<span>Let x be Joanna's heart rate immediately after running one mile.
After this heart rate x decreased by 2 over 5, Joanna's heart rate was 60 beats per minute. We can set up an equation to solve this question.
x - (2/5) x = 60
(3/5) x = 60
x = (5/3) 60
x = 300 / 3
x = 100
Joanna's heart rate immediately after running one mile was 100 beats per minute.</span>
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Answer:
yes
Step-by-step explanation:
The point is on the line.
The coordinate values satisfy the equation:
1/3x + y = 12
1/3(3) + 11 = 12 . . . substitute for x and y
1 + 11 = 12 . . . . . . . true
Any point that satisfies the equation is a solution. (3, 11) is a solution.
You have the correct approximate value of k. The part after that is where things get a bit strange.
You don't plug in t = 5 again. We don't know the value of t yet. We're trying to solve for it.
We do know u(t) is 135 as we want the temperature to be 135 degrees. Plug this in and isolate t.
So
u(t) = 70+380e^(-0.1004183888t)
135 = 70+380e^(-0.1004183888t)
135-70 = 380e^(-0.1004183888t)
65 = 380e^(-0.1004183888t)
380e^(-0.1004183888t) = 65
e^(-0.1004183888t) = 65/380
e^(-0.1004183888t) = 13/76
-0.1004183888t = ln(13/76)
-0.1004183888t = -1.7657839828248
t = -1.7657839828248/(-0.1004183888)
t = 17.5842692152893
So it takes about 17.58 minutes for the item to cool to the desired temp
