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3 years ago

Which ratios are equal to 64 when the scale factor is 8? Select all that apply.

Mathematics

1 answer:

Luden [163]3 years ago

5 0

Answer:

The scaled surface area of a square pyramid to the original surface area.

The scaled area of a triangle to the original area.

Step-by-step explanation:

Suppose that we have a cube with sidelength M.

if we rescale this measure with a scale factor 8, we get 8*M

Now, if previously the area of one side was of order M^2, with the rescaled measure the area will be something like (8*M)^2 = 64*M^2

This means that the ratio of the surfaces/areas will be 64.

(and will be the same for a pyramid, a rectangle, etc)

Then the correct options will be the ones related to surfaces, that are:

The scaled surface area of a square pyramid to the original surface area.

The scaled area of a triangle to the original area.

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Using compound interest, it is found that:

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Compound interest:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

A(t) is the amount of money after t years.
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 year.
t is the time in years for which the money is invested or borrowed.

In this problem:

The APR is of 2.25%, hence $r = 0.0225$ .

No information about the number of compounding per year, hence $n = 1$ .

Item a:

$P = 2000$ , hence:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

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Item b:

$A(t) = 4000$ , hence:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

$4000 = 2000\left(1 + \frac{0.0225}{1}\right)^{t}$

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$\log{(1.0225)^t} = \log{2}$

$t\log{1.0225} = \log{2}$

$t = \frac{\log{2}}{\log{1.0225}}$

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Item c:

$A(3) = 2000$ , hence:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

$2000 = P\left(1 + \frac{0.0225}{1}\right)^{3}$

$P = \frac{2000}{(1.0225)^3}$

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A similar problem is given at brainly.com/question/24850750

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