Answer:
Step-by-step explanation:
2 coins are 0.25 = 50 cents. That leaves 92-50 = 42 cents and 5 coins to go.
The only way to get 2 cents is to have 2 pennies. That leaves 40 cents and 3 coins to go.
The only way to get 40 cents with 3 coins is 1 quarter, 1 dime, and 1 nickel.
So you have 3 quarters = 75 cents.
2 pennies = 2 cents.
1 dime = 10 cents.
1 nickel = 5 cents.
92 cents total and 7 coins.The only way to get 40 cents
I'll explain how to do the first one:-
y = cos-1(x2)
This can be described as ' a function of a function' x^2 is a function of x and cos-1(x^2) is a function of x^2.
We need to apply the chain rule.
Personally I find this easier to understand if i let u = x^2, so
If y = f(u) and u is a function of x then
dy/dx = dy/ du * du/dx
Here u = x^2 and y = cos-1(u)
du/dx = 2x
so dy/dx = d(cos-1(x^2) dx = dy/du * du/dx
= -1 / √(1 - u^2) * 2x
= -2x / √(1 - u^2)
= -2x / √(1 - (x^2)^2)
= -2x / √(1 - x^4)
I hope this helps. but if not. you might like to employ the formulae in the question - The square boxes contain the 'u' s in my answer. These formulae are equivalent to my explanation.
