Answer:
The amount in the account after six years is $2,288.98
Step-by-step explanation:
In this question, we are asked to calculate the amount that will be in an account that has a principal that is compounded quarterly.
To calculate this amount, we use the formula below
A = P(1+r/n)^nt
Where P is the amount deposited which is $1,750
r is the rate which is 4.5% = 4.5/100 = 0.045
t is the number of years which is 6 years
n is the number of times per year, the interest is compounded which is 4(quarterly means every 3 months)
we plug these values into the equation
A = 1750( 1 + 0.045/4)^(4 * 6)
A = 1750( 1 + 0.01125)^24
A = 1750( 1.01125)^24
A = 2,288.98
The amount in the account after 6 years is $2,288.98
Answer:
![\cos (a-b)=\cos a \cos b+\sin a \sin b](https://tex.z-dn.net/?f=%5Ccos%20%28a-b%29%3D%5Ccos%20a%20%5Ccos%20b%2B%5Csin%20a%20%5Csin%20b)
Step-by-step explanation:
Given : ![\cos (180^{\circ}-q)=-\cos q](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D-%5Ccos%20q)
We have to write which identity we will use to prove the given statement.
Consider ![\cos (180^{\circ}-q)=-\cos q](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D-%5Ccos%20q)
Take left hand side of given expression ![\cos (180^{\circ}-q)](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29)
We know
![\cos (a-b)=\cos a \cos b+\sin a \sin b](https://tex.z-dn.net/?f=%5Ccos%20%28a-b%29%3D%5Ccos%20a%20%5Ccos%20b%2B%5Csin%20a%20%5Csin%20b)
Comparing , we get, a= 180° and b = q
Substitute , we get,
![\cos (180^{\circ}-q)=\cos 180^{\circ} \cos (q)+\sin q \sin 180^{\circ}](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D%5Ccos%20180%5E%7B%5Ccirc%7D%20%20%5Ccos%20%28q%29%2B%5Csin%20q%20%5Csin%20180%5E%7B%5Ccirc%7D)
Also, we know
and ![\cos 180^{\circ}=-1](https://tex.z-dn.net/?f=%5Ccos%20180%5E%7B%5Ccirc%7D%3D-1)
Substitute, we get,
![\cos (180^{\circ}-q)=-1\cdot \cos (q)+\sin q \cdot 0](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D-1%5Ccdot%20%5Ccos%20%28q%29%2B%5Csin%20q%20%5Ccdot%200)
Simplify , we get,
![\cos (180^{\circ}-q)=-\cos (q)](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D-%5Ccos%20%28q%29)
Hence, use difference identity to prove the given result.
Answer:
No Solution
Step-by-step explanation:
if one side is 4, another side -8z and +8z cancels, left -7
4 ≠ -7
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