Classify the following triangle as acute, obtuse, or right.

Find the length of the arc of the circular helix with vector equation r(t) = 2 cos t i + 2 sin t j + tk from the point (2, 0, 0)

USPshnik [31]

$\vec r(t)=2\cos t\,\vec\imath+2\sin t\,\vec\jmath+t\,\vec k$

$\implies\vec r'(t)=-2\sin t\,\vec\imath+2\cos t\,\vec\jmath+\vec k$

$\implies\|\vec r'(t)\|=\sqrt{(-2\sin t)^2+(2\cos t)^2+1^2}=\sqrt5$

Then the length of the arc is

$\displaystyle\int_0^{2\pi}\|\vec r'(t)\|\,\mathrm dt=\sqrt5\int_0^{2\pi}\mathrm dt=2\sqrt5\,\pi$

4 0

4 years ago

jamar has an 8-foot long piece of wood that he wants to cut to build a stepstool for his tree house if each piece is going to be

lesya [120]

The greates amount of pieces he would be able to use would be 9 because 8 divided by 5/6= 9 and 3/5.the 3/5 piece is too short.

7 0

4 years ago

Read 2 more answers

There are 9 performers who are to present their acts at a variety show. How many different ways are there to schedule their appe

nika2105 [10]

For this type of question it is easiest to think about it in terms of a simple multiplication. The way we can do this is by working out how many possibilities there are for each position on the program. This is as follows:
For the first act, there are 9 possible performers we can pick
For the second act, because we have already assigned a performer to the first act, there are only 8 possible performers
For the third act, because we have already assigned a performer to the first two acts, there are only 7 possible performers
This goes on and on until we reach the final act, where we have used all the performers except one.
Therefore we can say:
For the first act there are 9 possibilities
For the second act there are 8 possibilities
For the third act there are 7 possibilities
For the fourth act there are 6 possibilities and so on
If we want to write this mathematically we can just say that there are:
9 possibilities x 8 possibilites x 7 possibilities etc right down until we are at the final act where there is 1 possibility.
To write this out as an equation we just say:
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = the number of different ways
In maths however, we have a much simpler way of saying this, which we call "factorial".
That whole stream of numbers up there can just be said to be "9 factorial", or if we are writing it in an equation "9!". You may find that your calculator has a button which has an "!" on it. If you put in the number of performers and then press the "!" button, it will give you the answer to your question.
Hope this helped you :)

3 0

4 years ago

The charge for electricity consumption E is partly constant and partly varies as the number N of units used. The charge for 82 u

balandron [24]

The charge per unit of electricity is #415

The formula for E in terms of N is E = 375 + 40N

<h3>What is variation?</h3>

Variation is a mathematical term that establishes the relationship between quantities and variables in an equation.

Analysis:

E = K + CN

where K and C are constants

When E = 3655, N = 82 and when E = 2055, N = 42

3655 = K + 82C ---------------1

2055 = K + 42C----------------2

subtract equation 2 from 1

40C = 1600

C = 40

substitute C in equation 1

3655 = K + 82(40)

3655 = K + 3280

K = 3655 - 3280 = 375

charge per unit is N = 1

E = 375 + 40(1) = #415

Formula for E in terms of N is E = 375 + 40N

In conclusion, the charge per unit of electricity is 415 and the equation connecting E and N is E = 375 + 40N

Learn more about Variation: brainly.com/question/6499629

SPJ1

3 0

2 years ago

Luis bought stock at $66.80. The next day, the price increased $13.85. This new price changed by −2 3 /4 % the following day. Wh

larisa86 [58]

We know that
1) Luis bought stock at ---------------> $66.80
2) The next day, the price increased $13.85--------> $66.80+$13.85=$80.65
3) This new price changed by −2 3 /4 % the following day
2 3/4%----> (2*4+3)/4----> 11/4 %----> 2.75%
so
(100%-2.75%)-----> 97.25%
the final stock price is $80.65*0.9725-----> $78.43

the answer is
$78.43

6 0

4 years ago