Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.2x^2-1.1x+10.592, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?

Answers

Answer 1

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

Answer 2

Answer:

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 $C(x) = 0.2x^2 - 1.1x + 10.592$ .

The function $C(x) = 0.2x^2 - 1.1x + 10.592$ 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 $-b/2a$ , where a is the coefficient of the $x^2$ term (0.2) and b is the coefficient of the x term (-1.1).

Plugging in these values gives $x = -(-1.1) / 2*(0.2) = 2.75$ hundreds of bicycles or 275 bicycles.

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

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What times 16 equals 48

Answers

Number 3 times 16 is equals to 48.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The number 16 times is equal 48.

Let a number = x

Hence, We can formulate;

⇒ 16 × x = 48

Divide by 16;

⇒ x = 48 / 16

⇒ x = 3

Thus, 3 times 16 is equals to 48.

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The answer will be 3.

In order to get this answer you have to divide 48 by 16 to get 3 as your answer.

Hopes it Helps :]

How do I complete each pattern, Example 1 block, 3 blocks,6 blocks

Answers

Well,

This could be an arithmetic sequence.
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
15 + 6 = 21
...

This could also be a geometric sequence.
1*3=3
3*2=6
6*1=6
6*0=0
0*-1=0
0*(anything)=0
...

What are the solutions to the quadratic equation 4x2 = 64? A. x = −16 and x = 16 B.x = −8 and x = 8 C.x = −4 and x = 4 D.x = −2 and x = 2

Answers

Answer:

x = ±4

Step-by-step explanation:

4x^2 = 64

Divide each by 4

4x^2 /4= 64/4

x^2 = 16

Take the square root of each side

sqrt(x^2) = ±sqrt(16)

x = ±4

Answer:

$\boxed{\boxed{x=\pm 4}}$

Step-by-step explanation:

$4x^2 = 64$

Divide both sides by 4.

$(4x^2)/4 = 64/4$

Simplify.

$x^2 =16$

Take the square root on both sides.

$√(x^2 ) =\pm √(16)$

Simplify.

$x=\pm 4$

Please help me this is due in 2 hours you need to explain your answer plzzzzzz???????!!!!!!!

Answers

Answer:

1) one muffin costs $1.50

one quart of milk costs $3.00

2) 10 videos, 30 CDs

Step-by-step explanation:

m = cost of one muffin

q = cost of one quart of milk

System of equations:

3m + 1q = 7.5

8m + 2q = 18

I multiplied the first equation by -2 to eliminate the 'q' values

-6m - 2q = -15

+ 8m + 2q = 18

2m = 3

m = 3/2

find 'q':

3(3/2) + q = 7.5

9/2 + q = 15/2

q = 6/2 or 3

c = # of CDs sold

v = # of videos sold

System of equations:

c + v = 40

4c + 6v = 180

I solved first equation for 'c' to get c = 40 - v

4(40-v) + 6v = 180

160 - 4v + 6v = 180

2v = 20

v = 10

10 + c = 40

c = 30

A painter built a ladder using 18 rungs. The rungs on the ladder were 5.7 inches apart and 1.1 inches thick. What is the distance from the bottom of the lowest rung to the top of the highest rung?

Answers

The distance from the bottom of the lowest rung to the top of the highest rung 116.7 inch

What is Unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Total rungs = 18

distance between rungs = 5.7 inch

thickness = 1.1 inches

So, the distance from the the lowest rung to top of highest rung is

=18* 5.7 + 17* 1.1

=116.7 inch

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18(1.1)+18(5.7)
18.8+102.6
121.4
The distance is 121.4 inches

19 is 30% of what number