The values are a = 7, b = -9, c = -18.
<u>Step-by-step explanation:</u>
The given quadratic equation is ![7x^{2} - 9x = 18](https://tex.z-dn.net/?f=7x%5E%7B2%7D%20-%209x%20%3D%2018)
The general form of the quadratic equation is ![ax^{2} + bx + c = 0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2B%20bx%20%2B%20c%20%3D%200)
where,
- a is the coefficient of x².
- b is the coefficient of x.
- c is the constant term.
Now, you have to modify the given quadratic equation similar to the general form of quadratic equation.
So, bring the constant term 18 to the left side of the equation for equating it to zero.
⇒ ![7x^{2} - 9x - 18 = 0](https://tex.z-dn.net/?f=7x%5E%7B2%7D%20-%209x%20-%2018%20%3D%200)
Compare the above equation with general form ![ax^{2} + bx + c = 0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2B%20bx%20%2B%20c%20%3D%200)
⇒ a = 7
⇒ b = -9
⇒ c = -18
Therefore, the values of a, b, and c are 7, -9 and -18.
Answer:
1 5/9
Step-by-step explanation:
9 1/3 can be rewritten as 28/3. The question is asking for you to divide 28/3 by 6. 6 is 6/1, so the expression is 28/3 divided by 6/1. You then do the reciprocal of 6/1 and the expression is
. This gets you 28/18, which is simplified to 14/9 or 1 5/9. Hope this helps!
You can rewrite the differential equation as
![50\cdot\dfrac{dA}{A}=dt\\\\50\ln{(A)}+C=t\qquad\mbox{integrating}\\\\t=50\ln{\left(\dfrac{A}{4000}\right)}\qquad\mbox{applying the boundary condition}](https://tex.z-dn.net/?f=50%5Ccdot%5Cdfrac%7BdA%7D%7BA%7D%3Ddt%5C%5C%5C%5C50%5Cln%7B%28A%29%7D%2BC%3Dt%5Cqquad%5Cmbox%7Bintegrating%7D%5C%5C%5C%5Ct%3D50%5Cln%7B%5Cleft%28%5Cdfrac%7BA%7D%7B4000%7D%5Cright%29%7D%5Cqquad%5Cmbox%7Bapplying%20the%20boundary%20condition%7D)
This last expression looks like the one you describe. If you solve for A instead of t, you get
![A=4000\cdot e^{0.02t}](https://tex.z-dn.net/?f=A%3D4000%5Ccdot%20e%5E%7B0.02t%7D)
This is the same as your other answer.
Since there are 3 "2's" and 8 total options, the probability is 3/8 or C.