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
hram777 [196]
3 years ago
12

EXAMPLE 1 (a) Find the derivative of r(t) = (2 + t3)i + te−tj + sin(6t)k. (b) Find the unit tangent vector at the point t = 0. S

OLUTION (a) According to this theorem, we differentiate each component of r: r'(t) = Correct: Your answer is correct. . (b) Since r(0) = Incorrect: Your answer is incorrect. and r'(0) = j + 6k, the unit tangent vector at the point (2, 0, 0) is T(0) = r'(0) |r'(0)| = j + 6k = .
Mathematics
1 answer:
Tatiana [17]3 years ago
8 0

The correct question is:

(a) Find the derivative of r(t) = (2 + t³)i + te^(−t)j + sin(6t)k.

(b) Find the unit tangent vector at the point t = 0.

Answer:

The derivative of r(t) is 3t²i + (1 - t)e^(-t)j + 6cos(6t)k

(b) The unit tangent vector is (j/2 + 3k)

Step-by-step explanation:

Given

r(t) = (2 + t³)i + te^(−t)j + sin(6t)k.

(a) To find the derivative of r(t), we differentiate r(t) with respect to t.

So, the derivative

r'(t) = 3t²i +[e^(-t) - te^(-t)]j + 6cos(6t)k

= 3t²i + (1 - t)e^(-t)j + 6cos(6t)k

(b) The unit tangent vector is obtained using the formula r'(0)/|r(0)|. r(0) is the value of r'(t) at t = 0, and |r(0)| is the modulus of r(0).

Now,

r'(0) = 3t²i + (1 - t)e^(-t)j + 6cos(6t)k; at t = 0

= 3(0)²i + (1 - 0)e^(0)j + 6cos(0)k

= j + 6k (Because cos(0) = 1)

r'(0) = j + 6k

r(0) = (2 + t³)i + te^(−t)j + sin(6t)k; at t = 0

= (2 + 0³)i + (0)e^(0)j + sin(0)k

= 2i (Because sin(0) = 0)

r(0) = 2i

Note: Suppose A = xi +yj +zk

|A| = √(x² + y² + z²).

So |r(0)| = √(2²) = 2

And finally, we can obtain the unit tangent vector

r'(0)/|r(0)| = (j + 6k)/2

= j/2 + 3k

You might be interested in
Even integers from 11 and 111​
dem82 [27]

Answer:

Please see below :)

Step-by-step explanation:

Integers - Whole numbers (no fractions or decimals!)

11 to 111

12, 14, 16, 18, 20

22, 24, 26, 28, 30

32, 34, 36, 38, 40

42, 44, 46, 48, 50

52, 54, 56, 58, 60

62, 64, 66, 68, 70

72, 74, 76, 78, 80

82, 84, 86, 88, 90

92, 94, 96, 98, 100

102, 104, 106, 108, 110

Hope this helped!

6 0
3 years ago
(06.01)
MAVERICK [17]

After solving I have come up with 6 2/9 or 6.22222.

4 0
3 years ago
The first step in the process for factoring the trinomial x^2-3x-40 is to
jenyasd209 [6]

(x-8)(x+5)

First thing you do is put the X's into the parentheticals because it is x^2 meaning there are 2 factors with x's. Then, you wonder what factors of -40 could add to get -3. In this case, they are -8 and 5. -8 times 5 is -40 and -8 +5 is -3. Then, you just add -8 and 5 beside the x's in the parentheticals.

5 0
2 years ago
Read 2 more answers
There are 7 ushers and 11 technicians helping at the Harper Middle School fall play.
bearhunter [10]

Answer:

<h3>The ratio of technicians to all helpers  is 11 : 7, or \frac{11}{7} or 11 to 7.</h3>

Step-by-step explanation:

  • Given that there are 7 ushers and 11 technicians helping at the Harper Middle School fall play.
  • Let x be the number of ushers ( or helpers ).
  • Therefore x=7 helpers.
  • Let y be the number of technicians.
  • Therefore y=11 technicians.
<h3>To find the ratio of technicians to all helpers :</h3>

That is to find the ratio of y to x.

We can write the ratio of technicians to all ushers(helpers) as y : x

Which implies that 11 : 7,  (since y=11 and x=7)

Or \frac{11}{7} or 11 to 7

<h3>The ratio of technicians to all helpers  is 11 : 7, or \frac{11}{7} or 11 to 7</h3>
4 0
3 years ago
5x6=90divided by something
anastassius [24]
5 * 6 = 30

90/3 = 30

5 * 6 = 90/3 = 30
3 0
3 years ago
Read 2 more answers
Other questions:
  • Kira buys candy that costs $5 per pound.she will spend more than $45 on candy. What are the possible numbers of pounds she will
    13·1 answer
  • Help please!! I don’t know where to start. Need to know the number of views when the quote is first posted.
    10·1 answer
  • The table represents the speed of frog A at a frog jumping contest. Frog B travels 2 feet each second. If the course is 20 feet
    13·1 answer
  • Esther. Vida and Clair were asked to consider two different cash flows: GH¢1000 that theycould receive today and GH¢3000 that wo
    6·1 answer
  • Which of the following must be true PLEASE HELP ME ASAP
    14·1 answer
  • Evaluate the expression when g=72 and h-4 g/8=h
    10·2 answers
  • Help- i dont know what it is at all
    14·1 answer
  • A shirt is on sale for $42 if this is 4/5 of the original price of the shirt what was the original price of the shirt
    15·1 answer
  • A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs ​$69. A season ski pass costs ​$350. The
    15·1 answer
  • Carol Wynne bought a silver tray that originally cost ​$133 and was advertised at ​55% off. What was the sale price of the​ tray
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!