Why does y=cos(2x)sin(2x) simplify to y=sin(4x)/2 for derivatives?
1 answer:
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Before we start answering the question, let's define the compound interest formula:
Where:
<span>'A'</span> is the amount of money in dollars
'P' is the principal amount of money in dollars
'r' is the interest rate (decimal)
'n' is the number of times interest is compounded per year
't' is the time in years
<span>(A) Find Principal Amount
</span><u /><span><u>Given:</u>
</span>A = 12,000
P = ?
r = 0.08
n = 2 (semiannually)
t = 5
Now we plug our values in and solve:
∴ You would have to deposit $8106.77 in order to have $12,000 in 5 years from now.
(B) Find Principal Amount
Same given values as above, with the exception of 't' which is now 10 instead of 5.
∴ You would have to deposit $5476.64 in order to have $12,000 in 10 years from now.
Hope this helps!
Where:
<span>'A'</span> is the amount of money in dollars
'P' is the principal amount of money in dollars
'r' is the interest rate (decimal)
'n' is the number of times interest is compounded per year
't' is the time in years
<span>(A) Find Principal Amount
</span><u /><span><u>Given:</u>
</span>A = 12,000
P = ?
r = 0.08
n = 2 (semiannually)
t = 5
Now we plug our values in and solve:
∴ You would have to deposit $8106.77 in order to have $12,000 in 5 years from now.
(B) Find Principal Amount
Same given values as above, with the exception of 't' which is now 10 instead of 5.
∴ You would have to deposit $5476.64 in order to have $12,000 in 10 years from now.
Hope this helps!
Answer:
C
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
Here [ a, b ] = [ - 10, 10 ], thus
f(b) = f(10) = 10² + 9(10) + 18 = 100 + 90 + 18 = 208
f(a) = f(- 10) = (- 10)² + 9(- 10) + 18 = 100 - 90 + 18 = 28, thus
average rate of change = =
= 9