Help me solve this proportionalequation
1 answer:
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Question 1)
Given
Interest I = $18
Principle P = $200
t = 1.5 years
To determine
Interest rate r = ?
Using the formula
susbtituting I = 18, t = 1.5 and P = 200
or
r = 6% ∵ 0.06 × 100 = 6%
Therefore, we conclude that the interest rate required to accumulate simple interest of $18.00 from a principal of $200 over 1.5 years is 6% per year.
Question 2)
Given
Interest I = $60
Principle P = $750
Interest rate = 4% = 0.04
To determine
Time period t = ?
Using the formula to calculate the time period
years
Therefore, the time required to accumulate simple interest of $ 60.00
from a principal of $ 750 at an interest rate of 4% per year is 2 years.
This can be solved a couple of ways. One way is to use the Pythagorean theorem to write equations for the magnitude from the components of the forces. That is what was done in the graph here.
Another way is to use the Law of Cosines, which lets you make direct use of the angle between the vectors.
.. 13 = a^2 +b^2 -2ab*cos(90°)
.. 19 = a^2 +b^2 -2ab*cos(120°)
Subtracting the first equation from the second, we have
.. 6 = -2ab*cos(120°)
.. ab = 6
Substituting this into the first equation, we have
.. 13 = a^2 +(6/a)^2
.. a^4 -13a^2 +36 = 0
.. (a^2 -9)(a^2 -4) = 0
.. a = ±3 or ±2
The magnitudes of the two forces are 2N and 3N, in no particular order.
Another way is to use the Law of Cosines, which lets you make direct use of the angle between the vectors.
.. 13 = a^2 +b^2 -2ab*cos(90°)
.. 19 = a^2 +b^2 -2ab*cos(120°)
Subtracting the first equation from the second, we have
.. 6 = -2ab*cos(120°)
.. ab = 6
Substituting this into the first equation, we have
.. 13 = a^2 +(6/a)^2
.. a^4 -13a^2 +36 = 0
.. (a^2 -9)(a^2 -4) = 0
.. a = ±3 or ±2
The magnitudes of the two forces are 2N and 3N, in no particular order.