When you are looking at a graph, a minimum point would be where the curve is decreasing, then begins to increase. Right at the point where it switches, the slope is a horizontal line, or 0. We can take the derivative is f(x), then look for all the x values where the slope (which is equal to the first derivative) is equal to zero.
f'(x) = 2 * -4sin(2x - pi)
The 2 comes from the derivative of the inside, 2x-pi.
So now set the derivative equal to 0.
-8sin(2x-pi) = 0
We can drop the -8 by dividing both sides by -8.
sin(2x-pi) = 0
This can be rewritten as arcsin(0) = 2x-pi
So when theta equals 0, what is the value of sin(theta)? At an angle of 0, there is just a horizontal line pointing to the right on the unit circle with length of 1. Sine is y/h, but there is no y value so it is just 0. If arcsin(0) = 0, we can now set 2x-pi = 0
2x = pi
x = pi/2
This is a critical number. To find the minimum value between 0 and pi, we need to find the y values for the endpoints and the critical number.
f(0) = -4
f(pi/2) = 4
f(pi) = -4
So the minimum points are at x=0 and x=pi
The answer is 810
23*2.5=57.5
57.5*12=690
690+120=810
Juiuiiijkkkkkkkkkkkkkkkkkk
Umm... I really dont get maths in my brain. Dont mind me though :P .
but i can sure tell u a little i know .
4x-1+2x-5+30=180 (sum of interior angles of triangle)
or, 6x+24=180
or, 6x=156
therefore, X=26 degrees
thankyou :D
Answer:
21 in
Step-by-step explanation:
by the Pythagorean theorem we have

notice that the 841 and the 400 don't go squared because they already squared!