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3 years ago

Consider the circle above. What is the approximate area of the circle?

Mathematics

1 answer:

Olin [163]3 years ago

4 0

Answer:

The area of a circle is : π (Pi) times the Radius squared : A = π r 2 or, when you know the Diameter: A = (π /4) × D 2 or, when you know the Circumference: A = C 2 / 4 π

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HELLOOOO HELP PLEASE

MA_775_DIABLO [31]

Answer:

$2*log(x)+log(y)$

Step-by-step explanation:

So, there are two logarithmic identities you're going to need to know.

<em>Logarithm of a power</em>:

$log_ba^c=c*log_ba$

So to provide a quick proof and intuition as to why this works, let's consider the following logarithm: $log_ba=x\implies b^x=a$

Now if we raise both sides to the power of c, we get the following equation: $(b^x)^c=a^c$

Using the exponential identity: $(x^a)^c=x^{a*c}$

We get the equation: $b^{xc}=a^c$

If we convert this back into logarithmic form we get: $log_ba^c=x*c$

Since x was the basic logarithm we started with, we substitute it back in, to get the equation: $log_ba^c=c*log_ba$

Now the second logarithmic property you need to know is

<em>The Logarithm of a Product</em>:

$log_b{ac}=log_ba+log_bc$

Now for a quick proof, let's just say: $x=log_ba\text{ and }y=log_bc$

Now rewriting them both in exponential form, we get the equations:

$b^x=a\\b^y=c$

We can multiply a * c, and since b^x = a, and b^y = c, we can substitute that in for a * c, to get the following equation:

$b^x*b^y=a*c$

Using the exponential identity: $x^{a}*x^b=x^{a+b}$ , we can rewrite the equation as:

$b^{x+y}=ac$

taking the logarithm of both sides, we get:

$log_bac=x+y$

Since x and y are just the logarithms we started with, we can substitute them back in to get: $log_bac=log_ba+log_bc$

Now let's use these identities to rewrite the equation you gave

$log(x^2y)$

As you can see, this is a log of products, so we can separate it into two logarithms (with the same base)

$log(x^2)+log(y)$

Now using the logarithm of a power to rewrite the log(x^2) we get:

$2*log(x)+log(y)$

3 0

2 years ago

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four times

prohojiy [21]

Answer:

{36, 66, 78}

Step-by-step explanation:

Let the measures of the three angles be f, s and t, for first, second and third. Then s + t = 4f, t = 12 + s, and f + s + t = 180.

Subbing 12 + s for t in the first equation, we get s + 12 + s = 4f.

Subbing the same in the third equation, we get f + s + 12 + s = 180

This results in two equations in two unknowns (f and s):

2s - 4f = -12

2s + f = 168.

Let's eliminate s by subtracting the first of these two equations from the second. Doing so yields 5f = 180. Then the first angle, f, or x, is 36.

Then, from 2s + f = 168, we get 2s + 36 = 168, or 2s = 132. Thus, the second angle is s = y = 66.

The sum of the three angles must be 180. Thus, 36 + 66 + t = 180, or

102 + t = 180, or t = z = 78.

The three angles are

{36, 66, 78}.

3 0

3 years ago

What is -1/2 + n = -5/8 what does n equal

Stels [109]

Answer: n=0.4 or 2/5

Step-by-step explanation:

4 0

3 years ago

8 tins holds 42-2-3 liter of oil. How many liters can 1such tin hold

GarryVolchara [31]

Answer = 4.625

Solution =42-2-3=37

37 divided by 8 = 4.625

Holley Gus’s it’s the answer

8 0

3 years ago

Select the angle whose sine equals 12/37

Mazyrski [523]

Answer:

Step-by-step explanation:

sin is o/h so across from 12 would be the angle r

6 0

3 years ago