Ok, so remember that the derivitive of the position function is the velocty function and the derivitive of the velocity function is the accceleration function
x(t) is the positon function
so just take the derivitive of 3t/π +cos(t) twice
first derivitive is 3/π-sin(t)
2nd derivitive is -cos(t)
a(t)=-cos(t)
on the interval [π/2,5π/2) where does -cos(t)=1? or where does cos(t)=-1?
at t=π
so now plug that in for t in the position function to find the position at time t=π
x(π)=3(π)/π+cos(π)
x(π)=3-1
x(π)=2
so the position is 2
ok, that graph is the first derivitive of f(x)
the function f(x) is increaseing when the slope is positive
it is concave up when the 2nd derivitive of f(x) is positive
we are given f'(x), the derivitive of f(x)
we want to find where it is increasing AND where it is concave down
it is increasing when the derivitive is positive, so just find where the graph is positive (that's about from -2 to 4)
it is concave down when the second derivitive (aka derivitive of the first derivitive aka slope of the first derivitive) is negative
where is the slope negative?
from about x=0 to x=2
and that's in our range of being increasing
so the interval is (0,2)
Answer:
17.9 units is the answer
Step-by-step explanation:
points are (-7,-2) and (9,6)
Pythagorean theorem can be written as,
Rounding off,
d = 17.9 units
Answer:
2
Step-by-step explanation:
A commutative function means that when you insert one function in space of x in the other function, they will equal x. The equation is f(g(x)) = g(f(x)) = x
So, 2(
) - 1 = 
If you multiply both sides by <em>a</em>, you get 2<em>a</em>() - a = (2x-1)+1
Simplify it 2<em>a</em>() - <em>a</em> = 2x
Add <em>a</em> to both sides 2<em>a</em>() = 2x +<em>a</em>
The two <em>a</em>s on the left cancel out 2(x+1)=2x+<em>a</em>
Distribute the 2 2x+2=2x+<em>a</em>
Then subtract 2x from both sides 2 = <em>a</em>
Therefore, <em>a</em> = 2
Hope this helps!
Hey can you take another pic
