To find the straight-line distance David is from his car after walking 262626 yards north and 202020 yards east, we can use the Pythagorean theorem. The northward distance and eastward distance form the two legs of a right triangle, with the straight-line distance back to his car being the hypotenuse.
Let's denote:
- \( a = 262626 \) yards (northward distance)
- \( b = 202020 \) yards (eastward distance)
- \( c \) = the straight-line distance from the car
Using the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
Substituting the values:
\[ c = \sqrt{(262626)^2 + (202020)^2} \]
Now calculate each square:
\[ (262626)^2 = 69192227976 \] \[ (202020)^2 = 40808040400 \]
Now sum them:
\[ 69192227976 + 40808040400 = 110600368176 \]
Next, take the square root:
\[ c = \sqrt{110600368176} \approx 10514.7 \text{ yards} \]
Finally, rounding to the nearest tenth, David is approximately:
\[ \boxed{10514.7} \text{ yards} \]
from his car.
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