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MAXImum [283]
3 years ago
7

In a painting, The Great Pyramid of Giza is 45 centimeters tall.

Mathematics
1 answer:
777dan777 [17]3 years ago
6 0

Answer:

The scale is: 1 cm = 3.26 meter

Step-by-step explanation:

Given

Height of Pyramid in Painting = H_p = 45 cm

Actual Height of Pyramid = H_a = 146.5m

In order to find the scale, we can find the ratio between actual height and height in painting.

The ratio can be found by dividing the actual height by height in painting

Scale = \frac{H_a}{H_p}\\= \frac{146.5}{45}\\=3.25555 m/cm

Rounding off to nearest hundredth

= 3.26

This means that the scale is:

1 cm = 3.26 meter

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Law Incorporation [45]

Answer:

According to the rule of 72, the doubling time for this interest rate is 8 years.

The exact doubling time of this amount is 8.04 years.

Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

By the rule of 72, we have that the doubling time D is given by:

D = \frac{72}{Interest Rate}

The interest rate is in %.

In our exercise, the interest rate is 9%. So, by the rule of 72:

D = \frac{72}{9} = 8.

According to the rule of 72, the doubling time for this interest rate is 8 years.

Exact answer:

The exact answer is going to be found using the compound interest formula.

A = P(1 + \frac{r}{n})^{nt}

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

is double the initial amount, double the principal.

A = 2P

r = 0.09

The interest is compounded anually, so n = 1

A = P(1 + \frac{r}{n})^{nt}

2P = P(1 + \frac{0.09}{1})^{t}

2 = (1.09)^{t}

Now, we apply the following log propriety:

\log_{a} a^{n} = n

So:

\log_{1.09}(1.09)^{t} = \log_{1.09} 2

t = 8.04

The exact doubling time of this amount is 8.04 years.

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3 years ago
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