Answer:
The y-value of the vertex is 
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
where
(h,k) is the vertex of the parabola
In this problem we have
-----> this a vertical parabola open upward
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
The vertex is the point 
The y-value of the vertex is
Answer:
5
Step-by-step explanation:
Another triple integral. We're integrating over the interior of the sphere
Let's do the outer integral over z. z stays within the sphere so it goes from -2 to 2.
For the middle integral we have
x is the inner integral so at this point we conservatively say its zero. That means y goes from 
and 
Similarly the inner integral x goes between 
So we rewrite the integral
Let's work on the inner one,
There's no z in the integrand, so we treat it as a constant.
So the middle integral is
I gotta go so I'll stop here, sorry.
The is the concept of algebra, the weight of the spring can be modeled by the equation;
w=0.9sqrt E
where;
=energy in joules;
thus the weight of the spring when the energy is 12 j will be:
w=0.9sqrt12
w=3.18 g
Answer:
The first one is your answer.
Step-by-step explanation:
What you do is you have to look at the 2/18 in the square root. That can come out to be 1/3. So you know that a 3 is going to be on the bottom.
Now you look at the x^5. What you do is you make it until you have 5 x's like this x, x, x, x, x. You then put them in pairs of two.
x,x x,x x. There are two pairs of two so that comes out.
So you have 1x^2sqrtx/3. which is the first one.
#1 is your answer.
