Sam made $147 for 7 hours of work at the same rate how much would he make for 9 hours of work

The cost, in dollars, of producing x belts is given by Upper C (x )equals 594 plus 10 x minus 0.067 x squared. Find the rate a

alexandr402 [8]

Answer:

When 576 belts have been produced, the average cost is changing at 0.0652(decreasing) dollar per belt

Step-by-step explanation:

If x is the number of units of a product produced in some time interval then average cost function is given as,

$\overline{C}=\dfrac{C\left(x\right)}{x}$

Cost function is given as, $C\left(x\right)=594+10x-0.067x^{2}$

Substituting the value in formula for average cost function,

$\overline{C}=\dfrac{594+10x-0.067x^{2}}{x}$

Simplifying,

$\overline{C}=\dfrac{594}{x}+\dfrac{10x}{x}-\dfrac{0.067x^{2}}{x}$

$\overline{C}=\dfrac{594}{x}+10-0.067x$

To find the rate of average cost that is, $\dfrac{d\overline{C}}{dx}$ . So differentiating function $\overline{C}$ with respect to x,

$\dfrac{d\overline{C}}{dx}=\dfrac{d}{dx}\left (\dfrac{594}{x}+10-0.067x \right )$

Applying sum rule and difference rule of derivative,

$\dfrac{d\overline{C}}{dx}=\dfrac{d}{dx}\left(\dfrac{594}{x}\right)+\dfrac{d}{dx}\left(10\right)-\dfrac{d}{dx}\left(0.067x\right)$

Applying constant multiple rule of derivative,

$\dfrac{d\overline{C}}{dx}=594\dfrac{d}{dx}\left(\dfrac{1}{x}\right)+\dfrac{d}{dx}\left(10\right)-0.067\dfrac{d}{dx}\left(x\right)$

Since,

$\dfrac{1}{x}=x^{-1}$

$\dfrac{d\overline{C}}{dx}=594\dfrac{d}{dx}\left(x^{-1}\right)+\dfrac{d}{dx}\left(10\right)-0.067\dfrac{d}{dx}\left(x\right)$

Applying power rule and constant rule of derivative,

$\dfrac{d\overline{C}}{dx}=594\left(-1\:x^{-1-1}\right)+0-0.067\left(1\:x^{1-1}\right)$

$\dfrac{d\overline{C}}{dx}=594\left(-1\:x^{-2}\right)-0.067\left(1\:x^{0}\right)$

$\dfrac{d\overline{C}}{dx}=594\:x^{-2}-0.067$

$\dfrac{d\overline{C}}{dx}=\dfrac{594}{x^{2}}-0.067$

Substituting the value of $x=576$ ,

$\dfrac{d\overline{C}}{dx}=594\left(\dfrac{1}{\left(576 \right)^{2}}\right )-0.067$

$\dfrac{d\overline{C}}{dx}=-0.0652$

Negative sign indicates that rate of average cost is decreasing.

Therefore, the average cost is changing at the rate of 0.0652(decreasing) dollar per belt

7 0

3 years ago

Find the circumference of a circle with radius 1.4 in. long. Then use the approximation 3.14 for π and approximate the circumfer

Art [367]

The expression for the circumference of the circle is 2πr, where π is approximately 3.14 and the r is the radius of the circle, 1.4 inches. So the circumference of the circle is $2*1.4*3.14=8.792$ . So the circumference of the circle is 8.792 inches.