What are some real-life situations in which you can use circumference and
area of a circle?

The circumference and area of a circle can be used in real-life situations such as;

How large a circular disk is cam be determined by evaluating it's area.

Additionally, the circumference of car wheel provides a measure of the distance it is able to cover in one cycle.

The area of a closed cylindrical can only be evaluated when the area of the top and bottom circle is known.

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Estimating the wood in a tree, it may be more convenient to measure its circumference to estimate the volume than directly measuring the tree's diameter. Take your height and divide it by your circumference at the waist.

The wheel of a bicycle.

Coin.

Dinner plate.

Wall clock.

Ferris wheels

Finding the volume and surface area of a cylinder: A cylinder is a 3D object with two circular faces and one curved surface. ...

Surface area and volume of a cone: Cone is another very important three dimensional shape and students need to know how to find its surface area and volume.

Step-by-step explanation:

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}