tile Eddie decides to construct a path across his rectangular grass lawn using pairs of tiles. Each tile is 10 cm wide and 20 cm long. The following diagrams show the path after Eddie has laid one pair and three pairs of tiles. This pattern continues until Eddie reaches the other side of his lawn. When n pairs of tiles are laid, the path has a width of w, centimetres and a length 1,, centimetres. The following diagrams show this pattern for one pair of tiles and for three pairs of tiles, where the white space around each diagram represents Eddie's lawn. n=1 T W, = 20 4₁ = 30 a tile 40 diagram not to scale n=3 The following table shows the values of w, and 1, for the first three values of n. Number of pairs of tiles, n Width of lawn crossed by path, w,, (cm) 1 20 2 3 W, = 40 Length of lawn crossed by path, 1,, (cm) 30 b 50 4₂ = 50
tile Eddie decides to construct a path across his rectangular grass lawn using pairs of tiles. Each tile is 10 cm wide and 20 cm long. The following diagrams show the path after Eddie has laid one pair and three pairs of tiles. This pattern continues until Eddie reaches the other side of his lawn. When n pairs of tiles are laid, the path has a width of w, centimetres and a length 1,, centimetres. The following diagrams show this pattern for one pair of tiles and for three pairs of tiles, where the white space around each diagram represents Eddie's lawn. n=1 T W, = 20 4₁ = 30 a tile 40 diagram not to scale n=3 The following table shows the values of w, and 1, for the first three values of n. Number of pairs of tiles, n Width of lawn crossed by path, w,, (cm) 1 20 2 3 W, = 40 Length of lawn crossed by path, 1,, (cm) 30 b 50 4₂ = 50
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please answer question (f)
Transcribed Image Text:tile
Eddie decides to construct a path across his rectangular grass lawn using pairs of tiles.
Each tile is 10 cm wide and 20 cm long. The following diagrams show the path after Eddie
has laid one pair and three pairs of tiles. This pattern continues until Eddie reaches the other
side of his lawn. When n pairs of tiles are laid, the path has a width of w, centimetres and a
length 1,, centimetres.
The following diagrams show this pattern for one pair of tiles and for three pairs of tiles,
where the white space around each diagram represents Eddie's lawn.
n=1
T
W, = 20
4₁ = 30
a
tile
40
diagram not to scale
n=3
The following table shows the values of w, and 1, for the first three values of n.
Number of pairs
of tiles, n
Width of lawn crossed
by path, w,, (cm)
1
20
2
3
W, = 40
Length of lawn crossed
by path, 1,, (cm)
30
b
50
4₂ = 50
Transcribed Image Text:Find the value of
(i)
(ii)
(b) Write down an expression in terms of n for
(1)
W₁
(ii) 1₂.
Eddie's lawn has a length 740 cm.
(c) (i) Show that Eddie needs 144 tiles.
(ii)
Find the value of w, for this path.
(d) Find the total area of the tiles in Eddie's path. Give your answer in the form a × 10*
where 1 < a < 10 and k is an integer.
The tiles cost $24.50 per square metre and are sold in packs of five tiles.
(e) Find the cost of a single pack of five tiles.
To allow for breakages Eddie wants to have at least 8% more tiles than he needs.
(f) Find the minimum number of packs of tiles Eddie will need to order.
There is a fixed delivery cost of $35.
(g) Find the total cost for Eddie's order.
(a)
a.
b.
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