Category: Algebra

T1 = 0.1/h(T2 – T1)
T2 = 0.1/h(T1 – T2)

y=2^x, y=3^x
the slope of the tangent line at x < 1, x > 1

the exponential function

y = e^x -> slope of the tange line is exactly 1.

e = lim n->∞(1 + 1/N)^N = 2.7
e^π = (1+ 3.1416/10,000)^10,000

(1 + x/4)^4 = 1 + x + 3/8x^2 + 1/16x^3 + 1/256x^4

e^x = 1 + x + x^2/2 + x^3/6 + x^4/24 + …
e^x+h = e^x * e^h

dy(x)/dx = -3y(x)
y(0) = 5

e = 2.71828 18284 59045 23536 02874 71352

Euler’s number & the exponential function
5^1 = 5, 5^0 = 1, 5^-2= 1/25, 5^1/2= √5, 5^3*5^4=5^7, (5^3)^4=5^12

Velocity = Derivative = Rate of Change

v(t)=dx(t)/dt = x'(t) = x(t)
x(t)=(t+1)^3

(t+h+1)^3 – (t+1)^3 /h

Newton’s Second Law of motion
Force = mass * αacceleration
V = m/s / s = m / s^2

answer = 42
radius_of_earth = 6.371e6
#test number = 43.0
#13test = 44.4

a = 3 * answer + 4
b = radius_of_earth ** 2 + (a + 3) ** 0.5
answer += 7

c = 5 / 4
d = 5 / 4.
e = 1.0 * 5 / 4

print a, b, answer, c, d, e

======================== RESTART: C:/Python27/test.py ========================
130 4.0589641e+13 49 1 1.25 1.25
>>> 

Scientific notation
16777216
-> 16,000,000

2,000,000,000,000
-> 2trillion

6.37 x 10^-3
a x 10^exponent

Label, imageView, Button

One Whole: numerator / denominator
Recipracal

repeated multiplication base^exponent
3^0 = 1
4^-1 = 1/4
4^-2 = 1/16
4^-3 = 1/56

be care for negative exponent
-(1/3)^-2

a cell divides into 4 cells after 2hours. how many cells are there after one day?
4^12 = 16777216

y = mx + b
y = -1/3x + 5

slope-intercept form

y – y1 = m(x- x1)
m -> slope, (x, y)->coordinates of the point

steepness, comparing staircases
5feet, 10feet
slope = 5/5 = 1, 10 /5 = 2, 50/15 = 10/3

slope is vertical change/horizontal change = rize / run
positive slope is uphill, negative slope is downhill

y = mx + b
m is always the slope
b is the y-value of the y-intercept

y = 3x – 7
slope:3
y-intercept:(0, -7)

charged $10 per hour to rake leaves
5hour $50
10hour $100
x hour $10x

graphing is order pair
x-intercept(3,0)
y-intercept(0, -2)

horizontal line and vertical line
(2, 0),(2, 3),(2, -3)
x=2
-> x=3

properties of linear equations
x + 3 = 4

5(x+10)-30 = 5x – 18
equation is false means “Contradiction”, no solution.

pythagorean theorem
4^2 = 16
x^2 = 25, x = 5
√64 = 8
√1 = 1

right triangle 90°
a^2 + b^2 = c^2
hypotenuse 6, 8, 10