The slope of 6/2 and 6/-5 is 11/4
The two students didn’t take each bonus question because several people already had done it
Answer:
(0,0),(-4,6),(4,-6)
Step-by-step explanation:
Desmos is a helpful site for u to use for a graphing calculator. just type the expression in :)
Answer:
![y(t) = 6 -3cos(\frac{2\pi }{14} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-3cos%28%5Cfrac%7B2%5Cpi%20%7D%7B14%7D%20%29t)
![y(t) = 6 -3cos(\frac{2\pi }{7} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-3cos%28%5Cfrac%7B2%5Cpi%20%7D%7B7%7D%20%29t)
![y(t) = 6 - 6cos(\frac{2\pi }{14} ) t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-%206cos%28%5Cfrac%7B2%5Cpi%20%7D%7B14%7D%20%29%20t)
![y(t) = 3- 6cos(\frac{2\pi }{7} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%203-%206cos%28%5Cfrac%7B2%5Cpi%20%7D%7B7%7D%20%29t)
Step-by-step explanation:
Given that,
Hudson Bay tides vary between
and
.
Tide is at its lowest when ![t=0](https://tex.z-dn.net/?f=t%3D0)
Completes a full cycle in 14 hours.
To find:- What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
So, The periodic function of this model is
...................(1)
where, ![A- Amplitude of cycle](https://tex.z-dn.net/?f=A-%20Amplitude%20of%20cycle)
![\omega = Angular speed (in Radian.)](https://tex.z-dn.net/?f=%5Comega%20%3D%20Angular%20speed%20%28in%20Radian.%29)
Then putting the value in given Equation(1) we get,
Amplitude = ![\frac{9-3}{2} ft = 3ft](https://tex.z-dn.net/?f=%5Cfrac%7B9-3%7D%7B2%7D%20ft%20%3D%203ft)
![y^{'} = (3+ 3 )ft = 6ft](https://tex.z-dn.net/?f=y%5E%7B%27%7D%20%3D%20%283%2B%203%20%29ft%20%3D%206ft)
Now, At
it complete full cycle in
because it is at lowest at t=0sec.
∵ ![\omega t= 2\pi](https://tex.z-dn.net/?f=%5Comega%20t%3D%202%5Cpi)
![\omega (t+14) = 2\pi](https://tex.z-dn.net/?f=%5Comega%20%28t%2B14%29%20%3D%202%5Cpi)
∴
Hence ![y(t) = 6 -3cos(\frac{2\pi }{14} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-3cos%28%5Cfrac%7B2%5Cpi%20%7D%7B14%7D%20%29t)
![y(t) = 6 -3cos(\frac{2\pi }{7} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-3cos%28%5Cfrac%7B2%5Cpi%20%7D%7B7%7D%20%29t)
![y(t) = 6 - 6cos(\frac{2\pi }{14} ) t](https://tex.z-dn.net/?f=y%28t%29%20%3D%206%20-%206cos%28%5Cfrac%7B2%5Cpi%20%7D%7B14%7D%20%29%20t)
![y(t) = 3- 6cos(\frac{2\pi }{7} )t](https://tex.z-dn.net/?f=y%28t%29%20%3D%203-%206cos%28%5Cfrac%7B2%5Cpi%20%7D%7B7%7D%20%29t)
Roderigo will pay $7353.80 in interest.
Interest capitalization means the interest earned is added to the principle amount so first we will use compound interest formula.
<h3>
What is the formula for compound interest?</h3>
![Amount=p(1+\frac{r}{n} )^{nt}](https://tex.z-dn.net/?f=Amount%3Dp%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D)
p = 8575
r = 7.1% or 0.071
n = 12
t = 4
Putting the values in formula we get
![Amount=8575(1+\frac{0.071}{12} )^{12(4)}](https://tex.z-dn.net/?f=Amount%3D8575%281%2B%5Cfrac%7B0.071%7D%7B12%7D%20%29%5E%7B12%284%29%7D)
![Amount=8575(1+\frac{0.071}{12} )^{48}](https://tex.z-dn.net/?f=Amount%3D8575%281%2B%5Cfrac%7B0.071%7D%7B12%7D%20%29%5E%7B48%7D)
Solving this we get;
Amount = $11381.94
For the next part we have EMI formula as,
![EMI=\frac{pr(1+r)^{n} }{(1+r)^{n-1}}](https://tex.z-dn.net/?f=EMI%3D%5Cfrac%7Bpr%281%2Br%29%5E%7Bn%7D%20%7D%7B%281%2Br%29%5E%7Bn-1%7D%7D)
p = 11381.94
![r=\frac{7.1}{\frac{12}{100} }=0.005917](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B7.1%7D%7B%5Cfrac%7B12%7D%7B100%7D%20%7D%3D0.005917)
![n=(12)(10)\\n=120](https://tex.z-dn.net/?f=n%3D%2812%29%2810%29%5C%5Cn%3D120)
![EMI=\frac{11381.94(0.005979)(1+0.005979)^{120} }{(1+0.005979)^{120}-1}](https://tex.z-dn.net/?f=EMI%3D%5Cfrac%7B11381.94%280.005979%29%281%2B0.005979%29%5E%7B120%7D%20%7D%7B%281%2B0.005979%29%5E%7B120%7D-1%7D)
EMI = $132.74
Now total payments made in 120 months (10 years) =
dollars
interest paid =
dollars
Hence, Roderigo will pay $7353.80
To learn more about the interest visit:
brainly.com/question/25793394