Answer: For 10 sessions, the cost of the two plans the same.
Step-by-step explanation:
Let x= Number of sessions.
Given: Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.
Total charge for x sessions = 50+30x
Nicole's fitness center charges a yearly fee of $250 plus $10 for each session with a trainer.
Total charge for x sessions = 250+10x
When both plan charges the same, then
i.e. For 10 sessions, the cost of the two plans the same.
Answer:
the rate of change of the water depth when the water depth is 10 ft is;
Step-by-step explanation:
Given that:
the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.
We are meant to find the rate of change of the water depth when the water depth is 10 ft.
The diagrammatic expression below clearly interprets the question.
From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t
Then the similar triangles ΔOCD and ΔOAB is as follows:
( similar triangle property)
h = 2.5r
The volume of the water in the tank is represented by the equation:
The rate of change of the water depth is :
Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec
Then,
Therefore,
the rate of change of the water at depth h = 10 ft is:
Thus, the rate of change of the water depth when the water depth is 10 ft is;
Answer:
Step-by-step explanation:
In order to determine the information you're being asked for, you need to complete the square on that quadratic. The first step is to move the constant over to the other side of the equals sign:
Here would be the step where, if the leading coefficient isn't a 1, you'd factor it out. But ours is a 1, so we're good there. Now take half the linear term (the term with the single x on it), square it, and add it to both sides. Our linear term is a -2. Half of -2 is -1, and -1 squared is +1. We add +1 to both sides giving us this:
Now we'll clean it up a bit. The right side becomes a 4, and the left side is written as its perfect square binomial, which is the whole reason we did this. That binomial is
(set equal to the 4 here). Now we'll move the 4 back over and set the whole thing back equal to y:
From this it's apparent what the vertex is: (1, -4),
the axis of symmetry is x = 1, and
the y-intercept is found by setting the x's equal to 0 in the original equation and solving for y. So the y-intercept is (0, -3).
Your choice for the correct answer is the very last one there.
Is the slope really -2-2? Or is that a miss type?
I am only in middle school, this question is for college. sorry