Simplify each of the following expressions to find the length of the tightrope

Find the length of l on the curve r(t)=5cos(3t)i-5sin(3t)j+3tk over the interval [3,7]

stealth61 [152]

$\mathbf r(t)=5\cos3t\,\mathbf i-5\sin3t\,\mathbf j+3t\,\mathbf k$
$\mathrm d\mathbf r(t)=\mathbf r'(t)\,\mathrm dt=(-15\sin3t\,\mathbf i-15\cos3t\,\mathbf j+3\,\mathbf k)\,\mathrm dt$

$\displaystyle\int_C\mathrm d\mathbf r(t)=\int_{t=3}^{t=7}\|\mathbf r'(t)\,\mathrm dt\|=\int_{t=3}^{t=7}\sqrt{225\sin^23t+225\cos^23t+9}\,\mathrm dt$
$=\displaystyle3\sqrt{26}\int_{t=3}^{t=7}\mathrm dt$
$=12\sqrt{26}$

4 0

3 years ago

Find the distance between the two numbers on a number line. Write your answer as a decimal.

dangina [55]

Answer:

-0.574

Step-by-step explanation:

Subtract the two numbers to get the solution

7 0

3 years ago

How could you estimate the quotient 162 divided 19? i need help!!!

Ira Lisetskai [31]

It = 6.888888888 and you can round it to 7

6 0

3 years ago

What is the scientific notation of 6174798604

lesantik [10]

Here is your answer:

Since their no zeros (0) here's your answer:

6.174798604×10^9

7 0

3 years ago

Old Faithful in Yellowstone National Park has a predictable eruption time. The park

prisoha [69]

Answer:How often does Old Faithful blow?

The world's most famous geyser, Old Faithful in Yellowstone, currently erupts around 20 times a day. These eruptions are predicted with a 90 percent confidence rate, within a 10 minute variation, based on the duration and height of the previous eruption.

Step-by-step explanation:

How often does Old Faithful blow?

The world's most famous geyser, Old Faithful in Yellowstone, currently erupts around 20 times a day. These eruptions are predicted with a 90 percent confidence rate, within a 10 minute variation, based on the duration and height of the previous eruption.

5 0

3 years ago