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irina1246 [14]
3 years ago
10

A nick on the edge of a CD rotates to (−6, 5) during one song when represented graphically. What is the sine value of this funct

ion?
Mathematics
2 answers:
Musya8 [376]3 years ago
7 0
\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\\\\
-------------------------------\\\\
\begin{array}{rllll}
(-6&,&5)\\
\uparrow &&\uparrow \\
a&&b\\
x&&y
\end{array}\impliedby \textit{let's find the \underline{hypotenuse}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
c=\sqrt{(-6)^2+(5)^2}\implies c=\sqrt{36+25}\implies \boxed{c=\sqrt{61}}
\\\\\\
sin(\theta)=\cfrac{5}{\sqrt{61}}

now, let's rationalize the denominator

\bf \cfrac{5}{\sqrt{61}}\cdot \cfrac{\sqrt{61}}{\sqrt{61}}\implies \cfrac{5\sqrt{61}}{(\sqrt{61})^2}\implies \boxed{\cfrac{5\sqrt{61}}{61}}
12345 [234]3 years ago
6 0
The answer is 5 square root 61 divided by 61
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Cloud [144]

Answer:

The value of the account in the year 2009 will be $682.

Step-by-step explanation:

The acount's balance, in t years after 1999, can be modeled by the following equation.

A(t) = Pe^{rt}

In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.

$330 in an account in the year 1999

This means that P = 330

$590 in the year 2007

2007 is 8 years after 1999, so P(8) = 590.

We use this to find r.

A(t) = Pe^{rt}

590 = 330e^{8r}

e^{8r} = \frac{590}{330}

e^{8r} = 1.79

Applying ln to both sides:

\ln{e^{8r}} = \ln{1.79}

8r = \ln{1.79}

r = \frac{\ln{1.79}}{8}

r = 0.0726

Determine the value of the account, to the nearest dollar, in the year 2009.

2009 is 10 years after 1999, so this is A(10).

A(t) = 330e^{0.0726t}

A(10) = 330e^{0.0726*10} = 682

The value of the account in the year 2009 will be $682.

4 0
3 years ago
What is the decimal numeral for ten and five hundredths?
Lapatulllka [165]
Ten and five hundredths in decimal form is 10.05
5 0
3 years ago
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andrew-mc [135]
Homework help, vice versa. have fun!
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3 years ago
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sineoko [7]

Answer:

The width of the actual pool is 12 meters

Step-by-step explanation:

You can put Kiara's scale into a ratio or fraction to help visualize it better: 13/6. Now, let's put what we do know for the other ratio into a fraction. we know that the pool is 26 centimeters wide, and since the 26 matches with the 13, that goes in the numerater. since we don't know the denominator, we can just put 26/x (you can use whatever letter you like but I'll use x here)

So in order to get 13/6 to 26/x, we need to find how to figure out what we are doing to the original fraction. Since 13 x 2= 26, it looks like we are multiplying the ratios by 2. Now that we know that, we can multiply the denominator (6) by 2 to equal 12, our answer.

Hope this helps :)    

8 0
2 years ago
According to the United Nations, in the year 2002, the population of the world was 6.1 billion people and was growing at an annu
zmey [24]

Answer:

(a) 6.2843 billion

(b) 6.8716 billion

Step-by-step explanation:

Since there is a constant growth rate of 1.5% per year, and the population in 2002 was 6.1 billion people. The general equation for the total world population, in billions, after 2002 is:

P(t) = 6.1*(1+0.015)^t

With t being the time, in years, after 2002.

a) What was the population in 2004?

t=2004-2002=2\\P(2) = 6.1*(1.015)^2\\P(2) = 6.2843 \ billion

b) What was the population in 2010?

t=2010-2002=8\\P(8) = 6.1*(1.015)^8\\P(8) = 6.8716 \ billion

3 0
3 years ago
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