Math Flashcards

1
Q

mass

A
  • quantity of matter that an object contains
  • an intrinsic and constant property of the object
  • does not vary with surroundings or location
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2
Q

weight

A
  • the quantity of force exerted on an object by gravity
  • varies with strength of gravitational field
    A pound of force (lbf) is equivalent to a pound of mass (lbm) only at sea level on earth
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3
Q

gravitational acceleration, g

A
  • used with both SI and USCS units
  • relationship between weight and mass
    g= W/m [SI]
    g= Wgc/m [USCS]

on earth surface:
g= 32.3 ft/s^2 (USCS unit)
g= 9.81 m/s^2

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4
Q

gravitational constant, gc

A
  • used only with USCS units
  • needed for conversions between pound-force (lbf) and pound-mass (lbm)
    fc= 32.2 lbm-ft/ lbt-sec^2
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5
Q

slope m

A
m= (y2-y1) / (x2-x1) 
- standard slope intercept form 
y= mx + b 
- point slope form
y-y1 = m (x-x1) 
- distance between two points 
d= square root ( x2-x1) ^2 + (y2-y1) ^2 + (x2-x1)^2
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6
Q

two intersection lines

A

angle of intersection, α
α= arctan [(m2-m1)] / ( 1+ m2 m1) ]

slopes of perpendicular lines
m1 = -1/m2

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7
Q

general form of quadratic equation

A

ax^2 + bx + c =0

  • a, b, & c are constants (a cannot = 0)
  • the roots of a quadratic equation are the values of x for which the equation is true.
  • two common ways to solve a quadratic equation (find its roots) are factoring and use of the quadratic formula
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8
Q

quadratic formula

A

x = −b ± √(b2 − 4ac) 2a

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9
Q

general form of conic section equation

A

Ax^2 + Bxy + Cy^2 + Dx + Ey + F=0
if A=C then,
–> if A=C = 0 conic section is line
–> if A=C does not equal 0, conic section is a circle

if A cannot equal C then,

  • -> if B^2 - 4AC < 0, conic section is ellipse
  • -> if B^2-4AC>0, conic section is hyperbola
  • -> if B^2-4AC = 0, conic section is parabola
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10
Q

normal form of conic section equation

A

x^ 2 + y ^2 = 2ax + 2by + c = 0

  • simpler form of general equation
  • only 3 constants, a, b, and c
  • applied when principal axis of conic section is parallel to one coordinate axis

-center of conic

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11
Q

parabola

A
  • e=1
  • general form of horizontal parabola
    (y-k)^2 = 2p (x-h) [center (h,k)]
    -general form of vertical parabola
    (x-h)^2 = 2p (y-k)
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12
Q

ellipse

A

0

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13
Q

hyperbola

A
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