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3 years ago

If a teacher makes $13.50/ hour,:

Mathematics

1 answer:

Arte-miy333 [17]3 years ago

4 0

To answer this question you need to know how many hours the teacher works a day

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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

4 0

3 years ago

75 POINTS AND I'LL GIVE BRAINLIEST!!!

Slav-nsk [51]

Answer:

Step-by-step explanation:

area of the square =10*10=100

area of the circle =pi r^2=pi*1^2=3.142

part a

p(hitting the circle =3.142/100=0.03142 Which is closer to 0

part b

p( hitting the white portion ) =1-0.03142=0.96858 which is closer to 1

4 0

2 years ago

Read 2 more answers

What is the sum of -36 4/9 - (10 2/9) - (18 2/9)

grigory [225]

let's firstly convert the mixed fractions to improper fractions and then add them up.

$\bf \stackrel{mixed}{36\frac{4}{9}}\implies \cfrac{36\cdot 9+4}{9}\implies \stackrel{improper}{\cfrac{329}{9}} \\\\\\ \stackrel{mixed}{10\frac{2}{9}}\implies \cfrac{10\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{92}{9}}~\hfill \stackrel{mixed}{18\frac{2}{9}}\implies \cfrac{18\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{164}{9}} \\\\[-0.35em] ~\dotfill$

$\bf -\cfrac{329}{9}-\cfrac{92}{9}-\cfrac{164}{9}\implies \stackrel{\textit{using the LCD of 9}}{\cfrac{-329-92-164}{9}}\implies -\cfrac{585}{9}\implies -65$