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1 answer:
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Answer:
Table B
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or
<em>Verify table B</em>
For ----->
For ----->
For ----->
For ----->
The values of k are the same
therefore
The table B shows y as DIRECTLY PROPORTIONAL to x
<em>Verify table D</em>
For ----->
For ----->
For ----->
For ----->
the values of k are different
therefore
The table D not shows y as DIRECTLY PROPORTIONAL to x
Your answers are
A = 35.7°
B = 67.6°
C = 76.7°
cosine law
![a^2 = b^2 + c^2 -2bc \cos A \\ -2bc \cos A = a^2 - b^2 - c^2 \\ \\ \cos A = \dfrac{a^2 - b^2 - c^2}{-2bc} \\ \\ A = \cos^{-1}\left[ \dfrac{a^2 - b^2 - c^2}{-2bc} \right] \\ \\ A = \cos^{-1}\left[ \dfrac{12^2 - 19^2 - 20^2}{-2(19)(20)} \right] \\ \\ A = 35.723697](https://tex.z-dn.net/?f=a%5E2%20%3D%20b%5E2%20%2B%20c%5E2%20-2bc%20%5Ccos%20A%20%5C%5C%0A-2bc%20%5Ccos%20A%20%3D%20a%5E2%20-%20b%5E2%20-%20c%5E2%20%5C%5C%20%5C%5C%0A%5Ccos%20A%20%3D%20%5Cdfrac%7Ba%5E2%20-%20b%5E2%20-%20c%5E2%7D%7B-2bc%7D%20%5C%5C%20%5C%5C%0AA%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%20%5Cdfrac%7Ba%5E2%20-%20b%5E2%20-%20c%5E2%7D%7B-2bc%7D%20%5Cright%5D%20%5C%5C%20%5C%5C%0AA%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%20%5Cdfrac%7B12%5E2%20-%2019%5E2%20-%2020%5E2%7D%7B-2%2819%29%2820%29%7D%20%5Cright%5D%20%20%5C%5C%20%5C%5C%0AA%20%3D%2035.723697)
A = 35.723697
sine law for the rest of the angles
![\displaystyle \frac{\sin B}{b} = \frac{\sin A}{a} \\ \\ \sin B = \frac{b \sin A}{a} \\ \\ B = \sin^{-1} \left[ \frac{b \sin A}{a} \right] \\ \\ B = \sin^{-1} \left[ \frac{19 \sin 35.723697 }{12} \right] \\ \\ B \approx 67.58886795](https://tex.z-dn.net/?f=%5Cdisplaystyle%0A%5Cfrac%7B%5Csin%20B%7D%7Bb%7D%20%3D%20%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%20%5C%5C%20%5C%5C%0A%5Csin%20B%20%3D%20%5Cfrac%7Bb%20%5Csin%20A%7D%7Ba%7D%20%5C%5C%20%5C%5C%0AB%20%3D%20%5Csin%5E%7B-1%7D%20%5Cleft%5B%20%5Cfrac%7Bb%20%5Csin%20A%7D%7Ba%7D%20%20%5Cright%5D%20%5C%5C%20%5C%5C%0AB%20%3D%20%5Csin%5E%7B-1%7D%20%5Cleft%5B%20%5Cfrac%7B19%20%5Csin%2035.723697%20%7D%7B12%7D%20%20%5Cright%5D%20%20%5C%5C%20%5C%5C%0AB%20%5Capprox%2067.58886795)
B = 67.58886795
All angles in triangle sum to 180 so find C with that
A + B + C = 180
C = 180 - A - B
C = 180 - 35.723697 - 67.58886795
C = 76.7°
A = 35.7°
B = 67.6°
C = 76.7°
cosine law
A = 35.723697
sine law for the rest of the angles
B = 67.58886795
All angles in triangle sum to 180 so find C with that
A + B + C = 180
C = 180 - A - B
C = 180 - 35.723697 - 67.58886795
C = 76.7°
Answer:
a)
b)
The total amount accrued, principal plus interest, from compound interest on an original principal of $ 4,200.00 at a rate of 3.6% per year compounded 12 times per year over 10 years is $5667.28.
Step-by-step explanation:
a. Write the function that represents the value of the account at any time, t.
The function that represents the value of the account at any time, t
where
P represents the principal amount
r represents Annual Rate
n represents the number of compounding periods per unit t, at the end of each period
t represents the time Involve
b) What will the value be after 10 years?
Given
The principal amount P = $4200
Annual Rate r = 3.6% = 3.6/100 = 0.036
Compounded monthly = n = 12
Time Period = t
To Determine:
The total amount A = ?
Using the formula
substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 4,200.00 at a rate of 3.6% per year compounded 12 times per year over 10 years is $5667.28.