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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
Given: △ABC; AB=BC, m∠BDA = 60°, BD=4 cm, BD ⊥ BA . Find: DC, AC.
vekshin1

Answer:

DC = 10.93 cm ,  AC = 9.8 cm

Step-by-step explanation:

From trigonometry;

⇒ Tan 60 = AB/BD

⇒AB = BD Tan 60 ( where BD = 4 cm )

⇒ AB = 6.93 cm

Also, AB=BC , therefore;

⇒ BC = 6.93 cm

⇒ Cos 60 = BD/AD

⇒ AD = BD/ Cos 60 = 4/Cos 60

⇒ AD = 8 cm

From Pythagoras theorem;

⇒ AC^{2} = AB^{2} + BC^{2} = (6.93)^{2} + (6.93)^{2}

⇒ AC = \sqrt{96.05} = 9.80 cm

⇒ DC = BD + BC = 4 + 6.93

⇒ DC = 10.93 cm

8 0
3 years ago
If four tires can be changed in 3/4 of an hour gow long would it take to change 19 cars​
kobusy [5.1K]

Answer:

14.25 hours

Step-by-step explanation:

Four tires = 3/4 of an hour

=> 1 car = 3/4 of an hour

=> 19 cars = ?

=> If 1 = 3/4

=> 19 = 3/4 x 19

=> 3/4 x 19

=> 57/4

=> 14.25 hours

So, it would take 14.25 hours for 19 car's tires to be changed.

5 0
3 years ago
3 packs of soda cost $10 less than 5 packs of soda. Write and equation that models this, and solve.
zysi [14]
<span>Cost 1 pack = x
3x + 10 = 5x
2x = 10
x = 5
1 pack cost $5
Hope this helped</span>
8 0
3 years ago
In APQR, p = 690 cm, a = 290 cm and r=450 cm. Find the measure of ZQ to the
katen-ka-za [31]

9514 1404 393

Answer:

  16.8°

Step-by-step explanation:

The Law of Cosines can be rearranged to give the angle measure.

  angle Q = arccos((p² +r² -q²)/(2pr))

  angle Q = arccos((690² +450² -290²)/(2×690×450))

  angle Q = arccos(594500/621000) ≈ 16.7985°

The measure of angle Q is about 16.8°.

3 0
3 years ago
A club raised 175% of its goal for a charity. The club raises $875. What was the goal?
charle [14.2K]

Answer: The goal was $500

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

Work Shown:

x% = x/100

175% = 175/100 = 1.75

Let g be the goal, which is the amount of money the club wanted to raise

175% of goal = 175% of g = 1.75g

The expression 1.75g represents how much money was actually raised, which was $875. Set the two expressions equal to each other. Solve for g

1.75g = 875

g = 875/1.75 ....... divide both sides by 1.75

g = 500

The club's goal was to raise $500

Note how 75% of $500 is 0.75*500 = 375

When they raised 175% of the goal, this means they went 75% overboard and added on 375 additional dollars (on top of the 500 they wanted). So they got to 500+375 = 875 which lines up with the instructions. This helps verify the answer.

Or we can see that 1.75*g = 1.75*500 = 875 which helps confirm the answer as well.

3 0
3 years ago
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