$\cos4( \theta)=Re(\cos4( \theta)+i\sin4( \theta)) \\=Re(\cos ( \theta)+i\sin ( \theta))^4 \\ =Re(cos^4( \theta)+4cos^3( \theta)isin( \theta)+6cos^2( \theta)i^2sin^2( \theta)+4cosi^3( \theta)sin^3( \theta)+i^4sin^4( \theta)) \\cos( 4\theta) =cos^4( \theta)-6cos^2( \theta)sin^2( \theta)+sin^4( \theta) \\ =(1-\sin^2( \theta))^2-6(1-\sin^2( \theta))\sin^2( \theta)+sin^4( \theta) \\ = 1-2\sin^2( \theta)+\sin^4( \theta)-6\sin^2( \theta)+6\sin^4( \theta)+\sin^4( \theta) \\ =8\sin^4( \theta)-8\sin^2( \theta)+1$

7 0

3 years ago

leyroy opened a savings account 25 years ago with a deposit of 3080.43 the account has and inerest rate of 3.7 compounded monthl

neonofarm [45]

Answer: 4,676.96

Procedure:

The formula for compounded interest is:

$factor, f=(1+r)^n$

Future value = investment * factor

Interests = future value - investment

Where r is the monthly rate, which you calculate as the % yearly rate divided by 12.

And n is the number of months which is equal to the number of years times 12.

These are the calculations:

$r=(3.7/100)/12=0.037/12=0.0030833$

$n=25*12=300$

$factor=(1+0.0030833)^{300}=2.518$

Future value = 3080.43 *2.518 = 7,757.39

Interests = 7,757.39 - 3080.43 = 4,676.96

5 0

4 years ago

Dave measures his calculator with erasers and paperclips it is about 2 eraser long

allsm [11]

Answer:

yea

Step-by-step explanation:

i dont get the question

6 0

3 years ago