Hello,

$u_{1} =a\\
 u_{2} =b\\
 u_{3} =a+b\\
 u_{4} =a+2b\\
 u_{5} =2a+3b\\
 u_{6} =3a+5b\\
 u_{7} =5a+8b\\
 u_{8} =8a+13b\\
 u_{9} =13a+21b\\
 u_{10} =21a+34b\\
 u_{11} =34a+55b\\
 u_{12} =55a+89b\\

\boxed{\sum_{i=1}^{12}(u_i)=144a+232b\\}




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8 0

3 years ago

Two goals post are 8m apart. A footballer is 34m from one and 38m from the other. Within what angle must he kick the ball if he

dmitriy555 [2]

Answer:

11.06°

Step-by-step explanation:

The law of cosines can be used to find the angle. The sides adjacent to that angle are a=34, b=38, and the side opposite is c=8. Then the angle is found from ...

c² = a² +b² -2ab·cos(C)

cos(C) = (a² +b² -c²)/(2ab)

C = arccos((a² +b² -c²)/(2ab))

C = arccos((34² +38² -8²)/(2·34·38)) = arccos(317/323)

C ≈ 11.06°

From the footballer's viewpoint, the goal posts are 11.06° apart.

4 0

3 years ago