1) A swimming pool has the shape of a rectangular prism and a volume of 2100 m^3. The dimensions of the pool are x metres deep by 25x metres long by 10x + 1 metres wide. What are the actual dimensions of the pool?
Here's what I did:
(25X)(X)(10X+1)
(25x^2)(10x+1)
= 250x^3 + 2x^2 - 2100
25(10x^3 + x^2 - 84)
25(10x^2 + 21x + 42)(x-3) But I cannot factor the quadratic to get the dimensions!
2) A boardwalk that is x feet wide is built around a rectangular pond. The pond is 30 ft wide and 40 ft long. The combined surface are of the pond and the boardwalk is 2000 ft^2. What is the width of the boardwalk?
3) A monument consists of two cubical blocks of limestone. the smaller block rests on the larger. the total height of the monument is 5 m and the area of expose surface is 61 m^2. determine the dimensions of the blocks.
Please help!! I keep getting these 3 questions wrong no matter what
Here's what I did:
(25X)(X)(10X+1)
(25x^2)(10x+1)
= 250x^3 + 2x^2 - 2100
25(10x^3 + x^2 - 84)
25(10x^2 + 21x + 42)(x-3) But I cannot factor the quadratic to get the dimensions!
2) A boardwalk that is x feet wide is built around a rectangular pond. The pond is 30 ft wide and 40 ft long. The combined surface are of the pond and the boardwalk is 2000 ft^2. What is the width of the boardwalk?
3) A monument consists of two cubical blocks of limestone. the smaller block rests on the larger. the total height of the monument is 5 m and the area of expose surface is 61 m^2. determine the dimensions of the blocks.
Please help!! I keep getting these 3 questions wrong no matter what
-
x(25x)(10x + 1) = 2100
=> 250x³ + 25x² = 2100
so, 250x³ + 25x² - 2100 = 0
=> 10x³ + x² - 84 = 0
When x = 2, 10x³ + x² - 84 = 0....so, x - 2 is a factor
so, 10x³ + x² - 84 = (x - 2)(10x² + bx + 42)
=> 1 = b - 20
i.e. b = 21
Therefore, 10x³ + x² - 84 = (x - 2)(10x² + 21x + 42) = 0
x = 2 is the only solution as none exist for 10x² + 21x + 42 = 0
so, the pool measures 2 metres by 50 metres by 21 metres
:)>
=> 250x³ + 25x² = 2100
so, 250x³ + 25x² - 2100 = 0
=> 10x³ + x² - 84 = 0
When x = 2, 10x³ + x² - 84 = 0....so, x - 2 is a factor
so, 10x³ + x² - 84 = (x - 2)(10x² + bx + 42)
=> 1 = b - 20
i.e. b = 21
Therefore, 10x³ + x² - 84 = (x - 2)(10x² + 21x + 42) = 0
x = 2 is the only solution as none exist for 10x² + 21x + 42 = 0
so, the pool measures 2 metres by 50 metres by 21 metres
:)>
-
The dimensions given in the original problem specify that the pool is
x by 25x by 10x + 1
When x = 2, its dimensions are
2 x 50 x 21
LOL! You've spent too long on these.
x by 25x by 10x + 1
When x = 2, its dimensions are
2 x 50 x 21
LOL! You've spent too long on these.