I can’t see the picture so if you just want to comment and put it there I can help :)
<span>$628,119.20
The formula for calculating the periodic payment on a loan is:
P = r(PV)/(1-(1+r)^(-n))
where
P = Payment
PV = Present Value
r = Interest rate per period
n = number of periods
So for this loan, assuming that payments are made monthly, the value r will be 0.05575/12 = 0.004645833, the value n will be 30*12 = 360, and PV is 592000. So let's substitute these values into the equation and calculate:
P = r(PV)/(1-(1+r)^(-n))
P = 0.004645833(592000)/(1-(1+0.004645833)^(-360))
P = 2750.333333/(1-(1.004645833)^(-360))
P = 2750.333333/(1-0.188505723)
P = 2750.333333/0.811494277
P = 3389.220861
So each payment will be $3389.22
Arnold will make a total of 360 payments, so will spend
360 * $3,389.22 = $1,220,119.20
Since his loan was for only $592,000; let's subtract that from his total payments to get the interest.
$1,220,119.20 - $592,000 = $628,119.20
Therefore his total interest is $628,119.20</span>
<h2>
The greatest possible value of the second root, β = 54 </h2>
Step-by-step explanation:
The given quadratic equation:
![x^2-5mx+6m^2=0](https://tex.z-dn.net/?f=x%5E2-5mx%2B6m%5E2%3D0)
Let α and β be the roots of the given quadratic equation.
α = 36
To find, the greatest possible value of the second root ( β) = ?
∴ The sum of the roots,
α + β = ![\dfrac{-b}{a}](https://tex.z-dn.net/?f=%5Cdfrac%7B-b%7D%7Ba%7D)
⇒ 36 + β =
⇒ 5m = 36 + β ............. (1)
The product of the roots,
α.β = ![\dfrac{c}{a}](https://tex.z-dn.net/?f=%5Cdfrac%7Bc%7D%7Ba%7D)
⇒ ![36.\beta=\dfrac{6m^2}{1}](https://tex.z-dn.net/?f=36.%5Cbeta%3D%5Cdfrac%7B6m%5E2%7D%7B1%7D)
⇒
............. (2)
From equations (1) and (2), we get
⇒ ![(\dfrac{36+\beta}{5})^{2}=6\beta](https://tex.z-dn.net/?f=%28%5Cdfrac%7B36%2B%5Cbeta%7D%7B5%7D%29%5E%7B2%7D%3D6%5Cbeta)
⇒ ![\beta^2-78\beta+1296=0](https://tex.z-dn.net/?f=%5Cbeta%5E2-78%5Cbeta%2B1296%3D0)
⇒ ![\beta^2-54B\beta-24B\beta+1296=0](https://tex.z-dn.net/?f=%5Cbeta%5E2-54B%5Cbeta-24B%5Cbeta%2B1296%3D0)
⇒ β(β - 54) - 24(β - 54) = 0
⇒ (β - 54)(β - 24) = 0
⇒ β - 54 = 0 or, β - 24 = 0
⇒ β = 54 or, β = 24
∴ The greatest possible value of the second root, β = 54
Answer:
1.49216 x 10^11 m.
Step-by-step explanation:
That would be the following difference:
1.496 x 10^11 - 3.84 x 10^8
= 1.49216 x 10^11 m.