Could someone help me do #9? urgent! ((in the picture))

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:

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

Second derivative test

(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

Cruz is training to compete in a triathlon. He left his house at 6:00 and ran until 7:30. Then he rode his bike until 9:45. He c

Reika [66]

The speed in running is 10 mph and speed in biking is 16 mph

Solution:

Given that, Cruz is training to compete in a triathlon

He left his house at 6:00 and ran until 7:30

Time taken for running = 1.5 hours

Then he rode his bike until 9:45

7: 30 to 9: 45 is biking time

Time taken for biking = 2.25 hours

He covered a total distance of 51 miles

Total distance = 51 miles

Let "x" be the speed in running

His speed when biking was 1.6 times his speed when running

Speed in biking = 1.6x

Total distance = distance in running + distance in biking

The distance is given by formula:

$distance = speed \times time$

Therefore,

$Total\ Distance = x \times 1.5 + 1.6x \times 2.25\\\\51 = 1.5x + 3.6x\\\\5.1x = 51\\\\x = 10$

Thus speed in running is 10 miles per hour

Speed in biking = 1.6x = 1.6(10) = 16

Thus speed in running is 10 mph and speed in biking is 16 mph

8 0

4 years ago

The Really Spicy Hot Sauce Company decides to make a special-edition, extra-spicy version of its Really Spicy Hot Sauce. Expecte

valkas [14]

$32,00 because it is a lot of money

4 0

3 years ago

You are redecorating your bedroom and want to place two posters on the wall. Your wall is 11 feet, 6 inches long and each poster

lidiya [134]

Mark Brainliest please

Answer: not reasonable

Explanation

Let 'x' represent the distance between the posters and the distance from the posters to the nearest edge of the wall.

1 ft = 12 in

11 ft = 11*12 in

14 ft = 132 in

Now we can write the following equation:

6x + 2*36 = 132 + 3
6x + 72 = 135

X = 10.5 in

he poster should be placed 10.5 inches from the edge of the wall.

Your brother is not reasonable .

4 0

3 years ago

What is an equation of the line that passes through the point (-1, -3) and is

Soloha48 [4]

Answer:

y = 4x + 1

Step-by-step explanation:

1. Solve given equation for y

4x-y=2

4x=y+2

y=4x-2

2. Parallel in linear equations means the new line will have the same slope, so your new equation so far is

y=4x+b (formula being used is linear function y=mx+b)

3. (-1,-3) is a coordinate (x,y), so plug those values in for x and y so the only variable in your equation is b, the y-intercept

-3=4(-1)+b Solve for b

-3=-4+b

1=b

4. Rewrite your new equation with the m and b you now know

y=4x+1

7 0

3 years ago