While in orbit, a space shuttle travels at a speed of 28,200 kilometers per hour. What is the total number of kilometers travele
1 answer:
Answer:
The distance is 676,800 kilometers, which in scientific notation has a value of 6.748*10⁵ kilometers.
Step-by-step explanation:
A space shuttle travels at a speed of 28,200 kilometers per hour. Given that in 1 day there are 24 hours, it is possible to apply the following rule of three: if in 1 hour the space shuttle travels 28,200 kilometers, in 24 hours how much distance will the space shuttle travel?
distance= 676,800 kilometers
Scientific notation is a quick way to represent a number using powers of base ten. This notation is used to be able to express very large or very small numbers very easily.
The numbers are written as a product:
a*10ⁿ
where:
- a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.
- n is a whole number, which is called an exponent or an order of magnitude. Represents the number of times the comma is shifted. It is always a whole number, positive if it is shifted to the left, negative if it is shifted to the right.
To write the number 676,800 in scientific notation, perform the following steps:
The decimal point is moved to the left as many spaces until it reaches the right of the first digit. This number is then written, which will be the coefficient a in the expression of the previous product. In this case a=6.76800= 6.748
The base 10 is written with the exponent equal to the number of spaces that the comma moves. This is a positive number because the comma is shifted to the left. In this case n= 5
Then, <u><em>the distance is 676,800 kilometers, which in scientific notation has a value of 6.748*10⁵ kilometers.</em></u>
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The pattern in the given series of amount in the account are in the form of
arithmetic and geometric progression.
- The function for Option 1 is;
- The function for Option 2 is;
Reasons:
The given table of values is presented as follows;
In Option 1, the amount in dollars for each year has a common difference of d = 100
The first term, a = 1,100
Therefore;
The Option 1 can be represented as an arithmetic progression , A.P. in the
form, tₙ = a + (n - 1)·d as follows;
For the Option 1, we have;
- The amount in dollars after <em>n</em> years,
For Option 2, it is possible to find;
1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1
Therefore;
The terms in the Option 2 have a common ratio of r = 1.1
The Option 2 is a geometric progression, G.P.
The first term in Option 2 is a = 1,100
Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾
Therefor;
- The function for the Option 2 is;
Learn more about arithmetic and geometric progression here:
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c (m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (6, 0)
m = =
= - 1
Note the line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = - x + 6 or y = 6 - x ⇒ B