Answer:
The distance between the ships is changing at 42.720 kilometers per hour at 4:00 PM.
Step-by-step explanation:
Vectorially speaking, let assume that ship A is located at the origin and the relative distance of ship B with regard to ship A at noon is:
![\vec r_{B/A} = \vec r_{B} - \vec r_{A}](https://tex.z-dn.net/?f=%5Cvec%20r_%7BB%2FA%7D%20%3D%20%5Cvec%20r_%7BB%7D%20-%20%5Cvec%20r_%7BA%7D)
Where
and
are the distances of ships A and B with respect to origin.
By supposing that both ships are travelling at constant speed. The equations of absolute position are described below:
![\vec r_{A} = \left[\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i](https://tex.z-dn.net/?f=%5Cvec%20r_%7BA%7D%20%3D%20%5Cleft%5B%5Cleft%2840%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20t%5Cright%5D%5Ccdot%20i)
![\vec r_{B} = \left(170\,km\right)\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j](https://tex.z-dn.net/?f=%5Cvec%20r_%7BB%7D%20%3D%20%5Cleft%28170%5C%2Ckm%5Cright%29%5Ccdot%20i%20%2B%5Cleft%5B%5Cleft%2815%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20t%5Cright%5D%5Ccdot%20j)
Then,
![\vec r_{B/A} = (170\,km)\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j-\left[\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i](https://tex.z-dn.net/?f=%5Cvec%20r_%7BB%2FA%7D%20%3D%20%28170%5C%2Ckm%29%5Ccdot%20i%20%2B%5Cleft%5B%5Cleft%2815%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20t%5Cright%5D%5Ccdot%20j-%5Cleft%5B%5Cleft%2840%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20t%5Cright%5D%5Ccdot%20i)
![\vec r_{B/A} = \left[170\,km-\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j](https://tex.z-dn.net/?f=%5Cvec%20r_%7BB%2FA%7D%20%3D%20%5Cleft%5B170%5C%2Ckm-%5Cleft%2840%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20t%5Cright%5D%5Ccdot%20i%20%2B%5Cleft%5B%5Cleft%2815%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20t%5Cright%5D%5Ccdot%20j)
The rate of change of the distance between the ship is constructed by deriving the previous expression:
![\vec v_{B/A} = -\left(40\,\frac{km}{h} \right)\cdot i + \left(15\,\frac{km}{h} \right)\cdot j](https://tex.z-dn.net/?f=%5Cvec%20v_%7BB%2FA%7D%20%3D%20-%5Cleft%2840%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20i%20%2B%20%5Cleft%2815%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5Ccdot%20j)
Its magnitude is determined by means of the Pythagorean Theorem:
![\|\vec v_{B/A}\| = \sqrt{\left(-40\,\frac{km}{h} \right)^{2}+\left(15\,\frac{km}{h} \right)^{2}}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20v_%7BB%2FA%7D%5C%7C%20%3D%20%5Csqrt%7B%5Cleft%28-40%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5E%7B2%7D%2B%5Cleft%2815%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D%20%5Cright%29%5E%7B2%7D%7D)
![\|\vec r_{B/A}\| \approx 42.720\,\frac{km}{h}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20r_%7BB%2FA%7D%5C%7C%20%5Capprox%2042.720%5C%2C%5Cfrac%7Bkm%7D%7Bh%7D)
The distance between the ships is changing at 42.720 kilometers per hour at 4:00 PM.
Answer:
1 + 1/5= 1 1/5
Step-by-step explanation:
2 (10/5) - 4/5 = 6/5 (1 1/5)
Answer:
10:40
Step-by-step explanation:
I'm assuming it would be the same shape? That's also assuming that it's referring to congruent shapes and angles.
Answer:
So, Plane ABC and plane BCE _may_ be the same plane.
Step-by-step explanation:
This happens when E is on Plane ABC (or you could say, A is on Plane BCE). If not, then they are two different planes.