R represents radius or the distance between two points, the pythagorean expression will be
r² = Δx² + Δy²
Δ means the change, Δx means the change of x, Δy means the change of y
Given:
(x₁,y₁) = (-5,-1)
(x₂,y₂) = (0,2)
Input the numbers to the expression
r² = Δx² + Δy²
r² = (x₂ - x₁)² + (y₂ - y₁)²
r² = (0 + 5)² + (2 + 1)²
r² = 5² + 3²
r² = 25 + 9
r² = 34
r = √34
The distance is √34 unit length
Answer:
the average rate of change rc is 13 , 12.1 and 12.01 for h=1 , 0.1 and 0.01 respectively
Step-by-step explanation:
for
R(t) = 30*t − 3*t² ; t = 3
the average rate of change of R(t) over the time interval [t, t + h] is
rc= [R(t+h)-R(t)] / [(t+h) -t) = [R(t+h)-R(t)] /h = 1/h * [ 30*(t+h) − 3*(t+h)² - ( 30*t − 3*t² ) ] = (1/h) * ( 30*h - (3*t² + 6*t*h + t²) +3*t² ) = 30 - 6*t + h
then
rc= 30 - 6*t + h
for t=3 and h=1
rc= 30 - 6*3 + 1 = 13
for t=3 and h=0.1
rc= 30 - 6*3 + 0.1 = 12.1
for t=3 and h=0.01
rc= 30 - 6*3 + 0.01 = 12.01
for t=3 and h=0.001
rc= 30 - 6*3 + 0.01 = 12.001
when h goes smaller , the average rate of change gets closer to the instantaneous rate of change of R(t) in t=3 (the derivative of R in t=3) , that is
R'(t)= 30 - 6*t
Let y=f(x)
y=sqrt(10-3x)
you want to make x the subject
square both sides
y²=10-3x
3x=10-y²
x=(10-y²)/3
now replace y with x
f^-1(x)=(10-x²)/3
Answer:
24
Step-by-step explanation:
