What happens if you shift (x+3)^2+(y-2)^2=36 up 3 units?
1 answer:
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Answer:
Total Time = 4.51 s
Step-by-step explanation:
Solution:
- It firstly asks you to prove that that statement is true. To prove it, we will need a little bit of kinematics:
y = v_o*t + 0.5*a*t^2
Where, v_o : Initial velocity = 0 ... dropped
a: Acceleration due to gravity = 32 ft / s^2
y = h ( Initial height )
h = 0 + 0.5*32*t^2
t^2 = 2*h / 32
t = 0.25*√h ...... Proven
- We know that ball rebounds back to 7/8 of its previous height h. So we will calculate times for each bounce:
- How long it has been bouncing at nth bounce, we will look at the pattern between 1st, 2nd and 3rd and 4th bounce times calculated above. We see it follows a geometric series with formula:
Total Time ( nth bounce ) = Sum to nth ( )
- The formula for sum to infinity for geometric progression is:
S∞ = a / 1 - r
Where, a = 15 , r = ( 7 / 8 )
S∞ = 15 / 1 - (7/8) = 15 / (1/8)
S∞ = 120
- Then we have:
Total Time = 0.5*√S∞ - 0.25*√15
Total Time = 0.5*√120 - 0.25*√15
Total Time = 4.51 s
Answer:
<h2>There is a reduction of 16.5% in the boiling temperature due to addition of vacuum.</h2>Step-by-step explanation:
Water boils at 100 degree Celsius without vacuum.
With the addition of vacuum, the boiling temperature reduces to 83.5 degree Celsius.
The total reduction in boiling temperature is degree Celsius.
At first, the boiling temperature was 100 degree Celsius, which reduces by 16.5 degree Celsius.
The change in percentage is .