Answer:
The measure of the angles are 72 degrees and 18 degrees
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
Let
x -----> the measure of an angle
y-----> the measure of he other angle
we know that
x+y=90 -----> y=90-x -----> equation A
x=y+54 ----> equation B
substitute equation B in equation A and solve for y
y=90-(y+54)
y=90-y-54
2y=36
y=18°
Find the value of x
x=y+54 -----> x=18+54=72°
therefore
The measure of the angles are 72 degrees and 18 degrees
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:
4.8x + 0.5
Step-by-step explanation:
Both solutions:
x = -1, -7/3
4 Americans can arrange themselves in 4! ways.similarly ,3 Frenchmen can arrange themselves in 3! ways.3 Englishmen can arrange themselves in 3! ways.now these 3 groups of same nationality people can be arranged among themselves in 3! ways.so total number of ways = 3!4!3!3!
