The tank can hold 31.8 gallons of water.
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.
Answer:
Option D. h(2) = 16
Step-by-step explanation:
Verify each statement
case A) h(8) = 21
The statement is false
Because
we know that
h(8)=19 -----> given value
and
If h(8) = 21 then f(x) is not a function
case B) h(13) = 18
The statement is false
Because x=13 not belong to the domain of the function
case C) h(-3) = -1
The statement is false
Because
x=-3 belong to the domain
but
h(-3)=-1 not belong to the range of the function
case D) h(2) = 16
The statement could be true
Because
x=2 ----> belong to the domain of the function
h(2)=16 ----> belong to the range of the function