the observatory is made of a 3 foot tall cylinder and half of a sphere. what is the volume of the space inside the observatory?

Answer:at an angle of 90° to a given line, plane, or surface.

Step-by-step explanation:

Answer:

275 bicycles

Step-by-step explanation:

We are given the average cost per bicycle as;

C(x) = 0.2x² - 1.1x + 10.592

We will solve this by finding the derivative of the C(x) function which will give us the instantaneous slope. Thereafter, we will find the extremas which will occur when the instantaneous slope is equal to 0.

Thus, derivative of C(x) is;

C'(x) = 0.4x - 1.1

Equating to zero, we can find the extremas.

Thus;

0.4x - 1.1 = 0

x = 1.1/0.4

x = 2.75

To check if this is minimum of maximum, we will find the second derivative of C(x)

Thus;

C''(x) = 0.4

Thus is a positive value, and so it means the critical point is a minimum.

Thus, X = 2.75

We were told x is in hundreds of bicycles. Thus, X = 2.75 × 100 = 275 bikes

To Optimization minimize the average cost per bicycle, the shop should build 275 bicycles. This is determined by finding the x-coordinate of the vertex ('minimum point') of the parabolic graph represented by the average cost function .

The function is a quadratic function, and represents the average cost per bicycle. The shape of the graph of a quadratic function is a parabola.

In this case, because the coefficient of the x^2 term is positive, the parabola opens upwards,which means it has a minimum point.

Therefore, the minimum average cost per bicycle occurs at the vertex of the parabola.

To find the x-coordinate of the vertex (which is the number of bicycles), we use the formula , where a is the coefficient of the term (0.2) and b is the coefficient of the x term (-1.1).

Plugging in these values gives hundreds of bicycles or 275 bicycles.

Therefore, the shop should build 275 bicycles to minimize the average cost per bicycle.

Learn more about Optimization here:

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The correct answer would be B. When we find the range or domain we only list repeating values once.