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:
28, 29, and 30
Step-by-step explanation:
There's probably better ways but you can estimate by knowing 30*3=90 so it should be somewhere pretty close to 30. Guess and check with basic calculations to get 28, 29, and 30.
Answer:
24 ft
Step-by-step explanation:
Hypotenuse = √9²+16²=√81+256=√400=20ft
the upper side of the stuff = 4 ft
total = 20+4=24
Answer:
96 inches
Step-by-step explanation:
We can write a proportion to solve
60 inches x inches
--------------- = -------------
5 ft 8 ft
Using cross products
60 *8 = 5x
480 = 5x
Divide by 5
480/5 = 5x/5
96 = x
96 inches
1,2,3,5,6,10,15,30 because by looking at the number at the ones place, when it is 0 or an odd number, it could be divided by 2. When the places are added together and when it is divisible by 3, it is the factor of 3. Also, when there are 2 and 3 as a factor, it is also divisible by 6.
