Solve the equation by completing the square
1 answer:
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One may note you never quite asked anything, now, assuming simplification,
9514 1404 393
Answer:
a) 600
b) see below
c) 1.26 hours
Step-by-step explanation:
a) The value of y when x=0 is the coefficient of the exponential term:
y = 600·3^(-0) = 600·1 = 600
There were 600 atoms to start.
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b) see attached for a graph
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c) The graph shows 150 atoms at t = 1.26, about 1.26 hours after the start of time counting.
If you want to find that value algebraically, substitute for y and solve for x. Logarithms are involved.
150 = 600·3^(-x)
150/600 = 3^(-x)
log(1/4) = -x·log(3)
x = -log(1/4)/log(3) = log(4)/log(3) ≈ 1.2618595
After about 1.26 hours, there were 150 atoms.
Answer:
c) (-2, 1)
Step-by-step explanation:
3x - 3y = -9
2x + y = -3
2x + y = -3
-2x -2x
y = -2x - 3
3x - 3y = -9
y = -2x - 3
3x - 3(-2x - 3) = -9
3x + 6x + 9 = -9
9x + 9 = -9
- 9 -9
9x = -18
/9 /9
x = -2
y = -2x - 3
y = -2(-2) -3
y = 4 - 3
y = 1
(x, y) --> (-2,1)
Check your answer:
y = -2x - 3
1 = -2(-2) - 3
1 = 4 - 3
1 = 1
This statement is true
Hope this helps!
