Answer:
m = 10 , n = 5
Step-by-step explanation:
using the cosine and tangent ratio in the right triangle and the exact values
cos45° = 
and tan45° = 1 , then
cos45° = 
= 
= ( cross- multiply )
m = 5 × = 5 × 2 = 10
-----------------------------------------
tan45° = 
= 
= 1 , then
n = 5
B.......,.,.,.,,..,,.,.,.
The numbers get smaller in division and larger in multiplying
In can be less mental effort if the equation is multiplied by -1 first.
.. x^2 -10x +8 = 0
.. x^2 -10x +25 +8 -25 = 0
.. (x -5)^2 = 17
.. x -5 = ±√17
.. x = 5 ±√17
The values of x that satisfy the given equation are
.. x = 5 -√17 ≈ 0.877
.. x = 5 +√17 ≈ 9.123
<h3>Answer: 7366.96 dollars</h3>
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Use the compound interest formula:
A = P(1+r/n)^(n*t)
where in this case,
A = 12000 = amount after t years
P = unknown = deposited amount we want to solve for
r = 0.05 = the decimal form of 5% interest
n = 1 = refers to the compounding frequency (annual)
t = 10 = number of years
-------
Plug all these values into the equation, then solve for P
A = P(1+r/n)^(n*t)
12000 = P(1+0.05/1)^(1*10)
12000 = P(1.05)^(10)
12000 = P(1.62889462677744)
12000 = 1.62889462677744P
1.62889462677744P = 12000
P = 12000/1.62889462677744
P = 7366.95904248911
P = 7366.96
