Is 3.222222 a rational number
1 answer:
Answer:
<h2>YES</h2>Step-by-step explanation:
If the number is rational, I can write it as a fraction in which the numerator and denominator are integers (denominator other than 0).
If is repeating:
<em>multiply both sides by 10</em>
<em> make the difference 10x - x</em>
<em>divide both sides by 9</em>
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Answer:
Harry buys 6 apples and 5 oranges at the store.
Step-by-step explanation:
Given:
Cost of each apples = $0.8
Cost of each oranges = $0.95
Total money spend =$9.55
Number of fruits bought= 11
We need to find the number of apples bought and number of oranges were bought.
Solution:
Let the number of apples bought be 'a'.
Let the number of oranges were bought be 'o'.
Number of fruits bought= 11
So we can say that;
Number of fruits bought is equal to sum number of apples bought and number of oranges were bought.
framing in equation form we get;
⇒ equation 1
Now we can say that;
Total money spend is equal to number of apples bought multiplied by Cost of each apples plus number of oranges were bought multiplied by Cost of each oranges.
framing in equation form we get;
⇒ equation 2
Now Multiplying equation 1 by 0.8 we get;
⇒ equation 3
Subtracting equation 3 from equation 2 we get;
Dividing both side by 0.15 we get;
Substituting the value of o in equation 1 we get;
Hence Harry buys 6 apples and 5 oranges at the store.
Answer: P(t) = 1.25.sin(.t) + 5.65
Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:
y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D
where:
A is amplitude A=|A|
B is related to the period by: T =
C is the phase shift or horizontal shift:
D is the vertical shift
In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.
<u>Amplitude</u>:
a =
At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:
a =
a = 1.25
<u>b</u>
A time period for Pluto is T=66 years:
66 =
b =
<u>Vertical</u> <u>Shift</u>
It can be calculated as:
d =
d =
d = 5.65
Knowing a, b and d, substitute in the equivalent positions and find P(t).
P(t) = a.sin(b.t) + d
P(t) = 1.25.sin(.t) + 5.65
The Pluto's distance from the sun as a function of time is
P(t) = 1.25.sin(.t) + 5.65