A monument outside city hall has dimensions as shown below in the figure. If one gallon of paint can cover 213 ft^2, how many ga
llons of paint must be bought in order to paint the monument? Assume that the base of the monument cannot be painted and that paint can be bought only by the gallon.
1 answer:
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Part A
The pattern of squares is 1, 4, 9, ... which is the set of perfect squares
- 1 = 1^2
- 4 = 2^2
- 9 = 3^2
and so on
The 7th figure will have 49 squares because 7^2 = 49
<h3>Answer: 49</h3>==============================================================
Part B
Each pattern has one circle per corner (4 circles so far). In addition, there's one circle per unit side to form the perimeter.
- Pattern 1 has 4+4(1) = 8 circles
- Pattern 2 has 4+4(2) = 12 circles
- Pattern 3 has 4+4(3) = 16 circles
The nth term will have 4+4n circles. The first '4' is the number of circles at the corners. The 4n is the circles along the perimeter. If you wanted, 4+4n factors to 4(1+n).
Plug in n = 20 to find the 20th figure has 4+4n = 4+4(20) = 84 circles
<h3>Answer: 84</h3>==============================================================
Part C
- Pattern 1 has 1 square + 8 circles = 9 items total
- Pattern 2 has 4 squares + 12 circles = 16 items total
- Pattern 3 has 9 squares + 16 circles = 25 items total
This seems to suggest if the pattern number is odd, then we need an odd number of tiles (square + circular).
Let n be the pattern number. Pattern n needs n^2 square tiles and 4+4n = 4n+4 circular tiles. Overall, n^2+4n+4 tiles are needed.
It turns out that if n is odd, then n^2+4n+4 is always odd. The proof is shown below.
Side note: n^2+4n+4 factors to (n+2)^2
<h3>Answer: B) will always be odd</h3>
For this case we have:
x: Number of candies that Sydney has
The equation to find the amount of Sydney sweets is given by:
We want to clear x:
So, Sydney has 10 candies
Answer:
Sydney has 10 candies