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3 years ago

Please Help! Will mark brainiliest!! 1. y varies directly as x and inversely as z.

Mathematics

1 answer:

Paladinen [302]3 years ago

8 0

Answer:

x = 5

z =2

y =4.4

Step-by-step explanation:

y varies directly as x

y = kx

and inversely as z

y = kx/z

Putting in the numbers in the first line of the table, we can solve for k

13.75 = k * 25/4

Multiply by 4

13.75*4 = 25k

55 =25k

Divide by 25

55/25 = 25k/25

2.2 = k

Now we can fill in the table

y = 2.2 x/z

Row 2 we need to find x

1 = 2.2 x/11

Multiply by 11

11 = 2.2 x

Divide by 2.2

11/2.2 = 2.2x

5 =x

Row 3 we need to find z

18.7 = 2.2 *17/z

18.7 = 37.4 /z

Multiply by z

18.7z = 37.4

Divide by 18.7

18.7/18.7z = 37.4/18.8

z =2

Row 4 we need to find y

y = 2.2 *10/5

y = 22/5

y =4.4

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The question is in the image below.

sineoko [7]

Answer:

The Recursive Formula for the sequence is:

$\:a_n=\frac{1}{5}\left(a_{n-1}\right)$ ; a₁ = 125

Hence, option D is correct.

Step-by-step explanation:

We know that a geometric sequence has a constant ratio 'r'.

The formula for the nth term of the geometric sequence is

$a_n=a_1\cdot r^{n-1}$

where

aₙ is the nth term of the sequence

a₁ is the first term of the sequence

r is the common ratio

We are given the explicit formula for the geometric sequence such as:

$a_n=125\left(\frac{1}{5}\right)^{n-1}$

comparing with the nth term of the sequence, we get

a₁ = 125

r = 1/5

Recursive Formula:

We already know that

a₁ = 125

r = 1/5

We know that each successive term in the geometric sequence is 'r' times the previous term where 'r' is the common ratio.

i.e.

$a_n=ra_{n-1}$

Thus, substituting r = 1/5

$\:a_n=\frac{1}{5}\left(a_{n-1}\right)$

and a₁ = 125.

Therefore, the Recursive Formula for the sequence is:

$\:a_n=\frac{1}{5}\left(a_{n-1}\right)$ ; a₁ = 125

Hence, option D is correct.

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