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Nitella [24]
3 years ago
8

Find the volume of the rectangular prism. Express your answer as a simplified mixed number.

Mathematics
1 answer:
OverLord2011 [107]3 years ago
7 0

Answer:

Volume = = 138⁶/32 cubic meters

Step-by-step explanation:

Given:

Length = 8⅜ m

Width = 2 m

Height = 8¼ m

Required:

Volume as a mixed number

Solution:

Volume of rectangular prism = L*W*H

Plug in the values

V = 8⅜ × 2 × 8¼

Change to improper fraction

V = 67/8 × 2 × 33/4

= (67 × 2 × 33)/(8 × 4)

= 4,422/32

= 138⁶/32 m³

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Question<br> Find the distance between the points (-5, 8) and (-3,0).
Temka [501]

To calculate the distance between two points we use this formula:

\boxed{ \boxed{{d \:  =   \:  \sqrt{(x_2 \:  -  \: x_1)^{2} \:  +  \: (y_2 \:  -  \: y_1)^{2} } }}}

<h3>______________________</h3>

<h3>We organize the values:</h3>

  • x₁ = -5
  • x₂ = -3
  • y₁ = 8
  • y₂ = 0

______________________

We apply the values already obtained to the formula to get the distance:

d \:  =   \:  \sqrt{( - 3 \:  -  \:( - 5))^{2} \:  +  \: (0 \:  -  \: 8)^{2} }

d \:  =   \:  \sqrt{( - 3 \:  -  \: ( - 5))^{2} \:  +  \: ( - 8)^{2} }

d \:  =  \:  \sqrt{( - 3 \:  +  \: 5) ^{2}  \:  +  \: 64 }

d \:  =  \:  \sqrt{ {2}^{2} \:  +  \: 64 }

d \:  =  \:  \sqrt{4 \:  +  \: 64}

d \:  =  \:  \sqrt{68}

d \:  = \boxed{ \bold{  \: 2 \sqrt{17}  \:   units}}

<h2>Answer: </h2>

\huge{\boxed{ \bold{2 \sqrt{17} \: units }}}

<h3><em><u>MissSpanish</u></em></h3>
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2 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Factor the equation x^3-216=0 using formula for difference of the cubes:

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then

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1. The equation x-6=0 has real solution x=6.

2. The equation x^2+6x+36=0 has negative discriminant D=6^2-4\cdot 36=36-144=-108, then it has two complex solutions

x_{1,2}=\dfrac{-6\pm 6\sqrt{3}i}{2}=-3\pm3\sqrt{3}i.

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Answer:

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Step-by-step explanation:

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