Solve the following system of equations: x − 2y = 6 2x − 4y = 10
1 answer:
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The function has a y-intercept at (0, 2). Then the correct options are A, B, and E.
The complete question is attached below.
<h3>What is the maximum and minimum value of the function?</h3>The condition for the maximum will be
f"(x) < 0
The condition for the minimum will be
f"(x) > 0
Consider the inverse function.
f⁻¹(x) = -√(x - 2)
Then the conclusion of the function f(x) = x² + 2 will be
Differentiate the function, then we have
f ' (x) = 2x
Again differentiate, then we have
f" (x) = 2
f" (x) > 0
Then the function has a minimum value at (0, 2)
The function has a y-intercept at (0, 2)
Then the correct options are A, B, and E.
More about the maximum and minimum value of the function link is given below.
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Answer:
a) 8.16%
b) $65,762.50
c) $39,701.07
Step-by-step explanation:
Given:
15 years ago, Initial investment = $12500
5 years ago, Investment = $20000
Nominal interest = 8% semi annually for first 10 years
Interest2= 6.5% compunded annually for last five years
a) for the effective annual interest rate (EAR) in the first 10 years, let's use the formula:
[1+(nominal interest rate/number of compounding periods)]^ number of compounding periods-1
= 1.0816 - 1
= 0.0816
= 8.16%
The effective annual interesting rate, EAR = 8.16 %
b) To find the amount in my account today.
Let's first find the amount for $12500 for 10 years compounded semi annually
= 12,500 +( 12,500 * 8.160% * 10)
= $ 22,700
Let's also find the amount for $32,500($12,500+$20,000) for 5 Years compoundeed annually
$32,500 + ($32,500 * 6.5% *5)
= $ 43,062.50
Money in account today will be:
$22,700 + $43,062.50
= $65,762.50
c) Let's the amount I should have invested to be X
For first 10 years at 8.160%, we have:
Interest Amount = ( X * 8.160% * 10 ) = 0.8160 X
For next 5 years at 6.5%, we have:
Interest Amount = (X * 6.5% * 5) = 0.325 X
Therefore the total money at the end of 15 Years = 85000
0.8160X + 0.3250X + X = $85,000
= 2.141X = $85,000
X = 85,000/2.141
X = 39,701.074 ≈ $39,700
If I wish to have $85,000 now, I should have invested $39,700 15 years ago
Answer:
The unknown side is 15 in.
Step-by-step explanation: