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alexandr1967 [171]
3 years ago
15

Identify the 19th term of a geometric sequence where a1 = 14 and a9 = 358.80. Round the common ratio and 19th term to the neares

t hundredth.
a. a19 ≈ 9,195.53
b. a19 ≈ 31,035.73
c. a19 ≈ 13,185.66
d. a19 ≈ 20,690.
Mathematics
2 answers:
Molodets [167]3 years ago
6 0
The formula of geometric sequence is expressed in the following manner:
an = a1 * r^(n-1) where r is the ratio and n is an integer.
Substituting, to find r
358.80 = <span>14 * r^(8) 
r is equal to 1.5

hence, 
</span><span>a19 = 14* 1.5^(19-1)
</span>a19 <span> ≈ 20,690.</span>

Yuri [45]3 years ago
4 0

Answer:

D

Step-by-step explanation:

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Ben, Tim, and Sam have to do a certain job. Ben can finish the job in 5 hours. Tim can finish the job in 6 hours. Sam can finish
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x is 7.5 hours

Step-by-step explanation:

Ben, Tim, and Sam have to do a certain job

  • Ben can finish the job in 5 hours
  • Tim can finish the job in 6 hours
  • Sam can finish the job in x hours
  • The three of them can finish the job in 2 hours if they work together

We need to find x

∵ Ben can finish the job in 5 hours

∴ The rate of Ben = \frac{1}{5}

∵ Tim can finish the job in 6 hours

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∴ The rate of Sam = \frac{1}{x}

They will working together to finish the job in two hours, that means the sum of their rate is equal to 1/2

∵ They can finish the job in 2 hours if they work together

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To add the fractions find the LCM for all denominators to make all fractions with same denominators

∵ The LCM of 5, 6 ans x is (5 × 6 × x) = 30 x,

- Divide it by each denominator to find the new numerators

∵ 30 x ÷ 5 = 6 x , 30 x ÷ 6 = 5 x , 30 x ÷ x = 30

- Change all the denominators to 30 x and then write the new

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∴ \frac{6x}{30x}+\frac{5x}{30x}+\frac{30}{30x}=\frac{1}{2}

Add the numerators and put the sum over 30 x

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- By using cross multiplication

∴ 2(11 x + 30) = 1(30 x)

- Simplify the both sides

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- Subtract 22 x from both sides

∴ 60 = 8 x

- Divide both sides by 8

∴ 7.5 = x

∴ The value of x is 7.5 hours

x is 7.5 hours

Learn more:

You can learn more about the word problems in brainly.com/question/10712420

#LearnwithBrainly

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