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The smaller  gear  moves  through    (32pi)  / 3  * 1/60  =  32pi / 180  = (8/45) pi    rads /sec

And  the smaller gear  will have  the  same  linear velocity  as  the  large gear

So

12pi / 5  =  r ( 8/45) pi      multiply both sides  by  45/8....divide out pi

(45 * 12)   / (8 * 5)   =  r

540 / 40  =  r ≈  13.5  in  =    13.5 /12  =   1.125 ft

Yeah! No problem...sorry if it seemed like I was being rude or anything...

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I don't understand.

This problem was meant to show the person that the commutative property doesn't work for subtraction. If they check it themselves then they would understand it better.

Let me clear this up... the commutative property is a+b=b+a this only works for addition and multiplication.

In the problem, we'll call -56, a, and -40, b. a-b= -56 - (-40)= -56+40= -16; b-a= -40 - (-56)= -40 + 56= 16. This shows that a-b does not equal b-a.

I'm not saying there are no solutions... You said

"Commutative Property: 40-56=-16

So, we know our work is correct!"

You can't use the commutative property to show that your work is correct for subtraction. 40-56= -16 is correct, but that isn't the commutative property which I think is the source of our confusion.

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The two numbers are -56 and -40, when using a property you don't simplify -(-40) to 40 because that changes your proof.

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Edit:

Based on what you're saying, one might confuse that you just proved that the commutative property works for subtraction when in fact it doesn't.

For question 1 is says "Express your answer in simplest radical form."

Nice, HELPMEEEEEEEEEE :)

You can just add the topp numbers from the section, 0, 1, 2, 3, and 4.

One question (not trying to accuse anyone) Is this an online assignment, or assessment?

Using the commutative property, you would get (-40) - (-56)= (-40)+56= 16 proving that the commutative property does NOT work for subtraction.

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Edit:

You didn't use the commutative property correctly...

We can use Heron's formula  here

s = the semi-perimeter  =  [ 13 + 15 + 24]  / 2  =  52/ 2  = 26

The area is  given by

√ [ s (s - a) (s - b) (s - c)  ]      where a, b, c  are  the sides of the triangle

√ [ 26 ( 26 - 13) (26 - 15) (26 - 24)  ] =

√ [ 26  * 13 * 11 * 2  ] =

√ [26 * 26 * 11] =

26√11   in ^2

For this test, 50% or less means 4 or less questions correct. So the amount of people who got 4 or less questions correct is 1+7+5+3= 16 students.

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The fraction button is located ½ way past your asss and ¼ of the way to your balls.

-56 - (-40)= -56+40= -16. The commutative property states that a+b=b+a. The commutative property does NOT work for subtraction because a-b doesn't equal b-a.

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