Answer:
orientation
Step-by-step explanation:
Answer:
about 44 jumps per minute
Step-by-step explanation:
350/8=43.75
Answer:
56.35 km ≈ 56 km
Step-by-step explanation:
Conversion factor: 1 mi ≈ 1.61 km
Therefore:
![\frac{35 \textrm{ mi}}{1} \times \frac{1.61 \textrm{ km}}{1 \textrm{ mi}} = 56.35 \textrm{ km}](https://tex.z-dn.net/?f=%5Cfrac%7B35%20%5Ctextrm%7B%20mi%7D%7D%7B1%7D%20%5Ctimes%20%5Cfrac%7B1.61%20%5Ctextrm%7B%20km%7D%7D%7B1%20%5Ctextrm%7B%20mi%7D%7D%20%3D%2056.35%20%5Ctextrm%7B%20km%7D)
56.35 km ≈ 56 km
You can either use the inverse function theorem or compute the general derivative using implicit differentiation. The first method is slightly faster.
The IFT goes like this: if f(x) is invertible and f(a) = b, then finv(b) = a (where "finv" means "inverse of f").
By definition of inverse functions, we have
f(finv(x)) = finv(f(x)) = x
Differentiating both sides of the second equality with respect to x using the chain rule gives
finv'(f(x)) * f'(x) = 1
When x = a, we get
finv'(b) * f'(a) = 1
or
finv'(b) = 1/f'(a)
Now let f(x) = sin(x), which is invertible over the interval -π/2 ≤ x ≤ π/2. In the interval, we have sin(x) = √3/2 when x = π/3. We also have f'(x) = cos(x).
So we take a = π/3 and b = √3/2. Then
arcsin'(√3/2) = 1/cos(π/3) = 1/(1/2) = 2