Math

Question 1

mass

Answer 1

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

Question 2

weight

Answer 2

• 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

Question 3

gravitational acceleration, g

Answer 3

• 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

Question 4

gravitational constant, gc

Answer 4

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

Question 5

slope m

Answer 5

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

Question 6

two intersection lines

Answer 6

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

slopes of perpendicular lines
m1 = -1/m2

Question 7

general form of quadratic equation

Answer 7

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

Question 8

quadratic formula

Answer 8

x = −b ± √(b2 − 4ac) 2a

Question 9

general form of conic section equation

Answer 9

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

Question 10

normal form of conic section equation

Answer 10

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

Question 11

parabola

Answer 11

• 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)

Question 12

ellipse

Answer 12

0

Question 13

hyperbola