Marcos is baking a cake. He has a recipe for a large cake that calls for 6 cups of flour, 2 cups of sugar, and 1 cup of butter. Marcos only has ½ cup of sugar, so he's going to make a smaller cake. How much flour and butter should he use in his recipe?

3/2 cups of flour

1/4 cups of butter

Step-by-step explanation:

Cups of flour = 6

Cups of sugar = 2

Cup of butter = 1

Marcos only has ½ cup of sugar, so he's going to make a smaller cake.

Cups of sugar for big cake = 2

Cups of sugar for small cake = 1/2

Ratio of cups of sugar for big cake to small cake is

= 2 : 1/2

= 2 ÷ 1/2

= 2 × 2/1

= 4

This means to make smaller cake, all recipes should be divided by 4

Flour for small cake = flour for big cake / 4

= 6 / 4

= 3/2 cups of flour

= 1.33

Butter for small cake = Butter for big cake / 4

= 1 / 4 cups of butter

= 0.25

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}

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