If five times the smaller of two numbers is subtracted from twice the larger the result is 16 if the larger is increased by three times the smaller the result is 63 by the numbers

Smaller Number = 10

Larger Number = 33

Step-by-step explanation:

Let the smaller number be "x" and the larger number be "y"

5 TIMES smaller is SUBTRACTED from TWICE larger, the result is 16, we can write:

2y - 5x = 16

and

Larger increased by 3 TIMES SMALLER, result is 63, so we can write:

y + 3x = 63

We can write this in terms of x, as:

y = 63 - 3x

Now we put this in equation 1 and solve for x first:

2y - 5x = 16

Now,

y = 63 - 3x

y = 63 - 3(10)

y = 63 - 30

y = 33

Smaller Number = 10

Larger Number = 33

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

fdvs

step-by-step explanation: vsfdvsfvd