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In-s [12.5K]
3 years ago
9

Mathphys please notice me

Physics
2 answers:
eimsori [14]3 years ago
7 0

Answer:

24.2 s

29.2 m

Explanation:

First, convert each speed from km/h to m/s.

91.5 km/h = 25.42 m/s

77.5 km/h = 21.53 m/s

The speed of the cheetah relative to the gazelle is:

v = 25.42 m/s − 21.53 m/s

v = 3.89 m/s

So the time it takes for the cheetah to catch the gazelle is:

x = v t

94.2 m = (3.89 m/s) t

t = 24.2 s

If instead we want to find x so that t = 7.5 s, then:

x = v t

x = (3.89 m/s) (7.5 s)

x = 29.2 m

Marianna [84]3 years ago
3 0

Answer:

24.2 s

29.2 m

Explanation:

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2 years ago
A capacitor with initial charge q0 is discharged through a resistor. a) In terms of the time constant τ, how long is required fo
-BARSIC- [3]

Answer:

It would take \tau(\ln 9 - \ln 8) time for the capacitor to discharge from q_0 to \displaystyle \frac{8}{9} \, q_0.

It would take \tau(\ln 9 - \ln 7) time for the capacitor to discharge from q_0 to \displaystyle \frac{7}{9}\, q_0.

Note that \ln 9 = 2\,\ln 3, and that\ln 8 = 3\, \ln 2.

Explanation:

In an RC circuit, a capacitor is connected directly to a resistor. Let the time constant of this circuit is \tau, and the initial charge of the capacitor be q_0. Then at time t, the charge stored in the capacitor would be:

\displaystyle q(t) = q_0 \, e^{-t / \tau}.

<h3>a)</h3>

\displaystyle q(t) = \left(1 - \frac{1}{9}\right) \, q_0 = \frac{8}{9}\, q_0.

Apply the equation \displaystyle q(t) = q_0 \, e^{-t / \tau}:

\displaystyle \frac{8}{9}\, q_0 = q_0 \, e^{-t/\tau}.

The goal is to solve for t in terms of \tau. Rearrange the equation:

\displaystyle e^{-t/\tau} = \frac{8}{9}.

Take the natural logarithm of both sides:

\displaystyle \ln\, e^{-t/\tau} = \ln \frac{8}{9}.

\displaystyle -\frac{t}{\tau} = \ln 8 - \ln 9.

t = - \tau \, \left(\ln 8 - \ln 9\right) = \tau(\ln 9 - \ln 8).

<h3>b)</h3>

\displaystyle q(t) = \left(1 - \frac{1}{9}\right) \, q_0 = \frac{7}{9}\, q_0.

Apply the equation \displaystyle q(t) = q_0 \, e^{-t / \tau}:

\displaystyle \frac{7}{9}\, q_0 = q_0 \, e^{-t/\tau}.

The goal is to solve for t in terms of \tau. Rearrange the equation:

\displaystyle e^{-t/\tau} = \frac{7}{9}.

Take the natural logarithm of both sides:

\displaystyle \ln\, e^{-t/\tau} = \ln \frac{7}{9}.

\displaystyle -\frac{t}{\tau} = \ln 7 - \ln 9.

t = - \tau \, \left(\ln 7 - \ln 9\right) = \tau(\ln 9 - \ln 7).

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How many planets are there?
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Assuming you're asking about the solar system, there are nine planets. But, if you're wanting to know about the universe, there are trillions and trillions of planets (most of which we haven't yet discovered). 

Hope this helps!
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Both answers are going to be C

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