Answer:
(0,0) and (7,10)
Step-by-step explanation:
recall that the slope - intercept form of a linear equation can be given as
y = mx + b
where m = slope and b = y intercept
in our case, we are given that slope, m = 10/7, hence our equation becomes
y = (10/7) x + b
since we are not given any information about the y-intercept, we can simply pick a value for b that is most convenient for us.
We pick b = 0, hence the equation simplifies to:
y = (10/7) x ----- eq 1
we can see immediately that if x = 0, y must also = 0
proof if x = 0:
y = (10/7)(0) =0
since 0 is an integer, then (0,0) must be the first point.
we can also observe that for y to be an integer, we must get rid of the denominator 7. We can do this by multiply the right side by 7. Hence we let x = 7:
y = (10/7) x 7
y = 10
hence (7,10) is the second point.
Constant because of the fact that it has a zero slope, so it will never decrease nor decrease.
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Answer:
(a) 13.85 °C
Step-by-step explanation:
The temperature difference is a decaying exponential function of time. Here, it decreases from an initial difference of 15 °C to 10 °C after 25 minutes. So, that temperature difference can be modeled as ...
ΔT = 15(10/15)^(t/25)
We want to find the value of this at t=55. It is ...
ΔT = 15(2/3)^(55/25) ≈ 6.15
This is the amount the temperature of the drink is below room temperature.
drink temperature = (20 - 6.15) °C = 13.85 °C
The temperature of the drink after 55 minutes is about 13.85 °C.
