Answer:
(f⁻¹)'(b) = 1/f'(f⁻¹(b)) = 1/f'(a)
Step-by-step explanation:
The function f⁻¹(x) is the reflection of the function f(x) across the line y=x. Every point (a, b) that is on the graph of f(x) is reflected to be a point (b, a) on the graph of f⁻¹(x).
Any line with slope m reflected across the line y=x will have slope 1/m. (x and y are interchanged, so m=∆y/∆x becomes ∆x/∆y=1/m) Since f'(x) is the slope of the tangent line at (x, f(x)), 1/f'(x) will be the slope of the tangent line at (f(x), x).
Replacing x with f⁻¹(x) in the above relation, you get ...
... (f⁻¹)'(x) = 1/f'(f⁻¹(x)) will be the slope at (x, f⁻¹(x))
Putting your given values in this relation, you get
... (f⁻¹)'(b) = 1/f'(f⁻¹(b)) = 1/f'(a)
Answer:
she should beat a speed of v₂ = 6.04 m/s in order to win the competition
Step-by-step explanation:
Since the momentum p is defined as
p = m*v
where
m= mass of the ball
v= velocity of the ball
denoting 1 and 2 as the first and second bowler , then to reach the momentum of the first bowler
p₂=p₁
therefore
m₁*v₁ = m₂*v₂
v₂ = v₁ * (m₁/m₂)
replacing values
v₂ = v₁ * (m₁/m₂) =8.6 m/s * (4.5 kg/6.4 kg ball) = 6.04 m/s
then since the momentum p = m*v increases with increasing v (at constant m) , she should beat a speed of v₂ = 6.04 m/s in order to win the competition
The first thing we must keep in mind is the following unit conversion:
We have then that for 35 gigabytes:
Part A:
For this case we make the following rule of three:
2000 bytes --------------> 1 page
35*10^9 bytes ----------> x
From here, we clear x:
Part B:
Then, the number of 500-page books is:
Average rate of change can be calculated by the following
Δy/Δx
Our Δx refers to displacement.
Δx = 4 - 64 = -60
Our Δy refers to our Δf(x)
To get our f(x) values, we must plug in 64 and 4 into the function f(x)
f(64) = 8√64 = 64
f(4) = 8√4 = 16
Δf(x) = 16 - 64 = -48
So our rate of change is -60/-48 = 0.8
I believe the answer should be positive 0.8, but that's my best estimate.