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Sergio039 [100]
3 years ago
10

Solve the initial value problem. dy/dt = 1 + 6/t , t > 0, y = 8 when t = 1

Mathematics
1 answer:
nordsb [41]3 years ago
5 0
\displaystyle\frac{dy}{dt} = 1 + \frac{6}{t}\ \Rightarrow\ dy = \left( 1 + \frac{6}{t}\right) dt\ \Rightarrow\int 1\, dy = \int \left( 1 + \frac{6}{t}\right) dt \ \Rightarrow \\ \\
y = t + 6\ln|t| + C. \text{ But $t\ \textgreater \ 0$ so }y = t + 6\ln t + C. \\ \\ 
y(1) = 8\ \Rightarrow\ 8 = 1 + 6 \ln 1 + C \ \Rightarrow\ C = 7 \text{ so } \\ \\
y(t) = t + 6\ln t + 7
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36,000 people ride the city bus every day. On average, about how many people ride the bus each hour?
barxatty [35]
Day = 24 hours, right?
36000/24 = 1500

If I put this into words:
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On average, 1500 people ride the bus per hour (or each hour)
4 0
3 years ago
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soldier1979 [14.2K]

Let, coordinate of point A' is (x,y).

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Now, their center is given by :

C( \dfrac{x+3}{2}, \dfrac{y+2}{2})

Also, product of slope will be -1 .( Since, they are parallel )

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x = 2y - 1

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Also, C satisfy given line :

2\times ( \dfrac{2y + 2}{2})  + \dfrac{y+2}{2} = 12\\\\4y + 4 + y + 2 = 24\\\\5y = 18\\\\y = \dfrac{18}{5}

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7 0
2 years ago
what is 8+8? IM CRYING PLS. WILL GIVE BRAINLIEST. I DONT KNOW IVE BEEN UP ALL NIGHT STRESSING PLEASE.
Ahat [919]

Answer:

Hey buddy, here is your answer. Hope it helps you.

Step-by-step explanation:

8+8=16.

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Which of the following is most likely the next step in the series
Anon25 [30]
<h3>Answer: Choice D</h3>

=============================

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