What is the maximum possible vault of

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

8 0

3 years ago

If you need 2 liters of soda for every 12 students at the school dance, and you sold 360 student tickets to the dance. About how

GalinKa [24]

Answer:

60 liters

Step-by-step explanation:

360/12=30

30x2=60 liters

Hope this helps! :)

4 0

3 years ago

Read 2 more answers

Select all ratios that are in their simplest form. a29:26 b4:28 c25:10 d28:5 e12:19

xxTIMURxx [149]

The correct answer is Option A , D , E.

<h3>What is meant by ratio?</h3>

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other.

<h3>What is meant by ratio in simplest form?</h3>

Ratio in it's simplest form means when the ratio can't be simplified anymore by cancelling out the common factors.

The ratio in Option(A) can't be simplified anymore because 29 is a prime number.

The ratio in Option(B) can be simplified to 1 / 7.

The ratio in Option(C) can be simplified to 5 / 2.

The ratio in Option(D) can't be simplified.

The ratio in Option(E) can't be simplified because 19 is prime number.

Hence, the correct answer is Option A , D , E.

Learn more about ratios on:

brainly.com/question/2328454

#SPJ4

8 0

2 years ago

PLEASE HELP WIL MARK BRAINLIEST MY DUDE

mihalych1998 [28]

Answer:

I think the answer is D

Step-by-step explanation:

5 0

3 years ago

PLEASE HELP ME IM SORRY PLEASE

Gnom [1K]

Hello! (:

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5 less than 3.1 times a number n:

3.1n-5

Four more than the quotient of 12 and a number n:

n/12+4

Hope this helps you!

~SparklingFlower

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3 0

3 years ago