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
ehidna [41]
3 years ago
11

7. (1 point) A fighter plane, which can shoot a laser beam straight ahead, travels along the path ~r(t) = 5 − t, 21 − t 2 , 3 −

t 3 27 Show that there is precisely one time t at which the pilot can hit a target located at the origin.
Mathematics
1 answer:
maria [59]3 years ago
3 0

Answer:

<em>At t = 3</em>, pilot can hit the target located at the origin.

Step-by-step explanation:

We have been given displacement vector:

r(t) = 5 - t, 21 - t², 3-t³/27

so, in this case r(t) and r'(t) should be in the parallel but opposite direction.

In order to get r'(t) we need to differentiate r(t).

<em>r(t) = 5 - t, 21 - t², 3-t³/27 </em>

<em>r'(t) = -1, -2t, -t²/9</em>

Now perform the cross product among these two r(t) and r'(t).

r'(t) x r(t) = \left[\begin{array}{ccc}i&j&k\\-1&-2t&\frac{-t^{2} }{9}  \\5-t&21-t^{2} &3-\frac{t^{3} }{27} \end{array}\right]

            = i ((-6t + \frac{2t^{4} }{27} )+ ( \frac{21t^{2} }{9} - \frac{t^{2} }{9} )) -j ((-3 + \frac{t^{3} }{27} + \frac{5t^{2} }{9} - \frac{t^{2} }{9} )) + k ((-21 + t^{2}  + 10t -2t^{2}))

           = (\frac{-t^{4} }{27} + \frac{7t^{2} }{3} - 6t )i + (\frac{2t^{3} }{27} - \frac{5t^{2} }{9} +3) j + (-t² + 10t -21)k

In order to find the value of t, we need to put

\frac{-t^{4} }{27} + \frac{7t^{2} }{3} - 6t = 0

-t² + 10t -21 = 0

So, after solving for t, we will get

- ( t-3) (t-7) = 0

t = 3 or t = 7

In this case, only t = 3 satisfies the other two equations as well. t=7 is not satisfying. So take t =3 as the time. and for further assurance, we need to check are our vectors r(t) and r'(t) opposite at t = 3 or not. Let's check it out.

r(3) = 5-3, 21 - 3²,  3 - 3³/27

r (3) = 2, 12, 2

r'(3) = -1, -2(3) , -3²/9

r'(3) = -1, -6 -1

Here, we can easily see that, <em>r(3) = -2 r'(3) which is opposite and hence it is proved that, at exactly t = 3, pilot can hit a target located at the origin. </em>

You might be interested in
Solve.<br> 4. Find the value of x in the diagram at the right.
nadya68 [22]
The expression is consistent witch means and can keep going a long time the answer is x0x0
5 0
2 years ago
Into how many segments do n points divide a given line segment?
yulyashka [42]
n points would divide a given line into n+1 segments.

Just assume that you have a line and you added a point to that line, this point would divide your line into two segments.
If you add two points to a line, these two points would divide your line into three segments.
So the number of segments is always greater that the number of points by 1.
8 0
3 years ago
Help meh_________________<br><br><br><br>​
professor190 [17]

Answer:

binomial

Step-by-step explanation:

8 0
3 years ago
What is the result when 6x3 + 11x2 + 9x + 2 is divided by 3x + 1?
konstantin123 [22]

<u>Answer:</u>

<u>(6x^(3)+11x^(2)-19x+5)-:-(3x-2)</u>

<u>Step-by-step explanation:</u>63+112+32+1

for some reason it showed that but yeah hope this helps!

4 0
3 years ago
Hayden decided to take martial arts classes at his local gym. He pays $35 each month for his membership and $12 for every class
gizmo_the_mogwai [7]
Hayden had the membership for one month and took 6 classes.
8 0
3 years ago
Other questions:
  • I need major assistance for number 12,13
    9·1 answer
  • Addition of large numbers<br> 9,13,09,540+<br> 7,48,91,730+<br> 2,48,65,865
    8·1 answer
  • PLEASEEEE NEED HELP ASAP
    13·2 answers
  • What's the part of speech of mince
    5·2 answers
  • What is the difference between the Right of Occupancy and Original Indian Title?
    6·2 answers
  • Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Lou​'s car had 5.3
    6·1 answer
  • Which choice is the correct graph of [x] &gt; 3?
    5·1 answer
  • Help me please i need the right answer no links
    13·1 answer
  • An inflatable pool has sprung a leak. You place a 1-gallon cup under the leak and find that it fills up in 195 seconds. How many
    8·1 answer
  • yang company sold merchandise for $4,000. the event is subject to a state sales tax of 9%. based on this information, yang would
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!