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
slavikrds [6]
3 years ago
8

If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a

missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions for t 0. Do the particles collide? If they collide find t. If not enter NONE.r1(t)=r2(t)=<9t-14,t^2,13t-42>t=
Mathematics
1 answer:
EastWind [94]3 years ago
3 0

Answer:

The particles collide when t = 7 at the point (49, 49, 49).

Step-by-step explanation:

We know the trajectories of the two particles,

r_1(t)=\langle t^2,16t-63,t^2\rangle\\r_2(t)=\langle 9t-14,t^2,13t-42\rangle

To find if the tow particles collide you must:

  • Equate the x-components for each particle and solve for t

t^2=9t-14\\t^2-9t+14=0\\\left(t^2-2t\right)+\left(-7t+14\right)=0\\t\left(t-2\right)-7\left(t-2\right)=0\\\left(t-2\right)\left(t-7\right)=0

The solutions to the quadratic equation are:

t=2,\:t=7

  • Equate the y-components for each particle and solve for t

16t-63=t^2\\^2-16t+63=0\\\left(t^2-7t\right)+\left(-9t+63\right)=0\\t\left(t-7\right)-9\left(t-7\right)=0\\\left(t-7\right)\left(t-9\right)=0

The solutions to the quadratic equation are:

t=7,\:t=9

  • Equate the z-components for each particle and solve for t

t^2=13t-42\\t^2-13t+42=0\\\left(t^2-6t\right)+\left(-7t+42\right)=0\\t\left(t-6\right)-7\left(t-6\right)=0\\\left(t-6\right)\left(t-7\right)=0

The solutions to the quadratic equation are:

t=6,\:t=7

Evaluate the position vectors at the common time. The common solution is when t = 7.

r_1(7)=\langle 7^2,16(7)-63,7^2\rangle=\langle 49,49,49\rangle\\\\r_2(7)=\langle 9(7)-14,7^2,13(7)-42\rangle=\langle 49,49,49\rangle

For two particles to collide, they must be at exactly the same coordinates at exactly the same time.

The particles collide when t = 7 at the point (49, 49, 49).

You might be interested in
Elena has one and a half times as much money as ramon. together they have $225. how much money does each have? choices for ramon
torisob [31]
E= 1.5R
E+R=225
1.5R+R=225
2.5R=225
R= 90
6 0
3 years ago
A company sells boxes of duck calls (d) for $35 and boxes of turkey calls (t) for $45. they make batches of duck calls that fill
SIZIF [17.4K]

Answer:

Option A is the correct choice.

Step-by-step explanation:

Let d be the number of boxes of duck calls and t be the number of boxes of turkey calls.

We have been given that a company sells boxes of duck calls for $35 and boxes of turkey calls (t) for $45, so the revenue earned from selling d boxes of duck and t boxes of turkey call will be 35d and 45t respectively.

Further, the company plan to make $300. We can represent this information as:

35d+45t=300...(1)

We are also told that they make batches of duck calls that fill 6 boxes and batches of turkey calls that fill 8 boxes. the company only has 42 boxes. We can represent this information as:

6d+8t=42...(2)

6d=42-8t...(2)

Therefore, our desired system of equation will be:

35d+45t=300...(1)

6d=42-8t...(2)  


8 0
3 years ago
Please help me with this question, I'm stuck ;( .
sveticcg [70]

i think C but i dont know forsure

7 0
3 years ago
How are each term related to one another in the sequence 2,90,4,87,6,12,8,51,10 ?​
Setler [38]
Every other number from the first, 3rd, 5th, ..etc it adds 2 for the next number.
For the 2nd, 4th, 6th, etc term, its supposed to be 90, 78, 65, 51?
If so, It started with -12 then -13 after that -14 find the next term, all you need to do is to -15 to the current number, which is 51. then you get 36
5 0
3 years ago
Triangle PQR hAS vertices P (4,-1),Q(-2,7), and R (9,9). find an equation of the median from R
strojnjashka [21]
A median intersects at the midpoint of the opposite length. The midpoint is:

x,m = (4+-2)/2 = 1
y,m = (-1+7)/2 = 3

The midpoint is at (1,3). With this point and point R(9,9), the equation would be:

y = mx + b, where
m = (9 - 3)/(9 - 1) = 0.75
b is the y-intercept
Substituting any point,
3 = 0.75(1)+b
b = 2.25

Thus, the equation for the median is:

y = 0.75x + 2.25
7 0
3 years ago
Other questions:
  • Find the value of x (2x) (5x +15)
    13·1 answer
  • Maridel wants to find out how many of her classmates plan to come to the next football game. There are 800 students in her schoo
    12·2 answers
  • Which set of points represents equivalent ratios and would follow the same pattern on a graph? (6, 2), (3, 1), (9, 3), (10, 2) (
    13·1 answer
  • A recipe calls for 4 L of water. Arlene wants to make 0.3 more servings than the recipe makes.
    9·1 answer
  • Which figure does NOT appear to be a parallelogram ?
    6·1 answer
  • Given the points C(-6,10) and D(-3,-2) what is the length of CD
    14·1 answer
  • Unit sales for new product ABC have varied in the first seven months of this year as follows:
    5·1 answer
  • The graph represents a pair of equations. What point represents the solution to the pair of equations?
    5·2 answers
  • Im so confused can anyone help
    9·1 answer
  • Please help will r8 5 + brainliest
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!