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enot [183]
3 years ago
13

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive an

y points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A particle is moved along the x-axis by a force that measures 9/(6 x) pounds at a point x feet from the origin. Find the work W done in moving the particle from the origin to a distance of 12 ft.
Mathematics
1 answer:
maxonik [38]3 years ago
4 0

Answer:

5.0 ft-lbf

Step-by-step explanation:

The force is

F = \dfrac{9}{6^x}

This force is not a constant force. For a non-constant force, the work done, <em>W</em>, is

W = \int\limits^{x_2}_{x_1} {F(x)} \, dx

with x_1 and x_2 the initial and final displacements respectively.

From the question, x_1  =0 and x_2 = 12.

Then

W = \int\limits^{12}_0 {\dfrac{9}{6^x}} \, dx

Evaluating the indefinite integral,

\int\limits \dfrac{9}{6^x} \, dx  =9 \int\limits\!\left(\frac{1}{6}\right)^x \, dx

From the rules of integration,

\int\limits a^x\, dx = \dfrac{a^x}{\ln a}

9 \int\limits \left(\frac{1}{6}\right)^x \, dx = 9\times\dfrac{(1/6)^x}{\ln(1/6)} = -5.0229\left(\dfrac{1}{6}\right)^x

Returning the limits,

\left.-5.0229\left(\dfrac{1}{6}\right)^x\right|^{12}_0 = -5.0229(0.1667^{12} - 0.1667^0) = 5.0229 \approx 5.0 \text{ ft-lbf}

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Is 9.521521521 rational or irrational
enyata [817]

If the numbers after the decimal terminate, yes, it's rational.

9.521521521 = 9,521,521,521 / 1,000,000,000

If they don't terminate, but the pattern continues (which I suspect is the case here), yes, it's still rational.

If <em>x</em> = 9.521521521…, then

1000<em>x</em> = 9521.521521521…

Subtract <em>x</em> from this to eliminate the fractional part:

1000<em>x</em> - <em>x</em> = 9521.521521521… - 9.521521521…

999<em>x</em> = 9512

<em>x</em> = 9512/999

If they don't terminate, but the pattern does <em>not</em> continue, meaning the next few digits could be something random like

9.521521521<u>19484929271283583457</u>…

then the number would be irrational.

7 0
3 years ago
After allowing 20% discount on the marked price with 13%
saveliy_v [14]

<u>Answer:</u>

The marked price of the article is 22,600

<u>Explanation: </u>

Given, selling price of an article SP = Rs. 18080

To calculate marked price MP, the formula used is  

\mathrm{SP}=\mathrm{MP}\left(1-\frac{D \%}{100}\right)

Discount D = 20%

Substituting the given values

SP = \mathrm{MP}\left(1-\frac{20}{100}\right)

18080 = \mathrm{MP}\left(1-\frac{1}{5}\right)

18080=\mathrm{MP}\left(\frac{4}{5}\right)

\mathrm{MP}=\frac{18080 \times 5}{4}

MP = Rs. 22,600

Therefore the marked price of the article is 22,600

6 0
3 years ago
Please help me with this, I really need it, thanks.<br> (Geometry)
horsena [70]

Answer:

  a.  yes

  b.  Q

  c.  line MP

Step-by-step explanation:

a. "Collinear" means "on the same line". The diagram shows point K on the same line with M and P, so ...

  yes, M, P, and K are collinear

__

b. N, W, and U are the corners of face NUWQ, so point Q is also in that plane.

__

c. The plane MPQ includes face MPQN. The plane TVP includes face TVPM.

Line MP (or PM) is the line where these planes intersect.

8 0
3 years ago
Helppppppppppppppppppppppppppppppp
Alex Ar [27]
Edit: Bottom left is correct.
3 0
3 years ago
6.62 X 0.7= 2.68 X 1.35
Kobotan [32]

Answer:

3.934 = 3.634; hope this helps........

Step-by-step explanation:

Solve:

Multiply the numbers

5.62 ⋅ 0.7 = 2.68 ⋅ 1.35

3.934 = 2.68 ⋅ 1.35

Multiply the numbers

3.934 = 2.68 ⋅ 1.35

3.934 = 3.618

Result

3.934 = 3.618

The input is a contradiction: it has no solutions

5 0
3 years ago
Read 2 more answers
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