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
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
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
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
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
6
Q
two intersection lines
A
angle of intersection, α
α= arctan [(m2-m1)] / ( 1+ m2 m1) ]
slopes of perpendicular lines
m1 = -1/m2
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
8
Q
quadratic formula
A
x = −b ± √(b2 − 4ac) 2a
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
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
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)
12
Q
ellipse
A
0
13
Q
hyperbola
A