Answer:
Step-by-step explanation:
Given that:
The investment amount in account = $ 320
The rate of interest is = 8.1% compounded quarterly
Compunded quarterly means 8.1% / 4 = 0.02025
The time period = t years
The objective is to write a function showing the value of the account after t years.
From compound interest , compounded monthly.
![Amount = Principal * ( 1 + \dfrac{rate}{12*100})^{12*time}](https://tex.z-dn.net/?f=Amount%20%3D%20Principal%20%2A%20%28%201%20%2B%20%5Cdfrac%7Brate%7D%7B12%2A100%7D%29%5E%7B12%2Atime%7D)
![= $320 *(1 + \dfrac{0.02025}{12*100})^{12t}](https://tex.z-dn.net/?f=%3D%20%24320%20%2A%281%20%2B%20%5Cdfrac%7B0.02025%7D%7B12%2A100%7D%29%5E%7B12t%7D)
![= 320*(1+ 1.6875*10^{-5})^{12t}](https://tex.z-dn.net/?f=%3D%20320%2A%281%2B%201.6875%2A10%5E%7B-5%7D%29%5E%7B12t%7D)
![= 320 * ( 1.000016875)^{12t}](https://tex.z-dn.net/?f=%3D%20320%20%2A%20%28%201.000016875%29%5E%7B12t%7D)
Thus; the function after t years ![= $320 * ( 1.000016875)^{12t}](https://tex.z-dn.net/?f=%3D%20%24320%20%2A%20%28%201.000016875%29%5E%7B12t%7D)
The percentage of growth per year is :
= (1 + 0.02025)^4 - 1
= 1.083493758 - 1
= 0.083493758
= 8.4 % (APY) yearly
Sammy is the tallest one because he is 4.667 feet tall
Answer:
29
Step-by-step explanation:
We can use the formula (a+b)(a-b)=a^2-b^2 to help us simplify this problem.
![(6-\sqrt{7})(6+\sqrt{7})\\= 6^2-(\sqrt{7})^2\\= 36-7\\=29](https://tex.z-dn.net/?f=%286-%5Csqrt%7B7%7D%29%286%2B%5Csqrt%7B7%7D%29%5C%5C%3D%206%5E2-%28%5Csqrt%7B7%7D%29%5E2%5C%5C%3D%2036-7%5C%5C%3D29)
I hope this helps! Please comment if you have any questions.
Answer:
width 5
length 7
Step-by-step explanation:
W * L = 35
L = 4 * W - 13
W * (4W-13) = 35
4 W^2 - 13 W - 35 = 0
delta = 169 + 4*4*35 = 729 = 27^2
W = (13 + 27) / 8 = 5 (its the only solution since 13 - 27 is less than 0 which makes no sense)
L = 4 * 5 - 13 = 7
Answer:
The 3 and the 2 are not the same base so you need to convert them them to the same base.
Step-by-step explanation:
I hoope this helps!