Hot air balloon

Hot air balloon ascends 25 meters up for a minute after launch. Every minute ascends 75 percent of the height which climbed in the previous minute.

a) how many meters ascends six minutes after takeoff?
b) what is the overall height 10 minutes after launch?
c) how long take the balloon to gain over 110 meters high?
d) what will be the final height of the balloon?

Result

a =  5.93 m
b =  94.37 m
t =  NAN min
d =  100 m

Solution:

q=75/100=0.75 Δs(t)=250.75t1 a=Δs(6)=250.7561=5.93 mq = 75/100 = 0.75 \ \\ \Delta s(t) = 25\cdot 0.75^{ t- 1} \ \\ a = \Delta s(6) = 25\cdot 0.75^{ 6- 1} = 5.93 \ \text{m}
b=s6=a1q61q1=250.75610.751=94.37 mb = s_6 = a_1 \dfrac{q^6-1}{q-1} = 25 \cdot \dfrac{ 0.75^6-1}{ 0.75-1} = 94.37 \ \text{m}
st=25qt1q1=110 qt1=110(q1)/25 qt=110(q1)/25+1 tlogq=log(110(q1)/25+1) t=NAN min s_t = 25 \dfrac{q^t-1}{q-1} = 110 \ \\ q^t-1 = 110(q-1)/ 25 \ \\ q^t = 110(q-1)/ 25 + 1 \ \\ t \log q = \log (110 \cdot (q-1)/ 25 + 1) \ \\ t = NAN \ \text{min} \ \\
d=sinf=a11q=2510.75=100 md = s_{\inf} = \dfrac{ a_1 }{ 1-q} = \dfrac{ 25 }{ 1-0.75} = 100 \ \text{m}



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Balls
    stats We have n identical balls (numbered 1-n) is selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides.
  2. Piano
    piano If Suzan practicing 10 minutes at Monday; every other day she wants to practice 2 times as much as the previous day, how many hours and minutes will have to practice on Friday?
  3. Virus
    virus We have a virus that lives one hour. Every half hour produce two child viruses. What will be the living population of the virus after 3.5 hours?
  4. Five harvests
    zrno In the seed company, they know that, out of 100 grains of a new variety, they get an average of 2000 grains after harvest. Approximately how many grains do they get out of 100 grains after five harvests?
  5. A perineum
    sequence_geo_9 A perineum string is 10% shorter than its original string. The first string is 24, what is the 9th string or term?
  6. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  7. Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  8. Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  9. Sum of series
    question Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
  10. Geometric progression
    fractal Fill 4 numbers between 4 and -12500 to form geometric progression.
  11. GP - 8 items
    fn Determine the first eight members of a geometric progression if a9=512, q=2
  12. Sequence
    mandlebrot Find the common ratio of the sequence -3, -1.5, -0.75, -0.375, -0.1875. Ratio write as decimal number rounded to tenth.
  13. The determinant
    matrix_13 The determinant of the unit matrix equals 7. Check how many rows the A matrix contains.
  14. Five members
    pst3.JPG Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a1 = 3 q = -2
  15. Tenth member
    10 Calculate the tenth member of geometric sequence when given: a1=1/2 and q=2
  16. GP members
    sequence_geo_8 The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
  17. Geometric sequence 4
    Koch_Snowflake_Triangles It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).