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vekshin1
3 years ago
9

What is the volume of the prism if each cube is 1 cm to the third power?​

Mathematics
1 answer:
iogann1982 [59]3 years ago
7 0

Answer:

42 cm^3

Step-by-step explanation:

volume of a rectangular prism = L x W x H

the dimensions are7x3x2 so you multiply those numbers and get the volume which is 42

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saul85 [17]

\large\underline{\sf{Solution-}}

<u>Let us assume that:</u>

\sf \longmapsto x =  \sqrt{6 +  \sqrt{6 +  \sqrt{6 + ... \infty } } }

We can also write it as:

\sf \longmapsto x =  \sqrt{6 +  x }

Squaring both sides, we get:

\sf \longmapsto  {x}^{2}  =6 +  x

\sf \longmapsto  {x}^{2} - x - 6  =0

By splitting the middle term:

\sf \longmapsto  {x}^{2} - 3x + 2x - 6  =0

\sf \longmapsto x(x - 3) + 2(x - 3 ) =0

\sf \longmapsto (x+ 2)(x - 3 ) =0

<u>Therefore:</u>

\longmapsto\begin{cases} \sf (x+ 2) =0 \\ \sf (x - 3) = 0 \end{cases}

\sf \longmapsto x =  - 2,3

<u>But x cannot be negative. </u>

\sf \longmapsto x = 3

Therefore, the value of the expression is 3.

\large\underline{\sf{Verification-}}

Given:

\sf\longmapsto x=3

We can also write it as:

\sf\longmapsto x = \sqrt{9}

\sf\longmapsto x = \sqrt{6+3}

\sf\longmapsto x = \sqrt{6 + \sqrt{9}}

\sf\longmapsto x = \sqrt{6 + \sqrt{6+3}}

\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{9}}}

\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+3}}}

This pattern will continue.

\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+...\infty}}}

7 0
3 years ago
Find the slope of the line that passes through 7,12 and 10,10
vfiekz [6]

Answer:

2/3

Step-by-step explanation:

8 0
3 years ago
Cost of sled $99.50 markup 95%
DIA [1.3K]
Sled $99.50 X 0.95= $94.525
$94.525+ $99.50 = $194.025
Answer is $194.03
8 0
3 years ago
Helpppppppppppppppppppp pleaseeeeeeeeeee
Umnica [9.8K]

Answer:

FG = 16

Step-by-step explanation:

if df bisects <edg then  triangles DFE and DFG are similar AAA

since DF is the same in both triangles triangles DFE and DFG are congruent

therefore FE = FG

n+5 = 2n-6

subtract n from each side

n-n+5 = 2n-6-n

5 = n-6

add 6 to each side

5+6 = n

n=11

FG  = 2n-6

      =2*11 -6

    = 22-6

   = 16


6 0
3 years ago
Find the value of x.
lawyer [7]

Answer:

\huge\boxed{x=\sqrt{70}}

Step-by-step explanation:

ΔABC and ΔADB are similar (AAA).

Therefore the corresponging sides are in proportion:

\dfrac{AB}{AD}=\dfrac{AC}{AB}

Substitute:

AB=x\\AC=7+3=10\\AD=7

\dfrac{x}{7}=\dfrac{10}{x}       <em>cross multiply</em>

(x)(x)=(7)(10)\\\\x^2=70\to x=\sqrt{70}

4 0
3 years ago
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