Answer to Question #260962 in Algebra for bri

Question

(3) Showing all your working, find the solution set which describes the area shown in green below. Problem Set: D (1) State the appropriate formulae used in solving parts (i) and (ii) of this question then demonstrate the use of the formulae in finding your answers. (i) Determine how many rows are in the corner section of a stadium containing 3920 seats if the first row has 10 seats and each successive row has 6 additional seats? (ii) A new machine was purchased for $45,000. For tax purposes, the company depreciates the value by 5% annually. Determine the value of the machine after 7 years of use? 

Answer 1

a .Row 1-10seats

Row 2=16seats

Row n

$-a+(n-1)d seats\\3920$

Sn

$=\frac{n}{2}(a+(n-1)d)\\sn=3920\\a=10,d=6\\3920=\frac{n}{2}(20+(n-1)6)\\7860=n(14+6n)\\6n^2+14n-7860=0\\n=\frac{-14+\sqrt{196+4\times 6×7860}}{2×6}\\\frac{14+434}{12}\\=35$

There are 35 rows

b .

Initial price=4500

1st year=4500×0.95 due to 5% depreciation.

2nd year=4500×0.95²

7th year=45000×0.95⁷=31425.17

Price depreciated by 13575