An American football field has an area of 6.4 x 10^3 square yards. A Canadian football field is 3,350 square yards larger. What is the area of a Canadian football field? Write your answer in scientific notation to 2 decimal places.
? x 10^3 square yards
The area of a Canadian football field is 9.75 x 10^3 square yards.
To find the area of the Canadian football field, we need to add the additional 3,350 square yards to the area of the American football field.
Given that the American football field has an area of 6.4 x 10^3 square yards, we can express 3,350 in scientific notation as 3.35 x 10^3.
Now, let's add the two areas together:
6.4 x 10^3 + 3.35 x 10^3 = 9.75 x 10^3 square yards.
Therefore, the area of the Canadian football field is 9.75 x 10^3 square yards.
To find the area of the Canadian football field, we need to add 3,350 square yards to the area of the American football field.
The formula to calculate the area of a rectangle is A = l x w, where A represents the area, l represents the length, and w represents the width.
In this case, we have the area of the American football field given as 6.4 x 10^3 square yards. To determine the dimensions of the field, we need to solve the equation with respect to the width or length.
Since the problem does not provide us with the length or width explicitly, we need to make an assumption that the field is a perfect rectangle with equal dimensions. Let's assume the length and width of the American football field are both L yards.
Therefore, we can rewrite the area equation as A = L x L, which simplifies to A = L^2.
Substituting the given area of the American football field, we get (6.4 x 10^3) = L^2.
To solve for L, we take the square root of both sides of the equation: L = √(6.4 x 10^3).
Calculating the square root of 6.4 gives us 2.53, and calculating the square root of 10^3 gives us 10.00 (since the square root of 10^x is always 10^(x/2)).
Thus, L ≈ 2.53 x 10 ≈ 2.53 x 10^1 yards.
Now, to find the area of the Canadian football field, we add the given additional area of 3,350 square yards to the American football field's area: A (Canadian) = A (American) + 3,350 square yards.
Expanding the equation, we have A (Canadian) = (L + 3,350) x (L + 3,350).
Substituting the value of L we found earlier, we get A (Canadian) = (2.53 x 10^1 + 3,350) x (2.53 x 10^1 + 3,350) = (2.53 x 10^1 + 3.35 x 10^3) x (2.53 x 10^1 + 3.35 x 10^3).
Now, we can multiply the terms: A (Canadian) ≈ (2.53 x 10^1) x (2.53 x 10^1 + 3.35 x 10^3) + (3.35 x 10^3) x (2.53 x 10^1) + (3.35 x 10^3) x (3.35 x 10^3).
Calculating this equation gives us A (Canadian) ≈ 6.40 x 10^1 + 8.04 x 10^3 + 8.04 x 10^3 + 1.1225 x 10^7.
Simplifying further, we have A (Canadian) ≈ 1.608 x 10^2 + 2.245 x 10^7.
Rounding the answer to 2 decimal places, we get A (Canadian) ≈ 2.25 x 10^7 square yards.
Therefore, the area of the Canadian football field, in scientific notation to 2 decimal places, is 2.25 x 10^7 square yards.