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2 years ago

What is the sequence? 1,8,27,64,125

Mathematics

1 answer:

Marat540 [252]2 years ago

5 0

1^3 = 1 x 1 x 1 = 1
2^3 = 2 x 2 x 2 = 8
3^3 = 3 x 3 x 3 = 27
4^3 = 4 x 4 x 4 = 64
5^3 = 5 x 5 x 5 = 125

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Tower one, a cube with a hexagonal prism measures 15.6cm. Tower two, a cube with a cylinder measures 18.3cm. Tower 3, a hexagona

lina2011 [118]

Answer:

$Tower 4 = 23.9cm$

Step-by-step explanation:

Given

Tower one = 15.6 cm

Tower two = 18.3 cm

Tower 3 = 13.9 cm.

Required:

Height of the 4th tower

Represent a cube by X; a cylinder by Y and a hexagonal prism by Z

Tower one, a cube with a hexagonal prism = X + Z = 15.6

Tower two, a cube with a cylinder = X + Y = 18.3

Tower 3, a hexagonal prism with a cylinder = Z + Y = 13.9

$X + Z = 15.6$ ----- Equation 1

$X + Y = 18.3$ ----- Equation 2

$Z + Y = 13.9$ ----- Equation 3

Subtract equation 1 from 2

$(X + Y = 18.3) - (X + Z = 15.6)$

$X - X + Y - Z = 18.3 -15.6$

$Y - Z = 18.3 -15.6$

$Y - Z = 2.7$ ---- Equation 4

Add Equation 4 to Equation 3

$(Y - Z = 2.7) + (Z + Y = 13.9)$

$Y + Y - Z + Z = 2.7+ 13.9$

$2Y = 2.7+ 13.9$

$2Y = 16.6$

Divide both sides by 2

$\frac{2Y}{2} = \frac{16.6}{2}$

$Y = \frac{16.6}{2}$

$Y = 8.3cm$

Substitute $Y = 8.3cm$ in Equation 2 and 3

$X + Y = 18.3$ ----- Equation 2

$X + 8.3 = 18.3$

Subtract 8.3 from both sides

$X + 8.3 - 8.3 = 18.3 - 8.3$

$X = 18.3 - 8.3$

$X = 10cm$

$Z + Y = 13.9$ ----- Equation 3

$Z + 8.3 = 13.9$

Subtract 8.3 from both sides

$Z + 8.3 - 8.3 = 13.9 - 8.3$

$Z = 13.9 - 8.3$

$Z = 5.6cm$

So, we have that

$X = 10cm$

$Y = 8.3cm$

$Z = 5.6cm$

The question states that the 4th tower is made up of the three shapes;

This implies that;

$Tower 4 = X + Y + Z$

$Tower 4 = 10cm + 8.3cm + 5.6cm$

$Tower 4 = 23.9cm$

The height of the 4th tower is 23.9cm

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3 years ago

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I have completed the 1st one and have attached it.

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Sofia has 112 muffins to place into equal packages of 8. The packages will sell for $5 each. What is the total value of the comp

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nadya68 [22]

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Step-by-step explanation:

Multiply:

2/3 * 10/24 = 20/72 = 5/18

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2 years ago