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
Vera_Pavlovna [14]
3 years ago
13

Find r(t) if r'(t) = 5t4i + 6t5j + t k and r(1) = i + j.

Mathematics
1 answer:
Vladimir [108]3 years ago
8 0
\mathbf r(t)=\displaystyle\int(5t^4\,\mathbf i+6t^5\,\mathbf j+t\,\mathbf k)\,\mathrm dt
\mathbf r(t)=(t^5+C_1)\,\mathbf i+(t^6+C_2)\,\mathbf j+\left(\dfrac12t^2+C_3\right)\,\mathbf k

Given \mathbf r(1)=\mathbf i+\mathbf j, we have

\begin{cases}1^5+C_1=1\\\\1^6+C_2=1\\\\\dfrac121^2+C_3=0\end{cases}\implies C_1=0,C_2=0,C_3=-\dfrac12

so that the particular solution is

\mathbf r(t)=t^5\,\mathbf i+t^6\,\mathbf j+\dfrac12(t^2-1)\,\mathbf k
You might be interested in
2 ( n - 7 ) = 20<br><br> What is n?
Sunny_sXe [5.5K]

Answer:

The answer is n = 17

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve.

Hoped this helped!

brainly, please?

8 0
3 years ago
Angles X and Y form a straight line. Angles W and Z form a straight line. Angles X and W are beside each other. Angles Y and Z a
Zanzabum

Answer:

a

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Find the distance between the points (3, 7) and (2, 6)​
solong [7]

Answer:

1.414214

Step-by-step explanation:

I think this is right lol.

6 0
2 years ago
What is the word form for this mixed number?<br> 11 3/8
Zanzabum

Answer:

Just getting my points back don’t mind me

Step-by-step explanation:

6 0
2 years ago
You work 40 hours/week for 50 weeks and are given the option to be paid hourly or to go on salary. In which situation will you e
sasho [114]

The answer is:

$30,000/year with a 10% bonus

4 0
2 years ago
Other questions:
  • Based on the following graph, what is the most enjoyed candy and what is the approximate level of enjoyment?
    11·2 answers
  • If n= 5.3 cm and p= 6.25cm what is the measure of angle
    8·1 answer
  • 12. What is the diameter of a circle when the circumference is 75.4 inches?
    5·1 answer
  • Solve the following: -3(x - 8) + 7x = 12<br><br> Please explain!
    13·1 answer
  • Factor the Higher degree polynomial<br><br> 5y^4 + 11y^2 + 2
    6·2 answers
  • The weight of a basketball is normally distributed with a mean if 17 oz. And a standard version deviation of 2 oz. Suppose 50j0
    7·2 answers
  • 0.07 is what of 0.7
    14·1 answer
  • If r= 1 and 0 = 5pi/3, what is the approximate arc length?
    8·1 answer
  • Angles: Arcs &amp; Angles need help thank you!!
    6·1 answer
  • The perimeter of a rectangle is 52 cm. If its width is 2 cm more than one-third of its length, find the dimensions of rectangle.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!