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
kirill [66]
2 years ago
6

CALCULUS: For an object whose velocity in ft/sec is given by v(t) = sin(t), what is its distance, in feet, travelled on the inte

rval t = 1 to t = 5?
A. 0.45
B. 2.82
C. 0.03
Mathematics
1 answer:
rodikova [14]2 years ago
7 0

The linked answer is wrong because that integral gives you the net displacement of the object, not the total distance.

To get the distance, you have to integrate the speed (as opposed to velocity), which involves integrating the absolute value of the velocity function.

\mathrm{distance} = \displaystyle\int_1^5 |\sin(t)| \,\mathrm dt

By definition of absolute value,

|\sin(t)|=\begin{cases}\sin(t)&\text{for }\sin(t)\ge0\\-\sin(t)&\text{for }\sin(t)

Over this particular integration interval,

• sin(<em>t</em> ) ≥ 0 for 1 ≤ <em>t</em> < <em>π</em>, and

• sin(<em>t</em> ) < 0 for <em>π</em> < <em>t</em> ≤ 5

so you end up splitting the integral at <em>t</em> = <em>π</em> as

\mathrm{distance} = \displaystyle\int_1^\pi \sin(t)\,\mathrm dt + \int_\pi^5 (-\sin(t))\,\mathrm dt

Now compute the distance:

\mathrm{distance} = -\cos(t)\bigg|_1^\pi + \cos(t)\bigg|_\pi^5

\mathrm{distance} = -(\cos(\pi) - \cos(1)) + (\cos(5) - \cos(\pi))

\mathrm{distance} = -2\cos(\pi) + \cos(1) + \cos(5) \approx 2.82

making B the correct answer.

You might be interested in
What is 53 divide by 4
olga nikolaevna [1]

the answer is 13.25  




3 0
3 years ago
Read 2 more answers
What theorem shows that ΔACE ≅ ΔBCD?
jolli1 [7]

Answer:

sas

Step-by-step explanation:

3 0
3 years ago
Morgan rewrote the expression 90 + (10 + 4.8) as (90 + 10) + 4.8. How will this change the work that is needed to evaluate the e
serg [7]

Answer:

Answer is c

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Fill in the missing reason in proof.
KiRa [710]

Answer:

  • SAS

Step-by-step explanation:

<u>As per steps given the congruent pairs are:</u>

  • AB and AC
  • BD and CD
  • Angle B and angle C

So two sides and included angle - it represents side-angle-side or SAS congruency theorem

8 0
3 years ago
Why infinity ( ) can’t be included in an inequality?
Ksju [112]

Answer:

Step-by-step explanation:

Because then the value on the other side will be unbounded by the infinity sign while expressing the answers on a number line.

please click thanks and mark brainliest if you like :)

7 0
3 years ago
Other questions:
  • 12. Solve this equation for A: A ÷ 2 = 4
    6·2 answers
  • What is the x and y intercept for f(x)= 2/3-4
    5·1 answer
  • A cylindrical plastic pipe’s length is 12 cm and it’s radius is 2.5 cm. To the nearest tenth, what is the volume of the pipe?
    12·2 answers
  • What is 825 divided by 7
    8·1 answer
  • Evaluate -4 +(-3) - (-2)
    15·2 answers
  • Which of the following is not true about linear functions.
    11·2 answers
  • What is 6.89 divided by 2 ????????
    5·2 answers
  • Anyone good in geometry? need help.Extra points​
    13·1 answer
  • On June 4th 2020, a new language was created called Math - is - fun! This language is a place value system which is written hori
    10·1 answer
  • a boy purchased a party-length sandwich 53 in. long. He wants to cut it into three pieces so that the middle piece is 6 in. long
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!