Answer:
At t = 3, 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).
r(t) = 5 - t, 21 - t², 3-t³/27
r'(t) = -1, -2t, -t²/9
Now perform the cross product among these two r(t) and r'(t).
r'(t) x r(t) =
= i ((-6t + )+ ( - )) -j ((-3 + + - )) + k ((-21 + + 10t -2))
= ( + - 6t )i + ( - +3) j + (-t² + 10t -21)k
In order to find the value of t, we need to put
+ - 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, 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.
how many rectangular prism can you make out of 20 snap of cubes
3x + 3y = 45
Answer:
y=15-x
Step-by-step explanation:
3y=45-3x
y=15-x
If you want to solve for y, you need another one equation
Answer:
y = -x + 15
Step-by-step explanation:
Subtract 3x from each side (left and right side of the equal sign) which will leave you with 3y = -3x + 45. Then divide everything by 3 which gets you
y = -x +15
Answer: john is 33, paul is 19, george is 39
Step-by-step explanation:
B. 0.2, 1/4, 3/8, 7/8, 0.8
C. 1/4, 0.2, 3/8, 7/8, 0.8
D. 0.8, 1/4, 3/8, 0.2, 7/8
Answer:
It’s a
Step-by-step explanation:
Tell me if I’m wrong