If your teacher gave you instruction for constructing a regular pentagon inscribed in a circle, you would expect the pentagon to
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Let be the number of liters of the 10% solution to be used, and
the number of liters of the 4% solution. The chemist wants to end up with a 4 liter solution, so
For each liter used in the mixture, a concentration of either 10% or 4% acid will be contributed, and the goal is to make a 4L solution whose concentration is 7%, which means
Solving for gives
, so 2L of both solutions is needed.
Answer:
0.5 seconds (at 100 feet in the air).
Step-by-step explanation:
So, the height of the ball can be modeled by the function:
Where h(t) represents the height in feet after t seconds.
And we want to find its maximum height.
Notice that our function is a quadratic.
Therefore, the maximum height will occur at the vertex of our function.
The vertex of a quadratic function in standard form is given by the formula:
In our function, a=-16; b=16; and c=96.
Find the x-coordinate of the vertex:
So, the ball reaches its maximum height after 0.5 seconds of its projection.
Notes:
To find it’s maximum height, we can substitute 1/2 for our function and evaluate. So:
Evaluate:
So, the ball reaches its maximum height of 100 feet 0.5 seconds after its projection.