Example Problem:
Billy goes to the nurse and she says Billy is 4 Feet 6 Inches. Billy's mom wants to know how many inches tall Billy is. How tall is Billy on Inches?
Solution:
Billy is 54 Inches tall.
=(4 × 12) + 6
=48 + 6
=54 Inches
Explanation:
You are converting the larger unit to the smaller one because you are trying to find how tall Billy is in inches and you know Billy is 4 feet 6 inches, so you need to convert 4 feet to inches.
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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:
um
Step-by-step explanation:
Answer:
D. Inno
Step-by-step explanation:
You can estimate cube roots by trying to get the two closest cube roots. Inno used √9 and √16. These two roots are the closest to √10. The cube root of √9 and √16 are 3 and 4 respectively, which means the √10 is between these two numbers, because √10 is between √9 and √16. √9 is the closest to √10, so the cube root of 10 is a number close to 3.
My english can be confusing but I tried :) Hope you understand it.
