The formula for the volume of a sphere is mc012-1.jpg. what is the formula solved for r?

The formula to calculate the radius of a sphere if we know the volume is: Cubic root [3V/(4∏)].

Solution:

The formula for the volume (V) of a sphere is:

V=(4∏/3) r^3

Solving for r: Multiplying both sides of the equation by 3/(4∏):

3/(4∏) V = 3/(4∏) [(4∏/3) r^3]

3V/(4∏) = r^3

Cubic root both sides of the equation (raising to the power 1/3):

Cubic root [3V/(4∏)] =Cubic root (r^3)

Cubic root [3V/(4∏)] = r

r = Cubic root [3V/(4∏)]

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180

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}