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QUESTION 2
2.1 Study the following pattern and answer the questions that follow:
2.1.1 How many cubes are needed to build this tower?
2.1.2 How many cubes are needed to build a tower like this, but 12 cubes
2.1.3 Explain how you worked out your answer to question 2.1.2
2.1.4 How would you calculate the number of cubes needed for a tower high?

QUESTION $2$ $\newline$ $2$ . $1$ Study the following pattern and answer the questions that follow: $\newline$ $2$ . $1$ . $1$ How many cubes are needed to build this tower? $\newline$ $2$ . $1$ . $2$ How many cubes are needed to build a tower like this, but $12$ cubes $\newline$ $2$ . $1$ . $3$ Explain how you worked out your answer to question $2$ . $1$ . $2$ $\newline$ $2$ . $1$ . $4$ How would you calculate the number of cubes needed for a tower high?

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Mean, variance, and standard deviation of binomial distributions

Full solution

Q. QUESTION

2

\newline

2

.

1

Study the following pattern and answer the questions that follow:

\newline

2

.

1

.

1

How many cubes are needed to build this tower?

\newline

2

.

1

.

2

How many cubes are needed to build a tower like this, but

12

cubes

\newline

2

.

1

.

3

Explain how you worked out your answer to question

2

.

1

.

2

\newline

2

.

1

.

4

How would you calculate the number of cubes needed for a tower high?

Understand Tower Pattern: First, we need to understand the pattern of the tower. Let's assume the first level has ' $\newline$ ' cubes.
Calculate Total Cubes: If the tower is $12$ cubes high, then it means we have levels from $1$ to $12$ . We add up the cubes from each level.
Use Sum Formula: The total number of cubes is the sum of the first $12$ numbers, which is $1+2+3+\ldots+12$ .
Apply Formula: We can use the formula for the sum of the first $n$ natural numbers: $\frac{n(n+1)}{2}$ .
Calculate Total: Plugging in $12$ for $n$ , we get rac{12(12+1)}{2} = rac{12*13}{2} = 78.

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\newline

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\newline

1

\newline

g

\newline

f

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g

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\newline

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\newline

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\newline

1

\newline

g(c)=-3

for at least one

c

-1

4

\newline

g(c)=3

for at least one

c

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1

\newline

g(c)=-3

for at least one

c

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1

\newline

g(c)=3

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