Please someone help me!

12000 rad/min

Step-by-step explanation:

One formula we can use here is that the linear speed is the same, and the linear speed is equal to the angular speed multiplied by the radius.

Therefore, 2400π rad/min* 35 cm = 7 cm* x, with x representing the angular speed of the smaller wheel in radians per minutes. Dividing both sides by 7 cm, we get

2400π rad/min * 35 cm / 7 cm = x

2400 π rad/min * 5 = 12000 rad/min = x as our answer

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.