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
elena-s [515]
3 years ago
15

Two Tibetan monks are having a race along a straight path. They both start at the same time, and the race ends in a tie. Prove t

hat at some time during the race the two monks have exactly the same speed.
Mathematics
1 answer:
Triss [41]3 years ago
8 0
This is so provided that the velocity changes continuously in which case we can apply the mean value theorem. 
<span>Velocity (v) is the derivative of displacement (x) : </span>
<span>v = dx/dt </span>
<span>Monk 1 arrives after a time t* and Monk 2 too. </span>
<span>Name v1(t) and v2(t) their respective velocities throughout the trajectory. </span>
<span>Then we know that both average velocities were equal : </span>
<span>avg1 = avg2 </span>
<span>and avg = integral ( v(t) , t:0->t*) / t* </span>
<span>so </span>
<span>integral (v1(t), t:0->t*) = integral (v2(t), t:0->t*) </span>
<span>which is the same of saying that the covered distances after t* seconds are the same </span>
<span>=> integral (v1(t) - v2(t) , t:0->t*) = 0 </span>
<span>Thus, name v#(t) = v1(t) - v2(t) , then we obtain </span>
<span>=> integral ( v#(t) , t:0->t*) = 0 </span>
<span>Name the analytical integral of v#(t) = V(t) , then we have </span>
<span>=> V(t*) - V(0) = 0 </span>
<span>=> V(t*) = V(0) </span>
<span>So there exist a c in [0, t*] so that </span>
<span>V'(c) = (V(t*) - V(0)) / (t* - 0) (mean value theorem) </span>
<span>We know that V(0) = V(t*) = 0 (covered distances equal at the start and finish), so we get </span>
<span>V'(c) = v#(c) = v1(c) - v2(c) = 0 </span>
<span>=> v1(c) = v2(c) </span>
<span>So there exist a point c in [0, t*] so that the velocity of monk 1 equals that of monk 2. </span>
You might be interested in
5. 40 = -1/3(9x + 30)+ 2
Natali5045456 [20]

Answer:

x = -16

Step-by-step explanation:

-1/3 * 9x = -3x

-1/3 * 30 = -10

-10 + 2 = -8

40 = -3x - 8

+8          +8

48 = -3x

---     ----

-3    -3

-16 = x

x = -16

~ Zoe

6 0
3 years ago
T greater than negative 3
garri49 [273]

Answer:

yes

Step-by-step explanation:

6 0
3 years ago
WILL MEDAL
Valentin [98]
P(x) = 3x + 200
x=4 ⇒ p(4) = 3(4)+200=12+200=212
x=15 ⇒ p(15) = 3(15)+20=45+200=245

n(x) = 200(1.04)^x
x=4 ⇒ n(4) = 200 (1.04)^4 = 233.97
x=15⇒n(15)=200(1.04)^15 = 360.19

Then n(x) has the highest value in 4 years; n(x) has the highest value in 15 years
 

4 0
3 years ago
Please help i will give brainliest to the first person that answers correctly
timurjin [86]

Answer:

From what i know your answer will be a.

6 0
3 years ago
What brand is better ? Brand A: $2.50 Brand B: 35 for $3.25 Brand C: 50 for $5.25 Brand D: 100 for $10.00
arlik [135]

I belive that the answer should be D) 100 for $10.00 because I had this exact same question one time.

Hope my answer helps!

Thank you for letting me answer!

Thank you,

Florida Mermaid

3 0
2 years ago
Other questions:
  • A company sells desks for $155 each. To produce a batch of x desks, there is a cost of $83 per desk and a fixed or setup cost of
    14·1 answer
  • Gerry had a coupon for $0.25 off a
    10·2 answers
  • The point of intersection of the lines has an e-coordinate of?
    8·1 answer
  • I need help in Pre-Algebra! This assignment is due today &amp; I have no idea how to do it, PLEASE HELP!
    11·1 answer
  • Please help this is urgent
    8·1 answer
  • AMITA WANTS TO MAKE A MOLD FOR A CANDLE. SHE WANTS THE SHAPE OF THE CANDLE TO BE A RECTANGULAR PRISM WITH A VOLUME OF EXACTLY 28
    13·1 answer
  • PLease help me on 57 - 63
    5·1 answer
  • PLS HELP ASAP (no links)<br> 15% of n is 60<br><br> A. 4<br> B. 9<br> C. 400<br> D. 25<br> E. 30
    7·2 answers
  • Questions<br> 6. C<br> 12<br> 13
    12·1 answer
  • I'll give brainliest to the right answer!!!
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!