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3 years ago

Write the equation of the circle with center (−1, −3) and (−7, −5) a point on the circle.

1 answer:

3 0

Wait just a second, what's the radius of the circle anyway?

well, the radius is the segment going from the center of the circle to the circle itself, well, low and behold, if we just get the distance from those two points, that gives us the radius.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -1 &,& -3~) 
% (c,d)
&&(~ -7 &,& -5~)
\end{array}\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
r=\sqrt{[-7-(-1)]^2+[-5-(-3)]^2}\implies r=\sqrt{(-7+1)^2+(-5+3)^2}
\\\\\\
r=\sqrt{(-6)^2+(-2)^2}\implies r=\sqrt{40}\\\\
-------------------------------$

$\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{-1}{ h},\stackrel{-3}{ k})\qquad \qquad 
radius=\stackrel{\sqrt{40}}{ r}
\\\\\\\
[x-(-1)]^2+[y-(-3)]^2=(\sqrt{40})^2\implies (x+1)^2+(y+3)^2=40$

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From 1990 to 2000, the population of Florida increased by 2.13% per year. The population (in millions) in the year 1990 was 16 E

belka [17]

Answer:

19 million

Step-by-step explanation:

So generally whenever we express a exponential function, it's in the form: $y=a(b)^x$

where a=initial value aka when x=0

in this case, b can be expressed as: $1+r$ , where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213

This gives us the following equation: $y=16(1.0213)^x$

To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.

So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.

When x=1, we get: $1.0213(16)$ , which can be expressed as a 2.13% increase from year 0

When x=2, we get: $1.0213(1.0213(16))$ , which can be expressed as a 2.13% increase from year 1

when x=3, we get: $1.0213(1.0213(1.0213(16)))$ , which can be expressed as a 2.13% increase from year 2.

In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).

So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990

We get the following equation: $y=16(1.0213)^7$

Using a calculator this simplifies to approximately: $18.5436$

Rounding this to the nearest integer would yield 19, and since the values are expressed in millions, the answer would be 19 million

4 0

2 years ago

How do u calculate 1/5 x 3

Soloha48 [4]

Answer:

3/5

Step-by-step explanation:

turn 3 into 3/1, then multiply the top and bottom to get 3/5.

8 0

3 years ago

6×2p to the second power when p=5

geniusboy [140]

Answer:

3600

Step-by-step explanation:

Since the question gives you p, you replace p (which is just a placeholder) with 5.

Your equation should look like this:

$(6*2(5))^2 = 3600$

6 0

3 years ago

The graph of a linear function intersects with the x axis at a point with an abscissa of 4 and with the y axis at a point with a

goldenfox [79]

We know that

points are
x intercept
A (4,0)

y intercept
B (0,11)

step 1
find the equation of a line
m=(y2-y1)/(x2-x1)--------> m=(11-0)/(0-4)------> m=-11/4

with m and the point B (0,11)
y-y1=m*(x-x1)y-11=(-11/4)*(x-0)---------> y=-(11/4)x+11

the answer is
the formula of the function is y=-(11/4)x+11

see the attached figure

7 0

3 years ago

Trina and her mom are planting 45 plants in their garden.if their garden is 9 square feet how many plants can they put in each s

timurjin [86]

45÷9=5 they can put 5 plants in each square feet.

7 0

3 years ago