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
Answer:
<u>I will take around 1 year and 8 months to earn $ 45 of interest on this investment</u>
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Interest earned = $ 45
Investment = $ 790
Annual simple interest rate = 3.4% = 0.034
2. How much time would it take to earn $45?
Let's recall the formula for calculating the simple interest of an investment:
A = P * (1 + rt)
Replacing with the values we already have:
835 = 790 + (1 + 0.034t).
Where t is the time we want to calculate
835 = 790 + 26.86t
26.86t = 835 - 790
26.86t = 45
t = 1.68 (Rounding to the next hundredth)
<u>t ≅ 1 year and 8 months</u>
Answer:
16
Step-by-step explanation:
If one side of a square is 4 cm then all sides are 4 cm which means that both the base and the height is 4 cm, so you multiply 4 by 4 which gives you 16
Use the distance formula.
The distance, d, between points
and
is given by the distance formula below.
Now we can apply the formula to your points.
Let Point 1 be (2, 3) and Point 2 be (5, -4).
Then you have
Answer: the distance is sqrt(58)
Answer:
Here you go! :]
Step-by-step explanation: