Determine whether the relation represents a function.

The sum of the interior angles of a regular polygon is 1800 degrees. How many sides does is have? *

Rudik [331]

Answer:

12 sides

Step-by-step explanation:

To find the number of sides of a regular polygon with the sum of interior angles of 1800 degrees, we will follow the steps below;

first write down the formula for finding sum of the interior angle of a polygon

s= (n-2)180

where s is the sum of the interior angle and n is the number of side

from the question given, sum of the interior angle s=1800 degrees

substitute s=1800 degree into the formula and solve for n

s= (n-2)180

1800 = (n-2)180

divide both-side of the equation by 180

1800/180 = n-2

10 = n - 2

add 2 to both-side of the equation

10 + 2 = n

12 = n

n= 12

The polygon have 12 sides

5 0

3 years ago

A. Do some research and find a city that has experienced population growth.

horrorfan [7]

A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation $N_{t} =N _{0}e^{rt}$
where:
$N(t)$ is the population after $t$ years
$N_{0}$ is the initial population
$t$ is the time in years
$r$ is the growth rate in decimal form
$e$ is the Euler's constant
We now for our investigation that $N(t)=238300$ , $N_{0} =192157$ , and $t=10$ ; lets replace those values in our equation to find $r$ :
$238300=192157e^{10r}$
$e^{10r} = \frac{238300}{192157}$
$ln(e^{10r} )=ln( \frac{238300}{192157} )$
$r= \frac{ln( \frac{238300}{192157}) }{10}$
$r=0.022$
Now lets multiply $r$ by 100% to obtain our growth rate as a percentage:
$(0.022)(100)$ =2.2%
We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
Population in 2000: 951,307
Population in 2010: 713,777
We know from our investigation that $N(t)=713777$ , $N_{0} =951307$ , and $t=10$ . Just like before, lets replace those values into our equation to find $r$ :
$713777=951307e^{10r}$
$e^{10r} = \frac{713777}{951307}$
$ln(e^{10r} )=ln( \frac{713777}{951307} )$
$r= \frac{ln( \frac{713777}{951307}) }{10}$
$r=-0.029$
$(-0.029)(100)$ = -2.9%.
We just show that Detroit's population has been declining at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

C. Final equation from point A: $N(t)=192157e^{0.022t}$ .
Final equation from point B: $N(t)=951307e^{-0.029t}$
Similarities: Both have an initial population and use the same Euler's constant.
Differences: In the equation from point A the exponent is positive, which means that the function is growing; whereas, in equation from point B the exponent is negative, which means that the functions is decaying.

D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations $N(t)=192157e^{0.022t}$ and $N(t)=951307e^{-0.029t}$ and solve for t:
$192157e^{0.022t} =951307e^{-0.029t}$
$\frac{192157e^{0.022t} }{951307e^{-0.029t} } =1$
$e^{0.051t} = \frac{951307}{192157}$
$ln(e^{0.051t})=ln( \frac{951307}{192157})$
$t= \frac{ln( \frac{951307}{192157}) }{0.051}$
$t=31.36$
We can conclude that if Orlando's population keeps growing at the same rate and Detroit's keeps declining at the same rate, after 31.36 years in May of 2031 Orlando's population will surpass Detroit's population.

E. Since we know that the population of Detroit as 2000 is 951307, twice that population will be $2(951307)=1902614$ . Now we can rewrite our equation as: $N(t)=1902614e^{-0.029t}$ . The last thing we need to do is equate our Orlando's population growth equation with this new one and solve for t:
$192157e^{0.022t} =1902614e^{-0.029t}$
$\frac{192157e^{0.022t} }{1902614e^{-0.029t} } =1$
$e^{0.051t} = \frac{1902614}{192157}$
$ln(e^{0.051t} )=ln( \frac{1902614}{192157} )$
$t= \frac{ln( \frac{1902614}{192157}) }{0.051}$
$t=44.95$
We can conclude that after 45 years in 2045 the population of Orlando will exceed twice the population of Detroit.

8 0

3 years ago

The box-and-whisker plot describes the scores of golfers in a recent tournament.

romanna [79]

The minimum score was 70.

On a box-and-whisker, the dot on the left end is the lowest value.
The first line on the left is the lower quartile.
The second line is the median.
The third line is the upper quartile.
And finally, the dot on right end is the highest value.

Hope I could help :)

3 0

3 years ago

Kelly joins Powerhouse Gym. The cost is $30 per month and a one-time $100 joining fee. Lisa joins MegaMuscle Gym for $35 per mon

xeze [42]

In 10 months Lisa will have paid the same amount as Kelly, but in month 11 she will have paid more.

6 0

3 years ago

Read 2 more answers

Kate has scored 10 free throws out of 18 tries. She would really like to bring her free throw average up to at least 80%. How ma

wlad13 [49]

(10+t)/(18+t)=8/10
8(18+t)=10(10+t)
144+8t=100+10t
44=2t
t = 22 throws

3 0

3 years ago