An oil refinery is located 1 km north of the north bank of a straight river that

The point should be placed 3.362 km to the east of the refinery to minimize the cost.

Step-by-step explanation:

You should draw a graph that depicts the situation.

Let x be the distance from the refinery to the point P on the north bank in km and C the total cost of the pipeline.

According to the graph and using Pythagoras's theorem, the distance that the pipe should cover is given by

We know that the cost of laying pipe is $200,000/km over land to a point P on the north bank and $400,000/km under the river to the tanks. Therefore, the total cost of the pipeline is the cost of the part on land plus the cost of the amount underwater.

The domain of C(x) is [0, 5].

To find the minimum cost, we need to differentiate the cost function, set it to zero and solve for x to find the critical points.

Solving this equation with the help of graphing calculator (Desmos) we get that

We can use The Second Derivative Test to check if x is a minimum,

if C'(c) = 0 and C''(c) > 0, then C has a local minimum at c.

The second derivative is

Next, substitute into the second derivative

Because C''(3.362) > 0, then C(x) has a local minimum at 3.362.

Thus the point should be placed 3.362 km to the east of the refinery to minimize the cost.

The answer should be that the velocity and acceleration decreases ! :)

Step-by-step explanation: With velocity, the pure definitions are "quickness of motion," and "rapidity of movement." So with this, when you think about it, the speed/velocity of the baseball decreases the higher it goes because of gravity slowly getting stronger the higher up it goes. So the answer would be that the velocity and the acceleration decreases. (hope I helped :') )