c is the answer i know this because im smart and because c is the answer
Answer:
Originally
The number of coins in the first box was ![67\ coins](https://tex.z-dn.net/?f=67%5C%20coins)
The number of coins in the second box was ![83\ coins](https://tex.z-dn.net/?f=83%5C%20coins)
Finally
The number of coins in the first box is ![50\ coins](https://tex.z-dn.net/?f=50%5C%20coins)
The number of coins in the second box is ![100\ coins](https://tex.z-dn.net/?f=100%5C%20coins)
Step-by-step explanation:
Let
x-----> number of coins in the first box originally
y-----> number of coins in the second box originally
we know that
![x+y=150](https://tex.z-dn.net/?f=x%2By%3D150)
-----> equation A
-----> equation B
substitute equation A in equation B
![y+17=2x-34](https://tex.z-dn.net/?f=y%2B17%3D2x-34)
![y+17=2(150-y)-34](https://tex.z-dn.net/?f=y%2B17%3D2%28150-y%29-34)
![y+17=300-2y-34](https://tex.z-dn.net/?f=y%2B17%3D300-2y-34)
![y+2y=300-34-17](https://tex.z-dn.net/?f=y%2B2y%3D300-34-17)
![3y=249](https://tex.z-dn.net/?f=3y%3D249)
![y=83\ coins](https://tex.z-dn.net/?f=y%3D83%5C%20coins)
Find the value of x
![x=150-83=67\ coins](https://tex.z-dn.net/?f=x%3D150-83%3D67%5C%20coins)
therefore
Originally
The number of coins in the first box was ![67\ coins](https://tex.z-dn.net/?f=67%5C%20coins)
The number of coins in the second box was ![83\ coins](https://tex.z-dn.net/?f=83%5C%20coins)
Finally
The number of coins in the first box is ![(67-17)=50\ coins](https://tex.z-dn.net/?f=%2867-17%29%3D50%5C%20coins)
The number of coins in the second box is ![(83+17)=100\ coins](https://tex.z-dn.net/?f=%2883%2B17%29%3D100%5C%20coins)
On an investment of $5000 with an interest payment of 5% = $250 at one year. At 3.5 years, the interest payments would total $250 × 3.5 = $875
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 is 28
y+z=4 => y=4-z
yz=3 => (4-z)z=3
=> z^2-4z+3=0
=> z=1 y=3 OR z=3 y=1
=>y^3 + z^3 =3^3+1=28