Answer:
1176
Step-by-step explanation:
used calculator
1. A person would need to write 20 checks each month for the two banks to charge the same amount in fees.
2. The account from Bank A would cost less if a person were to write 10 checks in a month.
Explanation:
1. Bank A = 0.25x + 4, Bank B = 0.2x + 5
0.25x + 4 = 0.2x + 5
0.05x = 1
x = 20
2. Bank A = 0.25(10) + 4 = $6.5
Bank B = 0.2(10) + 5 =$7
Therefore, it would cost less to write 10 checks from Bank A.
Answer:
Solution : 6 + 6i
Step-by-step explanation:
![-3\left[\cos \left(\frac{-\pi }{4})\right+i\sin \left(\frac{-\pi }{4}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi }{2}\right)\right]](https://tex.z-dn.net/?f=-3%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%29%5Cright%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%5Cright%29%5Cright%5D%5Ccdot%20%5C%3A2%5Csqrt%7B2%7D%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B2%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B2%7D%5Cright%29%5Cright%5D)
This is the expression we have to solve for. Now normally we could directly apply trivial identities and convert this into standard complex form, but as the expression is too large, it would be easier to convert into trigonometric form first ----- ( 1 )
( Multiply both expressions )
![-6\sqrt{2}\left[\cos \left(\frac{-\pi }{4}+\frac{-\pi \:\:\:}{2}\right)+i\sin \left(\frac{-\pi \:}{4}+\frac{-\pi \:\:}{2}\right)\right]](https://tex.z-dn.net/?f=-6%5Csqrt%7B2%7D%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%2B%5Cfrac%7B-%5Cpi%20%5C%3A%5C%3A%5C%3A%7D%7B2%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%5C%3A%7D%7B4%7D%2B%5Cfrac%7B-%5Cpi%20%5C%3A%5C%3A%7D%7B2%7D%5Cright%29%5Cright%5D)
( Simplify
for both
and
)
= 
( Substitute )

Now that we have this in trigonometric form, let's convert into standard form by applying the following identities ----- ( 2 )
sin(π / 4) = √2 / 2 = cos(π / 4)
( Substitute )
=
= 
=
= 
=
- Therefore our solution is option a.