Answer:
The best mortgage option for them is (3).
Step-by-step explanation:
Mortgage offers (1) and (2) are similar since Damarco and Tanya's down payment of $34,000 (20% of the purchase price) requires them to pay interest over 30 years for both scenarios. Although option (1) entails approximately $750 monthly payments and option (2) requires about $9,000 annually, the total payments are quite comparable as option (2)'s interest rate, starting at 3.5%, could potentially rise but is unlikely to exceed 5%, while option (1) maintains a fixed annual interest rate of 4.25%.
Option (3), however, demands interest payments for only 8 years at a relatively lower annual rate of 4%. If they commit to $18,000 annually with a $34,000 down payment and repay the remaining balance (under $35,000) at the end of 8 years, it leads to the lowest total payment and quickest mortgage clearance among the three options. Therefore, this choice aligns best with their financial objectives.
Response:
The outcome is 4144.
Detailed explanation:
We need to determine the peak value of f(x)=
when 
We can represent
as 
Plugging the value of y

= ![3x^{2}(8-x)^{2}[-x+8-x]+3[-x+8-x]](https://tex.z-dn.net/?f=3x%5E%7B2%7D%288-x%29%5E%7B2%7D%5B-x%2B8-x%5D%2B3%5B-x%2B8-x%5D)
= ![3(8-2x)[x^{2}(8-x)^{2}+1]](https://tex.z-dn.net/?f=3%288-2x%29%5Bx%5E%7B2%7D%288-x%29%5E%7B2%7D%2B1%5D)
To find the maximum, we'll set the equation to 0.
Thus, we find:
=> x = 4
And since
> y = 4
Hence, we will substitute these values into the equation to ascertain the maximum value.
= 
= 
= 
=
= 4144
0 ounces remain; since he distributed it evenly among four individuals, each cup contained 8 ounces, meaning he consumed the entire cup.
We recognize that two angles, ∠UVW and ∠XYZ, are complementary, which means their sum is 90°.
Their measures are given as:
∠UVW = x - 10
∠XYZ = 4x - 10
Adding these, we have:
(x - 10) + (4x - 10) = 90
Simplifying:
5x - 20 = 90
Adding 20 to both sides:
5x = 110
Dividing by 5:
x = 22
Substituting back:
∠UVW = 22 - 10 = 12°
∠XYZ = 4(22) - 10 = 78°
Therefore, the values are:
x = 22°
∠UVW = 12°
∠XYZ = 78°