Volume=(pi)(radius^2)(height)
Volume=(pi)(5^2)(12)
V=(pi)(25)(12)
V=(pi)(300)
The last side would be 10
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: 8 inches
Step-by-step explanation: So you know that to get the circumference of a circle is 2πr, right? So you divide 16 by 2 to get your radius. So that's how you 8 inches.
Answer:
Angle BCD is 13 degrees
Step-by-step explanation:
Here, we want to find the measure of angle BCD
To get this, we need an appropriate diagram. The diagram can be seen in the attachment.
To find the value of BCD, we can use an important triangle theorem.
This is that the sum of opposite interior angles of a triangle equals the exterior angle.
Thus, we have that;
BCD + DBC = CDE
hence;
3x + 5 + 2x + 3 = 9x-12
5x + 8 = 9x -12
9x-5x = 8 + 12
4x = 20
x = 20/4
x = 5
So the measure of BCD will be 2(5) + 3 = 10 + 3 = 13
