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IceJOKER [234]
3 years ago
6

I need a answer asap Please!!

Mathematics
1 answer:
Ganezh [65]3 years ago
7 0

Answer:

The ordered pairs (3 , 6) , (5 , 10) show a proportional relationship ⇒ last answer

Step-by-step explanation:

* Lets explain how to sole the problem

- Proportional relationship describes a simple relation between

 two variables

- In direct proportion if one variable increases, then the other variable

 increases and if one variable decreases, then the other variable

 decreases

- In inverse proportion if one variable increases, then the other variable

 decreases and if one variable decreases, then the other variable

 increases

- The ratio between the two variables is always constant

- Ex: If x and y are in direct proportion, then x = ky, where k

 is constant

 If x and y in inverse proportion, then x = k/y, where k is constant

* Lets solve the problem

# Last table

∵ x = 3 and y = 6

∴ x/y = 3/6 = 1/2

∵ x = 5 and y = 10

∴ x/y = 5/10 = 1/2

∵ 1/2 is constant

∵ x/y = constant

∴ x and y are proportion

* The ordered pairs (3 , 6) , (5 , 10) show a proportional relationship

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Find the 6th term of a geometric sequence t3 = 444 and t7 = 7104. So I have to find r. But is this right: 7104 = 444r^4 r^4 = 16
galben [10]

Third term = t3 = ar^2 = 444           eq. (1)

Seventh term = t7 = ar^6 = 7104         eq. (2)

By solving (1) and (2) we get,

              ar^2 = 444    

                => a = 444 / r^2       eq. (3)

And  ar^6 = 7104

 (444/r^2)r^6 = 7104

 444 r^4 = 7104

 r^4 = 7104/444

            = 16

 r2 = 4

 r = 2

Substitute r value in (3)

                         a = 444 / r^2

                             = 444  / 2^2

                             = 444 / 4

                              = 111

Therefore a = 111 and r = 2

Therefore t6 = ar^5

                       = 111(2)^5

                       = 111(32)

                       = 3552.

<span>Therefore the 6th term in the geometric series is 3552.</span>

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