1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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}

You might be interested in
12/18 reduced to the lowest term
melomori [17]
2/3 is it's simplified form
8 0
3 years ago
In the rectangle below, E1=2x -2, FH=3x+6, and m 4IHG =35°.Find Gl and m LIEH
Tpy6a [65]

Recall that the diagonals of a rectangle bisect each other and are congruent, therefore:

\begin{gathered} FH=2EI, \\ GI=EI. \end{gathered}

Substituting the given expression for each segment in the first equation, we get:

3x+6=2(2x-2).

Solving the above equation for x, we get:

\begin{gathered} 3x+6=4x-4, \\ 3x+6+4=4x, \\ 3x+10=4x, \\ 4x-3x=10, \\ x=10. \end{gathered}

Substituting x=10 in the equation for segment EI, we get:

EI=2*10-2=20-2=18.

Therefore:

GI=18.

Now, to determine the measure of angle IEH, we notice that:

\Delta HFG\cong\Delta GEH,

therefore,

\measuredangle GHF\cong\measuredangle HGE.

Using the facts that the triangles are right triangles and that the interior angles of a triangle add up to 180° we get:

m\measuredangle IEH=90^{\circ}-35^{\circ}=55^{\circ}.

<h2>Answer: </h2>\begin{gathered} m\operatorname{\measuredangle}IEH=55^{\operatorname{\circ}}, \\ GI=18. \\  \end{gathered}

4 0
1 year ago
The volume of a cylinder is 169 in.3 and the height of the cylinder is 1 in. What is the radius of the cylinder?
LenKa [72]

Answer:

4.71

Step-by-step explanation:

6 0
3 years ago
I am thinking of two numbers.
taurus [48]

Answer:

6 and 8

Step-by-step explanation:

6+8=14 difference 2

5 0
2 years ago
Read 2 more answers
In decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twel
Kitty [74]

Answer: 0.4 which is choice C

====================================

Work Shown

Focus on the "riverside high school" row only

A = number of twelfth graders = 200

B = number of students = 500

P = probability of picking a twelfth grader

P = A/B

P = 200/500

P = 2/5

P = 0.4

8 0
3 years ago
Read 2 more answers
Other questions:
  • Explain why each number is not in scientific notation
    8·1 answer
  • Identify the type of function that models the situation below: A can of coffee is supposed to contain one pound of coffee. Which
    15·2 answers
  • Which line segment is correct for this answer to the question?
    9·1 answer
  • the ratio of boys to girl in Mr. Claytons class is 2:3. If there are 30 total students how many more girls are in the class than
    7·2 answers
  • 3.7+6=. A:-1. B:1. C:13 D:-13
    5·2 answers
  • 4. What percent relates to when an event will definitely happen?
    7·2 answers
  • Evaluate: a). 25 −12 [5+4 − (3 + 2−1+3)] b). 36 − [18− (14− (15−4÷2×2))]
    14·2 answers
  • There are 24 students in a class. Only -- of the students remembered to bring their hat and mittens to class.
    15·2 answers
  • 8+4-{-2-[5+(2-7)-(5-15)+20]+6-3}+8​
    12·2 answers
  • Jada has 18 Fruit by the Foot snacks. She and her 4 friends are going to share them all so that all 5 people get
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!