$90 ok I think so if this is for homework
Answer:
$64 is the answer
Step-by-step explanation:
If I am correct the x and y values are the ones values of the overall $60 so if you on the x axis to where the 6 is it matches up with the 4 on the y axis so therefore the answer must be $64.
I hope this helps
Answer:
x = ![\frac{a(a + b)}{a-b}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%28a%20%2B%20b%29%7D%7Ba-b%7D)
Step-by-step explanation:
Step 1: Write out formula
a(x - b) = a² + bx
Step 2: Distribute
ax - ab = a² + bx
Step 3: Add <em>ab</em> to both sides
ax = a² + bx + ab
Step 4: Subtract <em>bx</em> on both sides
ax - bx = a² + ab
Step 5: Factor
x(a - b) = a² + ab
Step 6: Divide (a - b) on both sides
x = ![\frac{a^{2} + ab}{a-b}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B2%7D%20%2B%20ab%7D%7Ba-b%7D)
Step 7: Factor
x = ![\frac{a(a + b)}{a-b}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%28a%20%2B%20b%29%7D%7Ba-b%7D)
And we have our final answer!
Answer:
The intesection points are:
![\vec r_{2} = (0,19,-17)](https://tex.z-dn.net/?f=%5Cvec%20r_%7B2%7D%20%3D%20%280%2C19%2C-17%29)
![\vec r_{1} = (0, 53,-71)](https://tex.z-dn.net/?f=%5Cvec%20r_%7B1%7D%20%3D%20%280%2C%2053%2C-71%29)
Step-by-step explanation:
The acceleration vector is:
![\vec a = (2,-4,-8)](https://tex.z-dn.net/?f=%5Cvec%20a%20%3D%20%282%2C-4%2C-8%29)
The velocity vector is found by integrating the previous vector as a function of time:
![\vec v = (-8+2\cdot t, 1 +4\cdot t, 5 - 8\cdot t)](https://tex.z-dn.net/?f=%5Cvec%20v%20%3D%20%28-8%2B2%5Ccdot%20t%2C%201%20%2B4%5Ccdot%20t%2C%205%20-%208%5Ccdot%20t%29)
Afterwards, the position vector is constructed by means of integrating velocity vector:
![\vec r = (15-8\cdot t+t^{2},-2+t+2\cdot t^{2}, 4+5\cdot t - 4\cdot t^{2})](https://tex.z-dn.net/?f=%5Cvec%20r%20%3D%20%2815-8%5Ccdot%20t%2Bt%5E%7B2%7D%2C-2%2Bt%2B2%5Ccdot%20t%5E%7B2%7D%2C%204%2B5%5Ccdot%20t%20-%204%5Ccdot%20t%5E%7B2%7D%29)
The particle trajectory intersects the yz-plane when x = 0, then:
![t^{2}-8\cdot t +15 = 0](https://tex.z-dn.net/?f=t%5E%7B2%7D-8%5Ccdot%20t%20%2B15%20%3D%200)
The polynomial roots are:
![t_{1}=5, t_{2}= 3](https://tex.z-dn.net/?f=t_%7B1%7D%3D5%2C%20t_%7B2%7D%3D%203)
The intesection points are:
![\vec r_{2} = (0,19,-17)](https://tex.z-dn.net/?f=%5Cvec%20r_%7B2%7D%20%3D%20%280%2C19%2C-17%29)
![\vec r_{1} = (0, 53,-71)](https://tex.z-dn.net/?f=%5Cvec%20r_%7B1%7D%20%3D%20%280%2C%2053%2C-71%29)