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
Tcecarenko [31]
3 years ago
11

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: r1(t)= r2(t)=<4t-3, t^2, 5t-6> for t>=0.Do the particles collide?
Mathematics
1 answer:
galina1969 [7]3 years ago
6 0

Answer:

<em>Both objects collide at t=3 in the point  <9,9,9></em>

Step-by-step explanation:

<em>Collision Of Moving Objects </em>

Two objects can describe different trajectories in the space. Those trajectories can intersect in one or more points but it doesn't mean they collide. Collision occurs if they are in the same position at the same time. If we know the positions as a function of time of each object, we could try so find if, for a given time, they are in the same position.

The positions of two object are given as

r1(t)=

r2(t)=

Let's find out if there is at least one value of t that makes both positions to be the same. We can try by equating one of the three coordinates and testing if the value of t make both have the same x,y,z coordinate. Let's try equating the x-components of both

t^2=4t-3

Rearranging

t^2-4t+3=0

Factoring

(t-1)(t-3)=0

We found two solutions

t=1,\ t=3

for t=1 the x-coordinates are

x1=t^2=1

x2=4t-3=1

For t=3

x1=t^2=9

x2=4t-3=9

Now we'll test both values in the y-coordinates

y1=7t-12

y2=t^2

For t=1

y1=-5

y2=1

Thus they don't collide at t=1. Let's try t=3

y1=7(3)-12=9

y2=3^2=9

Now let's try the z-coordinate for t=3

z1=t^2=9

z2=5t-6=9

Since the three coordinates match, we can say both objects collide at t=3 in the point  <9,9,9>

You might be interested in
Write the slope-intercept form of the equation of each line. X-3y=6
Alecsey [184]
<span>x -3y=6
3y = x - 6
  y = x/3 - 2

answer
</span>slope-intercept form of the equation:  y = x/3 - 2
4 0
3 years ago
Changle. Show all work. Round each length to the nearest tenth and each angle to the
Sedaia [141]

Answer:

Part 1) BC=12.2\ units

Part 2) m\angle A=55^o

Part 3) m\angle C=35^o

Step-by-step explanation:

Part 1) Find AC

we know that

In the right triangle ABC of the figure

Applying the Pythagorean Theorem

AC^2=AB^2+BC^2

substitute the given values

AC^2=7^2+10^2

AC^2=149\\AC=12.2\ units

Part 2) Find the measure of angle A

we know that

In the right triangle ABC

tan(A)=\frac{BC}{AB} ----> by TOA (opposite side divided by the adjacent side)

substitute the values

tan(A)=\frac{10}{7}

using a calculator

m\angle A=tan^{-1}(\frac{10}{7})=55^o

Part 3) Find the measure of angle C

we know that

In the right triangle ABC

m\angle A+m\angle C=90^o ----> by complementary angles

substitute the given value

55^o+m\angle C=90^o

m\angle C=90^o-55^o=35^o

8 0
3 years ago
What is the solution, if any, to the inequality |3x|≥0?
Murljashka [212]

The inequality is all real numbers.

<h3>What is inequality?</h3>

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

|3x|≥0

3x = 0

Divide both sides of the equation by the coefficient of variable

x= 0/3

x=0 = RHS

Learn more about inequality here:

brainly.com/question/20383699

#SPJ1

4 0
1 year ago
I confused on this question
Fynjy0 [20]
42 degrees. Comment down if you need the explanation why
6 0
3 years ago
Read 2 more answers
Find log1/4 rounded to the nearest hundredth.
erastovalidia [21]

Answer:

-log_4

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • Can someone help me I’m so confuse on this question help me
    9·2 answers
  • Who can Help me please...
    7·1 answer
  • Which expression is equivalent 5y3/(5y)-2
    9·1 answer
  • the lengths of three pieces of wire are in the ratio 10:15:8. if the length of the shortest piece of wire is 2.4 m, find the dif
    6·1 answer
  • Find the correct sum of the polynomials (6x3 − 8x − 5) + (3x3 + 6x + 2).
    8·1 answer
  • HELP ME PLEASE!!!!!!
    15·1 answer
  • The freezer contains vanilla and chocolate ice cream. Chocolate ice cream contains 12 servings less than vanilla. How many servi
    13·1 answer
  • 10000 POINTS I NEED HELP THESE HAVE TO BE MADE AND PUT INTO FROM IMPOPER FRACTIONS TO MIXED NUMBERS I AM TIMED PLZ HELP I WILL G
    14·1 answer
  • Help please! No links!
    11·1 answer
  • Find the missing value in the graph below there are two
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!