Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost: r(x) = 30x - 0.5x 2 c(x) = 2x + 8. 9) a) 32 units b) 36 units

The profit is maximum when 28 units are sold.

Step-by-step explanation:

The given revenue function is

The given cost function is

Profit is the difference of revenue and cost. So the profit function is

On combining like terms, we get

It is a quadratic function. Leading coefficient is negative so it is a downward parabola. Vertex of a downward parabola is the point of maxima.

If a quadratic function is , then the vertex of the parabola is

In the profit function a=-0.5, b=28 and c=-8, the function is maximum at

Therefore the profit is maximum when 28 units are sold.

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

here you hope this .

step-by-step explanation:

hypotenuse = √(15² + 8²)

=  √(225 +64)

=  √(289) = 17

sin(x) = cos(y) = 8/17

they are identical so long as you are doing the sine of one angle and the cosine of the only other angle that isn't the right angle.