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4 years ago

Pls help with this problem

Mathematics

1 answer:

Gekata [30.6K]4 years ago

8 0

Answer:

Step-by-step explanation:

Isolate the variable:

6x - 5 = 7

+5 +5

6x = 12

/6 /6

x = 2

Check our work:

6(2) - 5 =7

12 - 5 = 7

7 = 7

Correct!

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The velocity of a particle moving along a line is given by v(t) = e ^ t * sin(e ^ t) the interval 0<= t<= pi 2 . What is t

Butoxors [25]

Answer:

0.44237 units

Step-by-step explanation:

Given

$v(t) = e^t*sin(e^t)$

$0 \le t \le \frac{\pi}{2}$

Required

The distance traveled in this interval

We have:

$v(t) = e^t*sin(e^t)$

The distance is calculated as:

$d(t) = \int\limits^a_b {v(t)} \, dt$

So, we have:

$d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(e^t)} \, dt$

Let:

$u = e^t$

Differentiate

$\frac{du}{dt} = e^t$

So:

$dt = e^{-t} du$

So, we have:

$d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(e^t)} \, dt$

$d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(u)} \, e^{-t} du$

Rewrite as:

$d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t* e^{-t}*sin(u)} \, du$

$d(t) = \int\limits^{\frac{\pi}{2}}_0 {sin(u)} \, du$

Integrate:

$d(t) = -\cos(u)|\limits^{\frac{\pi}{2}}_0$

Substitute $u = e^t$

$d(t) = -\cos(e^t)|\limits^{\frac{\pi}{2}}_0$

Split

$d(t) = -\cos(e^\frac{\pi}{2}) - [-\cos(e^0)]$

$d(t) = -\cos(e^\frac{\pi}{2}) +\cos(e^0)$

$d(t) = -0.09793 + 0.5403$

$d(t) = 0.44237$

The distance traveled in this interval is: 0.44237 units

dt =

d(t) = \int\limits^2_0 {e^t*sin(e^t)} \, dt

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3 years ago

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Elodia [21]

Answer:

28(1 + 2t +w)

Step-by-step explanation:

28 + 56t + 28w.

Factor out a 28 from the expression.

28(1 + 2t + w)

8 0

3 years ago

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Aleksandr-060686 [28]

Answer:

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Step-by-step explanation:

Option A is correct:

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Option B is correct:

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