Answer:
subject?
Step-by-step explanation:
The total amount is $ 1015.82 and interest amount is $ 165.82
<em><u>Solution:</u></em>
<em><u>The formula for amount when interest is compounded annually is:</u></em>
![\mathrm{A}=P\left(1+r}\right)^{n}](https://tex.z-dn.net/?f=%5Cmathrm%7BA%7D%3DP%5Cleft%281%2Br%7D%5Cright%29%5E%7Bn%7D)
Where,
"A" is the total amount
"P" is the principal
"r" is the rate of interest in decimal form
"n" is the number of years
<em><u>From given, $850 at 2% for 9 years, compounded annually</u></em>
P = 850
t = 9 years
![r = 2 \% = \frac{2}{100} = 0.02](https://tex.z-dn.net/?f=r%20%3D%202%20%5C%25%20%3D%20%5Cfrac%7B2%7D%7B100%7D%20%3D%200.02)
<em><u>Substituting the given values we get,</u></em>
![A = 850(1+0.02)^9\\\\A = 850 \times 1.02^9\\\\A = 850 \times 1.1950\\\\A = 1015.82](https://tex.z-dn.net/?f=A%20%3D%20850%281%2B0.02%29%5E9%5C%5C%5C%5CA%20%3D%20850%20%5Ctimes%201.02%5E9%5C%5C%5C%5CA%20%3D%20850%20%5Ctimes%201.1950%5C%5C%5C%5CA%20%3D%201015.82)
Thus total amount is $ 1015.82
Interest amount = Total amount - principal
Interest amount = 1015.82 - 850
Interest amount = 165.82
Thus total amount earned is $ 1015.82 and interest amount is $ 165.82
In a tangent segment, no part of it is in the interior of the circle. with a secant, there is a part in the interior called the chord. hope it helps
if you need help with anything else just ask me
Answer:
Arc length ![=\int_0^{\pi} \sqrt{1+[(4.5sin(4.5x))]^2}\ dx](https://tex.z-dn.net/?f=%3D%5Cint_0%5E%7B%5Cpi%7D%20%5Csqrt%7B1%2B%5B%284.5sin%284.5x%29%29%5D%5E2%7D%5C%20dx)
Arc length ![=9.75053](https://tex.z-dn.net/?f=%3D9.75053)
Step-by-step explanation:
The arc length of the curve is given by ![\int_a^b \sqrt{1+[f'(x)]^2}\ dx](https://tex.z-dn.net/?f=%5Cint_a%5Eb%20%5Csqrt%7B1%2B%5Bf%27%28x%29%5D%5E2%7D%5C%20dx)
Here,
interval ![[0, \pi]](https://tex.z-dn.net/?f=%5B0%2C%20%5Cpi%5D)
Now, ![f'(x)=\frac{\mathrm{d} }{\mathrm{d} x} \int_0^{4.5x}sin(t) \ dt](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B%5Cmathrm%7Bd%7D%20%7D%7B%5Cmathrm%7Bd%7D%20x%7D%20%5Cint_0%5E%7B4.5x%7Dsin%28t%29%20%5C%20dt)
![f'(x)=\frac{\mathrm{d} }{\mathrm{d} x}\left ( [-cos(t)]_0^{4.5x} \right )](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B%5Cmathrm%7Bd%7D%20%7D%7B%5Cmathrm%7Bd%7D%20x%7D%5Cleft%20%28%20%5B-cos%28t%29%5D_0%5E%7B4.5x%7D%20%5Cright%20%29)
![f'(x)=\frac{\mathrm{d} }{\mathrm{d} x}\left ( -cos(4.5x)+1 \right )](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B%5Cmathrm%7Bd%7D%20%7D%7B%5Cmathrm%7Bd%7D%20x%7D%5Cleft%20%28%20-cos%284.5x%29%2B1%20%5Cright%20%29)
![f'(x)=4.5sin(4.5x)](https://tex.z-dn.net/?f=f%27%28x%29%3D4.5sin%284.5x%29)
Now, the arc length is ![\int_0^{\pi} \sqrt{1+[f'(x)]^2}\ dx](https://tex.z-dn.net/?f=%5Cint_0%5E%7B%5Cpi%7D%20%5Csqrt%7B1%2B%5Bf%27%28x%29%5D%5E2%7D%5C%20dx)
![\int_0^{\pi} \sqrt{1+[(4.5sin(4.5x))]^2}\ dx](https://tex.z-dn.net/?f=%5Cint_0%5E%7B%5Cpi%7D%20%5Csqrt%7B1%2B%5B%284.5sin%284.5x%29%29%5D%5E2%7D%5C%20dx)
After solving, Arc length ![=9.75053](https://tex.z-dn.net/?f=%3D9.75053)
16•10=(10+6)•10
=(160•10)+(160•10)
=1600+1600
=320000