ANSWER
36√3 square units.
EXPLANATION
The area of a parallelogram is obtained by multiplying the base by the height.
We use the sine ratio to obtain the height.
The area becomes:
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.
It is not too difficult. Just do this
50-15
5(10-3)
The answer is 5(10-3)
Perimeter = (2x -3y) + (x² + 7) + (2x + y)
Perimeter = 2x -3y + x² + 7 + 2x + y
Perimeter = x² + 4x - 2y + 7
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Answer: x² + 4x - 2y + 7
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F(x) = 2x² + 7x - 5
g(x) = -8x² - 3x + 5
g(x) + f(x)
-8x² - 3x + 5 + 2x² + 7x - 5
-8x² + 2x² - 3x + 7x + 5 - 5
-6x² + 4x + 0
-2x(3x - 2)
