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:
44/12 = 11/3 = 3 2/3
Step-by-step explanation:
The recipe makes 8 pancakes.
He wants to make 12 pancakes.
First, find out how many times what he needs is compared to the recipe.
He wants 12 pancakes; the recipe makes 8 pancakes.
12/8 = 1.5
He wants to make 1.5 times the recipe.
Now multiply every ingredient amount by 1.5 to find what he needs to make 12 pancakes.
240 g of plain flour.
240 g * 1.5 = 360 g of plain flour
2 egs
2 eggs * 1.5 = 3 eggs
600 ml milk
600 ml * 1.5 = 900 ml
Answer: 360; 3; 900
Answer:
The equation of a circle is 
.
Step-by-step explanation:
-The equation of a circle is:
(where center is 
, the point 
and the radius known as 
).
-Use the center (5,-4) and the point (5,-2) for the equation:
-Solve the equation:
-After you found the radius, use the center (5, -4) and radius 2 to get the equation of a circle:
-Then, after you have the equation, the radius needs to simplified by the exponent:
If the expression needs to be full it will look like this:
(6*24)-10
If the expression needs to be simplified it will either look like:
144-10
or
134
