Given:
The recurring decimal is .
To prove:
Algebraically that the recurring decimal can be written as .
Proof:
Let,
Multiply both sides by 100.
...(i)
Multiply both sides by 10.
...(ii)
Subtract (i) from (ii).
Divide both sides by 900.
So, .
Hence proved.
Answer:
The answer w'll be obtained using formulas
cos(a+b) = cosacosb - sinasinb
cos(a-b) = cosacosb + sinasinb
Step-by-step explanation:
Using the trigonometric formula of addition and subtraction of cosine
cos(a+b) = cosacosb - sinasinb
cos(a-b) = cosacosb + sinasinb
w'll get the desired answer.
To be solve
L.H.S = R.H.S
sinasinb = (cos(a-b)-cos(a+b)/2
as we know that <u><em>cos(a+b) = cosacosb - sinasinb</em></u>
sinasinb = (cos(a-b) - (cosacosb -sinasinb))/2
as we know that <u><em>cos(a-b) = cosacosb + sinasinb</em></u>
sinasinb = ((cosacosb + sinasinb) - (cosacosb -sinasinb))/2
sinasinb = (cosacosb + sinasinb - cosacosb + sinasinb)/2
sinasinb = (2sinasinb)/2
sinasinb = sinasinb
hence L.H.S = R.H.S
For time-speed-distance problems, you use the relationship
.. speed = distance/time
in any of its various forms.
The distance traveled at A mph is
.. distance = speed * time
.. distance = A*3
The time required for the rest of the journey is
.. time = distance / speed
.. time = (C -3A)/B
The the total time required to travel C miles is the 3 hours for the first part plus the time for the rest of the journey.
.. total journey time = 3 + (C -3A)B . . . . . hours
Answer: You too whos next
Man.
5/7 is the answer to your question.