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3 years ago

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]

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

Let us assume that:

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

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:

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

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

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

Therefore:

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

$\sf \longmapsto x = - 2,3$

But x cannot be negative. 

$\sf \longmapsto x = 3$

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:

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

$\dfrac{x}{7}=\dfrac{10}{x}$ cross multiply

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

4 0

3 years ago

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

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