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Hatshy [7]
2 years ago
13

Name 3 types of rational numbers you can plot on a number line.

Mathematics
2 answers:
balu736 [363]2 years ago
5 0
Anything above zero anything negative from zero and 0 itself
adelina 88 [10]2 years ago
4 0

Answer:

  • Center of the number line (origin)
  • Positive rational numbers are marked on the right side of zero
  • Negative rational numbers are marked on the left side of the zero
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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
Nathan wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram A
valentina_108 [34]
<h3><u>Answer:</u></h3>

The formula determine the distance from C to D is:

\sqrt{(0-a)^2+(-b)^2}=\sqrt{a^2}=a

<h3><u>Step-by-step explanation:</u></h3>

The formula that can be used to determine the distance from point C to point D is:

\sqrt{(0-a)^2+(-b)^2}=\sqrt{a^2}=a

We know that distance between two points A(a,b) and B(c,d) is equal to the length of the line segment AB and is calculated by the help of the formula:

\sqrt{(c-a)^2+(b-d)^2}

So, here we have:

(a,b)=(a,b) and (c,d)=(0,b)

3 0
3 years ago
The net of a prism is shown on the coordinate plane. What is the surface area of the prism?
nata0808 [166]

Answer:

Option C. 10 square inch

Step-by-step explanation:

Net of a prism is shown on the coordinate plane. We have to calculate the surface area of the prism.

To calculate the surface area of the net we will calculate the area of the four large rectangles and two squares given in the picture.

Total surface area of the net = 2× small squares + 4×large rectangles

= 2×(1×1) + 4×(1×2) = 2 + 8 = 10 square inch.

Therefore option C. 10 square inch is the answer.

6 0
3 years ago
Find the hypotenuse
Anika [276]
A^2+b^2=c^2
11^2+4^2=c^2
121+16=c^2
137=c^2
\sqrt{137}  =  \sqrt{c}
11.70=c

8 0
3 years ago
Read 2 more answers
You invest 1,600 in an account that pays an interest rate of 6.5% compounded continuously calculate the balance after 6 years
tangare [24]

The amount A when the principal P is compounded continuously is given by the formula :

A=P E^{rt}

Here r is rate of interest and t is time .

In the question P=1600 ,r=6.5%=0.065 ,t= 6 years

Substituting these values in the formula

A=(1600) e^{0.065 times 6}

A= 1600(1.48)

A=2363.17

Balance after 6years is $2363.17

6 0
3 years ago
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