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3 years ago

Matt made a large rug using red, green, and blue carpet tiles.

Mathematics

1 answer:

Temka [501]3 years ago

8 0

Answer:

Matt used 65 carpet tiles.

Step-by-step explanation:

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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

Find the slope of the line

vichka [17]

Answer:

4/5

Step-by-step explanation:

y2-y1/x2-x1. (5,3), (0,-1).

-1-3/0-5.

-4/-5

4/5

Therefore, slope=4/5

If this helps please mark as brainliest

8 0

3 years ago

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if bill puts $3,500 into an account that has a 2.5% interest rate compounded annually, how much money will bill have after 3 yea

lyudmila [28]

Answer:

$26,250

Step-by-step explanation:

$3,500×(2.5)^3

8 0

3 years ago

In order to increase the circumference of a circle from 12π cm to 18π cm, by how much must the diameter increase?

Vadim26 [7]

Answer:

Step-by-step explanation:

It's actually 6 cm. This is because the diameter of the smaller circle is 12pi/pi which is 12, and the diameter of the bigger one is 18pi/pi which is 18. 12 + 6 = 18, so the diameter increases by 6.

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4 years ago

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I need help somebody please help me ill give brainlist’s, this is on math:

ratelena [41]

Answer: -3 and 3

Step-by-step explanation:

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3 years ago