 - 4ac = 0$

For a quadratic equation

$ax^2 + bx + c = 0$

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$a = 2$

$b = -2r$

$c =7$

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Add 56 to both sides

$4r^2 - 56 + 56= 0 + 56$

$4r^2 = 56$

Divide through by 4

$r^2 = 14$

Take square roots

$\sqrt{r^2} = \±\sqrt{14$

$r = \±\sqrt{14$

Hence, the possible values of r are:

$\sqrt{14$ or $-\sqrt{14$

and the product is:

$Product = \sqrt{14} * -\sqrt{14}$

$Product = -14$

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