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3 years ago

What is scientific notation? Why is it useful? How is it used in the real world?

Mathematics

2 answers:

VladimirAG [237]3 years ago

7 0

is used to write very large or very small numbers using less digits. Discover examples of scientific notation used in real life and acquire the comprehension of complex concepts such as polynomials and exponents.

Alex_Xolod [135]3 years ago

7 0

Very big and very small numbers are hard to write down because of all the zeroes and they're also hard to quickly evaluate and compare.

Instead of using a long sequence of decimal digits to represent numbers, scientific notation uses a shorter number multiplied by a power of 10 and it's always in that form and if it's not, it's not in proper scientific notation.

Scientific notation uses positive exponents to represent very large numbers and negative exponents to represent very small numbers.

I have attached an image which shows what scientific can be used for and an example of a number written in scientific notation.

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5x+10=115 what is the value of x

ololo11 [35]

X = 21

Hope this helped :)

6 0

3 years ago

Can someone translate this into a verbal expression 3(4j + 4 + j)?

dalvyx [7]

3(5j+4)
15j+12

final answer 15j+12

5 0

3 years ago

A customer buys 15.5 cheese pizzas which are $10.50 each. What is the total? Round it to the nearest hundredth.

Cerrena [4.2K]

First of all, how do you buy exactly 15.5 pizzas?
what is a 0.5 pizza?

anyway

cost=cost per pizza times number of pizzas
cost per pizza=10.50
number of pizzas=15.5

cost=10.50 times 15.5
cost=162.75

total cost is $162.75

5 0

3 years ago

3x+17 less than or equal to 2(1-x)

MrRa [10]

Answer:

x ≤ -5

Step-by-step explanation:

According to given condition:

3x + 17 ≤ 2(1 - x)

By simplifying:

3x + 17 ≤ 2 - 2x

Adding 2x - 17 on both sides we get:

3x + 2x ≤ 2 - 17

5x ≤ - 15

Dividing both sides by 5 we get:

x ≤ -5

i hope it will help you!

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