How is 0.136¯¯¯¯ written as a fraction in simplest form?
1 answer:
Answer:
Step-by-step explanation:
the bar above 36 means that the digits 36 are being repeated
we require 2 equations with the repeating digits placed after the decimal point.
let x = 0.13636.. ( multiply both sides by 10 and 1000 )
10x = 1.3636... (1)
1000x = 136.3636... (2)
subtract (1) from (2) thus eliminating the repeating digits
990x = 135 ( divide both sides by 990 )
x = =
← in simplest form
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Answer:
a) j(t) = -16t^2 +20t +6
b) 1 second
c) less time
Step-by-step explanation:
The general equation for vertical motion is ...
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a) j(t) = -16t^2 +20t +6 . . . . . filling in the given initial values, with g=32 ft/s^2
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b) We want to find the larger of the solutions to ...
j(t) = 10 = -16t^2 +20t +6
Subtracting 6 and dividing by -4, we have ...
-1 = 4t^2 -5t
4t^2 -5t +1 = 0 . . . . add 1, put in standard form
(4t -1)(t -1) = 0 . . . . . factor
t = 1/4 or 1
The ball is in the air 1 second before reaching the hoop.
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c) In generic terms, the equation of motion for a given shooting height at the same upward velocity will be ...
10 = -16t^2 +20t + h0
-16t^2 +20t +(h0 -10) = 0
Using the quadratic formula, we find the larger solution to be ...
t = (-(20) -√(20² -4(-16)(h0 -10)))/(2(-16))
t = (5/8) + √(64h0 -240)/32 = (5 +√(4h0 -15))/8
This value increases as h0 increases, so the ball will be in the air less time when Raymond shoots.
