Answer:
Here,
, hence the quadratic equation has two distinct real roots.
Step-by-step explanation:
Given quadratic equation is
.
Let, the quadratic equation is
[where,
are the constants]
The Discriminant ![(D)=b^{2}-4ac](https://tex.z-dn.net/?f=%28D%29%3Db%5E%7B2%7D-4ac)
Case
:
, if the discriminant is greater than
, it means the quadratic equation has two real distinct roots.
Case
:
, if the discriminant is less than
, it means the quadratic equation has no real roots.
Case
:
, if the discriminants is equal to
, it means the quadratic equation has two real identical roots.
Now,
we have
, where ![a=6,b=10,\ and\ c=-1](https://tex.z-dn.net/?f=a%3D6%2Cb%3D10%2C%5C%20and%5C%20%20c%3D-1)
∴![D=b^{2}-4ac](https://tex.z-dn.net/?f=D%3Db%5E%7B2%7D-4ac)
![=(10)^{2}-(4\times 6\times\ -1)](https://tex.z-dn.net/?f=%3D%2810%29%5E%7B2%7D-%284%5Ctimes%206%5Ctimes%5C%20-1%29)
![=100+24](https://tex.z-dn.net/?f=%3D100%2B24)
![= 124](https://tex.z-dn.net/?f=%3D%20124)
Here,
, hence the quadratic equation has two distinct real roots.
Answer:
$1348.07
Step-by-step explanation:
Hello!
<h3>Compound Interest Formula:
![A = P(1 + \frac rn)^{nt}](https://tex.z-dn.net/?f=A%20%3D%20P%281%20%2B%20%5Cfrac%20rn%29%5E%7Bnt%7D)
</h3>
- A = Account Balance
- P = Principle/Initial Amount
- r = Rate of Interest (decimal)
- n = Number of times compounded (per year)
- t = Number of Years
<h3>Given Information</h3>
- Account Balance = ?
- Principle Amount = $1000
- Rate of Interest = 0.02
Why is the Rate 0.02?
This is because we are gaining money, so the multiplier should be greater than 1. We already added 1, which is 100% so you simply add the 0.02 for the extra 2%.
- Number of times compounded per year = 6
This is because it is being compounded bi-monthly, or once every 2 months. 12 months divided by 2 months is 6 months, so 6 times a year.
<h2>Solve </h2>
Solve by plugging in the given values into the formula.
This is really close to the first option, and since there is rounding involved with the repeating decimal, the first option should be correct.
The answer is $1348.07.
This is the answer I got.
A=p+(p*0.03t)<span />
<u>Given</u>:
The radius of the circle is 10 cm
The central angle of the circle is (360 - 90)° = 270°
We need to determine the area of the composite figure.
<u>Area of the composite figure:</u>
The area of the figure can be determined using the area of the sector formula.
Thus, we have;
![A=(\frac{\theta}{360}) \times \pi r^2](https://tex.z-dn.net/?f=A%3D%28%5Cfrac%7B%5Ctheta%7D%7B360%7D%29%20%5Ctimes%20%5Cpi%20r%5E2)
Substituting
and
in the above formula, we get;
![A=(\frac{270}{360}) \times (3.14) (10)^2](https://tex.z-dn.net/?f=A%3D%28%5Cfrac%7B270%7D%7B360%7D%29%20%5Ctimes%20%283.14%29%20%2810%29%5E2)
Simplifying, we get;
![A=(\frac{270}{360}) \times (314)](https://tex.z-dn.net/?f=A%3D%28%5Cfrac%7B270%7D%7B360%7D%29%20%5Ctimes%20%28314%29)
Multiplying, we get;
![A=\frac{84780}{360}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B84780%7D%7B360%7D)
Dividing the terms, we get;
![A=235.5 \ cm^2](https://tex.z-dn.net/?f=A%3D235.5%20%5C%20cm%5E2)
Thus, the area of the composite figure is 235.5 cm²
Hence, Option C is the correct answer.