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MA 242 Calculus III (Test 1)
NCSU calculus course taught by L. Kurtz
6
Mathematics
Undergraduate 2
01/29/2012

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Cards

Term

 

What is the formula for a sphere?

Definition

 

r2=(x-h)2+(y-k)2+(z-l)2

Term

 

Multiplying a vector by a scalar (s) affects it how?

Definition

 

It increases or decreases the magnitude by a factor of s

Term

 

What is the formula for the magnitude of a vector?

Definition

 

|v|=√(x2+y2+z2)

Term

 

How do you turn a vector into its unit vector form?

Definition

 

Divide the entire vector by the magnitude.

Term
For ever vector (except 0) there are 2 unit vectors. How?
Definition

 

They have a magnitude of 1 and -1

Term
Solving a tension problem (when tensions cancel) that holds an object up
Definition

1) T1+T2=<0,mg>

2) Find θ using trigonometry

3) Find the tension vectors in terms of |T1| or |T2|

Tx = < ±|Tx|cos(θ) , |Tx|sin(θ) >

4) Add the two vectors so that the x coordinate cancels and you can set y equal to mg and solve

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