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Given A = k(B2/C2), solve for A and percentage change in A under specified conditions.
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2 partsStep-by-step solution
5 stepsHere's the solution to question 3, parts i) and ii):
From the previous question, the relationship between A, B, and C is:
Part i· 2 steps
Given that when A=20, B=5 and C=9. Find A when B=7 and C=25.
Find the constant using the initial values .
Substitute these values into the equation:
To solve for , multiply both sides by :
Use the value of to find when and .
Substitute , , and into the equation:
Rounding to a reasonable number of decimal places, for example, two:
The value of A when B=7 and C=25 is .
Part ii
If B is increased by 20% and C decreased by 36%, find the percentage change in A.
Express the new values of B and C in terms of their original values.
Let the original values be and .
If B is increased by 20%, the new value is:If C is decreased by 36%, the new value is:
Write the original and new expressions for A.
Original A ():
New A ():
Substitute and into the equation for :
Recognize that is :
Calculate the percentage change in A.
Percentage change =
Rounding to two decimal places:
The percentage change in A is an increase of .
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