Answer:
Step-by-step explanation:
A) The dealer bought Birr 8000 at 7% tax.
Total amount to be paid = cost price (1 + r%)
r = 7% = 0.07
Total amount to be paid
B) To find the VAT, it is the difference between the tax paid when the good was bought and the tax put on it after it was sold.
Tax paid when the shoes were bought = 7% of cost price
Tax paid when the shoes were sold = 9% of selling price
VAT = tax recovered on sale - Tax paid on purchase
Answer:
4733
Step-by-step explanation:
Please refer to the attached diagram.
Point A can be assigned x-coordinate "p". Then its y-coordinate is 6p^2. The slope at that point is y'(p) = 12p.
Point B can be assigned x-coordinate "r". Then its y-coordinate is 6r^2. The slope at that point is y'(r) = 12r.
We want the slopes at those points to have a product of -1 (so the tangents are perpendicular). This means ...
(12p)(12r) = -1
r = -1/(144p)
The slope of line AB in the diagram is the ratio of the differences of y- and x-coordinates:
slope AB = (ry -py)/(rx -px) = (6r^2 -6p^2)/(r -p) = 6(r+p) . . . . simplified
The slope of AB is also the tangent of the sum of these angles: the angle AC makes with the x-axis and angle CAB. The tangent of a sum of angles is given by ...
tan(α+β) = (tan(α) +tan(β))/1 -tan(α)·tan(β))
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Of course the slope of a line is equal to the tangent of the angle it makes with the x-axis. The tangent of angle CAB is 2 (because the aspect ratio of the rectangle is 2). This means we can write ...
slope AB = ((slope AC) +2)/(1 -(slope AC)(2))
So, now we can figure the coordinates of points A and B, and the distance between them. That distance is given by the Pythagorean theorem as ...
d^2 = (6r^2 -6p^2)^2 +(r -p)^2
d^2 = (6(1/6)^2 -6(-1/24)^2)^2 +(1/6 +1/24)^2 = 25/1024 +25/576 = 625/9216
Because of the aspect ratio of the rectangle, the area is 2/5 of this value, so we have ...
Rectangle Area = (2/5)(625/9216) = 125/4608 = a/b
Then a+b = 125 +4608 = 4733.
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<em>Comment on the solution</em>
The point of intersection of the tangent lines is a fairly messy expression, and that propagates through any distance formulas used to find rectangle side lengths. This seemed much cleaner, though maybe not so obvious at first.
