Acompany has a manufacturing plant that is producing quality canisters. they find that in order to produce 300 canisters in a month, it will cost $7400. also, to produce 310 canisters in a month, it will cost $7550. find an equation in the form y = mx + b, where r is the number of canisters produced in a month and y is the monthly cost to do so.
y =

Step-by-step explanation:

Given:

A company has find that in order to produce 300 canisters in a month, it will cost $7400. Also, to produce 310 canisters in a month, it will cost $7550.

Let , , , and

Find an equation in the form ------(1)

where x is the number of canisters produced in a month and y is the monthly cost to do

we know slope of line m =

Put all required value in above equation.

m =

m =

Put m value in equation 1.

For b we put and in above equation.

Put m and b value in equation 1.

Therefore, the equation is

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}

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i