Mathematics, 22.08.2019 02:30 emberferran

Arectangular box has dimensions 5ft by 4ft by 3ft. increasing each dimension of the box by the same amount yields a new box with volume seven times the old. use the aleks graphing calculator to find how much each dimension of the original box was increased to create the new box. round your answer to two decimal places.

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Answer from: wolfsilvereye10

Each dimension increased by 3.53 ft

Step-by-step explanation:

* Lets explain how to solve the problem

- A rectangular box has dimensions 5 ft by 4 ft by 3 ft

∵ The volume of the rectangular box = l × w × h , where

l , w , h are its dimensions

∵ l = 5 ft , w = 4 ft , h = 3 ft

∴ Its volume = 5 × 4 × 3 = 60 ft³

- Each dimension of the box is increasing by the same amount

to yield a new box

- Let each dimension will increase by x ft

∴ The new dimensions are l = (5 + x) , w = (4 + x) , h = (3 + x)

- The volume of the new box is seven times the old

∵ The volume of the old box is 60 ft³

∴ The volume of the new box = 7 × 60 = 420 ft³

∵ The volume of new box = (5 + x)(4 + x)(3 + x)

∴ (5 + x)(4 + x)(3 + x) = 420

- Multiply the 3 brackets

∵ (5 + x)(4 + x) = 20 + 9x + x²

∴ (20 + 9x + x²)(3 + x) = 60 + 47x + 12x² + x³

∴ 60 + 47x + 12x² + x³ = 420

- Subtract 420 from both sides and arrange the terms

∴ x³ + 12x² + 47x - 360 = 0

- Use the ALEKS graphing calculator to find x

∴ x = 3.53

* Each dimension increased by 3.53 ft

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

Answer from: Quest

the answer is 8.64

step-by-step explanation:

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Arectangular box has dimensions 5ft by 4ft by 3ft. increasing each dimension of the box by the same...

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