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erik [133]
4 years ago
5

The circle below is centered at the point (4,3) and has a radius length 5. What is its equation

Mathematics
1 answer:
marusya05 [52]4 years ago
6 0
Well, equation of circle is (X-X1)^2 + (Y-Y1)^2 = R^2

so, (X-4)^2 + (Y-3)^2 = 25

X^2 + 16 -8X + Y^2 + 9 - 6Y = 25

X^2 + Y^2  - 8X - 6Y = 0

this is the correct answer hope it helped :)
inbox me and tell me if it was correct or not
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A model for the population in a small community after t years is given by P(t)=P0e^kt.
LUCKY_DIMON [66]
\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
\end{cases}

a)

so, if the population doubled in 5 years, that means t = 5.  So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &2\\
I=\textit{initial amount}\to &1\\
r=rate\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r
\\\\\\
\boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\
\textit{how long to tripling?}\quad 
\begin{cases}
A=3\\
I=1
\end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}

\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t
\\\\\\
\cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t

b)

A = 10,000, t = 3

\bf \begin{cases}
A=10000\\
t=3
\end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I
\\\\\\
6597.53955 \approx I
3 0
3 years ago
In the triangle below, ∠Q is a right angle. Which ratio would be equivalent to the ratio of sin∠R?
MrMuchimi

Answer:

  • b) cos∠S

Step-by-step explanation:

sin ∠R = SQ/SR

<u>This is same as:</u>

  • cos S

Correct option is b)

4 0
3 years ago
Alex and Charlene are playing a card game, where each card has a value, he has a total of -16.5 points . What was his cards valu
borishaifa [10]
-8.25 i know this because i divided it by two
8 0
3 years ago
8 and 11/100 into a mixed number and a decimal
tiny-mole [99]

Answer:

8 11/100, 8.11, Hope this helpe :)

Step-by-step explanation:

8 0
3 years ago
The polynomial p(x)=x^3-19x-30 has a known factor of (x+2)
riadik2000 [5.3K]

Answer:

(x+2) (x+3) (x-5)

Step-by-step explanation:

x³-19x-30 = (x+2) (x²+ax-15)  ... x³=x*(1*x²)   while -30= (2)*(-15)

x³ +<u> 0</u>*x² - 19x -30 = x³ + (<u>2+a</u>)x² + (2a-15)x -30

2+a = 0

a = -2

x³-19x-30 = (x+2) (x²-2x-15) = (x+2) (x+3) (x-5)

8 0
3 years ago
Read 2 more answers
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