6×1/6=0 what properly

Assume that it costs Apple approximately E(x) 25,600 + 100x + 0.012 dollars to manufacture x 32GB iPods in a day. (a) The averag

uranmaximum [27]

Answer:

(a) $C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)x=1600, Minimum Average Cost Per iPod=$132

(c) $C''(x)=\dfrac{5120000}{x^3}$

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

Step-by-step explanation:

Given that it costs Apple approximately $ C(x) to manufacture x 32GB iPods in a day, where:

$C(x)=25,600+100x+0.01x^2$

(a)The average cost per iPod when they manufacture x iPods in a day is given by:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}$

The average cost per iPod is therefore:

$C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)To minimize average cost of x iPods per day, we set the average cost per iPod=0 and solve for x.

$C'(x)=\dfrac{x^2-2560000}{x^2}=0\\x^2-2560000=0\\x^2=2560000\\x=\sqrt{2560000}=1600$

The resulting minimum average cost (at x=1600) is given as:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}\\\dfrac{25,600+100(1600)+0.01(1600)^2}{1600}\\=\$132$

<u>Second derivative test</u>

(c)The answer above is a critical point for the average cost function. To show it is a minimum, we calculate the second derivative of the average cost function.

$C''(x)=\dfrac{5120000}{x^3}$

At the critical point, x=1600

$C''(1600)=\dfrac{5120000}{1600^3}=0.00125$

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

3 0

3 years ago

Help 15 points to brainlist that answers also please give me 2 formulas for this

kakasveta [241]

Area rectangle: L * W
5 * 9
Area triangle: (1/2) * b * h
(1/2) * 3 * 4

Rectangle = 45
Triangle = 6
45 + 6 = 51 cm^2

7 0

4 years ago

Enter the value for x that makes the equation 1/2(4x-8)+3x=36 true

MrRissso [65]

Answer:

the correct answer for x is 8

Step-by-step explanation:

since: 1/2 ((4) (8) - 8) + (3) (8) = 36

4 0

3 years ago

Karen works for 85 hours throughout a two-week period. She earns $2,891.25 throughout this period. How much does karen earn for

valentinak56 [21]

$271.11 or $271.12 if you round up. Not sure how this one is complicated. Correct me if I’m wrong... 2.891.25 divided by 85. You then take that number and multiple it by 8. Seems very straight up.

3 0

3 years ago

When solving a mass/particle or particle/mass conversion calculation what piece(s)

Lana71 [14]

Answer:

i would cry if i had to do this tbh

Step-by-step explanation:

6 0

3 years ago