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3 years ago

Differentiate. The answer is supposed to be -3/ sqrt 4-x^2

Mathematics

1 answer:

Margarita [4]3 years ago

6 0

Answer:

Step-by-step explanation:

$g(x)=\cos^{-1} (\frac{x}{2})\\g'(x)= \frac{- 1}{\sqrt{1-(\frac{x}{2})^2}}*\frac{1}{2} \\=\frac{-1}{\sqrt{4-x^2} }$

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What is the exact circumference of the circle?

WITCHER [35]

The circle has a diameter of 16.
The formula for the circumference of a circle is diameter*pi
So, the circumference is 16*pi, or 16pi. (answer choice C.)

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4 years ago

Read 2 more answers

-5/4 = x -7/10 solve for x and show work please

tekilochka [14]

First lets start by making the denominators the same. I multiplied the 4 by 5 and 10 by 2.

-25/20 = x -14/20
Add 14/20 on both sides (do the opposite to cancel out and whatever you do to one side you need to do to the other.
You should get -11/20 = x

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3 years ago

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

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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4 years ago

A triangle with angle measures of 20° and 30° is a (FILL IN THE BLANK) triangle.

White raven [17]

Obtuse triangle, if the two angles add up to 50 degrees and a whole triangle equals 180 degrees. That means the third angle is greater than 90 degrees and only obtuse angles are greater than 90 degrees

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3 years ago

Is it an irrational number

Vilka [71]

Answer:

Step-by-step explanation:

A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333 (the threes go on forever). However, one third can be express as 1 divided by 3, and since 1 and 3 are both integers, one third is a rational number.

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3 years ago