Charlie is watching hot air balloons. Balloon A has risen at a 50° angle. Balloon B has risen at a 78° angle. If the distance from balloon A to the ground is 1,000 feet, how far is balloon B from balloon A? Round your answer to the nearest whole number. Two points labeled Balloon A and Balloon B are connected to a point labeled Charlie, which is on a straight line labeled Ground. A dashed line connects point Balloon A to line Ground; another dashed line connects point Balloon B to line Ground; both dashed lines form a right angle with line Ground; the angle formed from point Balloon A, point Charlie, and line Ground measures x degrees; and the angle formed by point Balloon B, point Charlie, and line Ground measures y degrees. 999 feet 1,005 feet 1,052 feet 1,102 feet

1st answer is d, 2nd answer is d ,3rd answer is d, 4th answer is c,5th answer is c and 6th answer is c

Step-by-step explanation:

        we get the series 2,4,8,16

        The general term for first difference GP we have an=c×2∧n+d

        by  putting n=1 we get 5=2c+d and by n=2 we get 7=4c+d

        By solving the two equations we get c=1 and d=3

         an=2∧n+3

    2. tn+1= -1×tn+3

        By analysis the option we get tn=4 then we tn+1=-1  so only d option

       satisfy the condition rest options don't satisfy so answer is option d                    

    3. Given t1=5 and the condition is given that tn+1=3×tn

        putting n=1 we get t2=3×t1  

      ∵By substituting we get t2=3×5=15

   4. The sequence is given as 8,11,14,17,20,23,26

       This is an A.P. so the general term of A.P. is given as tn=t(n-1)+d

       where t(n-1)is the previous  term and d is the common difference which

       is equal to 3 in this case

       ∵The answer is tn=t(n-1)+3

   5.The sequence is given as 5,8,11,14,17 we have to find

       the 43rd term of the sequence  

       The given sequence is an A.P.

       ∵The general term is an=a+(n-1)d where a is the first term and d be

       the common difference which is equal to 3 in this case

       We have to find the 43rd term so n=43

       By substituting in the given equation we get a43=5+(43-1)×3=129

       ∴The 43rd term of the given sequence is equal to  129

  6. When we count the boxes we get that they follow a pattern given as

      1,5,9,13 This follow an series of A.P.

      ∵ The general term is an=a+(n-1)d where a is the first term and d be the      

      common difference which is equal to 4 in this case

       we have to find the number of boxes in 10th step of pattern so n=10 for        

        case a10=1+(10-1)×4=37

      ∴The number of boxes in the 10th step is 37