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3 years ago

13

A ladder is 10 feet long and rests on a wall. The base of the ladder is 5 feet from the wall. Determine how high the ladder touc

hes the wall.

2 answers:

mr Goodwill [35]3 years ago

8 0

Answer:

8.66

Step-by-step explanation:

Alex Ar [27]3 years ago

5 0

8.660 ft a squared + b squared = c squared

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Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

bonufazy [111]

Answer:

Using the rule of 72, the doubling time is 9.35 years.

The exact answer is that the doubling time is 8.89 years.

Step-by-step explanation:

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 7.7%. So, by the rule of 72:

$D = \frac{72}{7.7} = 9.35$ .

Exact answer:

The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).

The compound interest formula is given by:

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

Where 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.

$A = 2P$

$r = 0.077$

There are 52 weeks in a year, so $n = 52$

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

$2P = P(1 + \frac{0.077}{52})^{52t}$

$2 = (1.0015)^{52t}$

Now, we apply the following log propriety:

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

So:

$\log_{1.0015}(1.0015)^{52t} = \log_{1.0015} 2$

$52t = 462.44$

$t = \frac{462.44}{52}$

$t = 8.89$

The exact answer is that the doubling time is 8.89 years.

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The variables x and y vary inversely. When y is 5 x is 3, so when y is 15 x is 9.

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Answer: B

Step-by-step explanation:

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Step-by-step explanation:

Let's examine the statements ...

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