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Scrat [10]
2 years ago
9

The total cost of producing a type of tractor is given by C(x)=11000−20x+0.02x2, where x is the number of tractors produced. How

many tractors should be produced to incur minimum cost?
Mathematics
1 answer:
marissa [1.9K]2 years ago
5 0

Answer:

Step-by-step explanation:

You need to complete the square.

C(x) = 0.02(x^2 - 1000x  ...)  + 11000

C(x) = 0.02 (x^2 - 1000x + 500^2) + 11000 - 5000

C(x) = 0.02 (x^2 - 1000x + 500^2) + 6000

C(x) = 0.02(x - 500)^2 + 6000

Now if you look at the answer you will find that the square is completed. That means that number of tractors you could produce is 500 at a cost of 6000

There is a flow to this question that you may have trouble understanding.

First of all the 500^2. That comes from taking 1/2 of 1000 and squaring it. That's what you need to complete the square.

Bur that is not what you have adding into the equation. Remember that there is a 0.02 in front of the brackets.

500^2 = 250000

0.02 * 250000 = 5000

So that number must be subtracted to make the square = 0. When you remove the brackets, you should get 11000 all in all.

So what you have outside the brackets is 11000 - 5000 = 6000

The rest is just standard for completing the square.

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What is an equation of the line that passes through the points ( 0,-7) and ( 5, -1)
tresset_1 [31]

Answer:

y = 5/6x - 5.167

Or

y = 5/6x - 31/6

Step-by-step explanation:

The equation of a line

y = mx + c

Step 1: find the slope

m = y2 - y1 / x2 - x1

Given points

( 0 , -7) ( 5 , -1)

x1 = 0

y1 = -7

x2 = 5

y2 = -1

Insert the values into the equation

m = -1 - (-7) / 5 - 0

m = -1 + 7 / 5

m = 6/5

y = 6/5x + c

Step 2: sub any of the two points given into the equation

y = 5/6x + c

( 5 , -1)

x = 5

y = -1

-1 = 5/6(5) + c

-1 = 5*5/6 + c

-1 = 25/6 + c.

c = -1 - 25/6

LCM = 6

c = -6 - 25 / 6

c = -31/6

c = -5.167

Step 3: sub c into the equation

y = 5/6x + c

y = 5/6x - 31/6

Or

y = 5/6x - 5.167

The equation of the line is

y = 5/6x - 5.167

7 0
2 years ago
Equivalent to 4^7•4^-5
nekit [7.7K]

Answer:

<h2>16</h2>

Step-by-step explanation:

\text{Use}\ a^n\cdot a^m=a^{n+m}\\\\4^7\cdot4^{-5}=4^{7+(-5)}=4^{7-5}=4^2=4\cdot4=16

3 0
3 years ago
7th grade math help me pleasee
zimovet [89]

Answer:

a, c, b

Step-by-step explanation:

ITS CORRECT TRUST MEEE

7 0
3 years ago
Read 2 more answers
Verify that your point from Question 2 is a solution to 2x-y=-12x−y=−1 AND is also a solution to y=5x-5y=5x−5. What does it mean
Vera_Pavlovna [14]

Answer:

(a) Verified

(b) They are simultaneous equations

Step-by-step explanation:

Given

2x - y = -1

y =5x - 5

Required

Verify that: (x,y) = (2,5) is a solution

We have:

2x - y = -1

Substitute: (x,y) = (2,5)

2 * 2 - 5 = -1

Evaluate all products

4 - 5 = -1

Subtract:

-1 = -1

<em>Because both sides of the equation are equal, then the point is a solution</em>

<em></em>

Also: y =5x - 5

Substitute: (x,y) = (2,5)

5 = 5 * 2 - 5

Evaluate all products

5 = 10 - 5

Subtract:

5 = 5

<em>Because both sides of the equation are equal, then the point is a solution</em>

<em></em>

<em></em>

Because the given point is a solution to both equations, then they are simultaneous equation

7 0
3 years ago
........................​
shtirl [24]

Answer:

Step-by-step explanation:

Figure (1)

x° = 107° [Vertically opposite angles]

Since, vertical angles are equal in measure.

Figure (2)

x + 71° = 90° [Given, complementary angles]

x = 90° - 71°

x = 19°

Figure (3)

x + 21° = 180° [Given as supplementary angles]

x = 180° - 21°

x = 159°

Figure (4)

x = 129° [Vertical angles]

Figure (5)

x° = 90° [Given]

z° + 34° = 90°

z° = 90° - 34°

z° = 56°

Since, x° + y° + z° = 180° [Linear angles]

90° + y° + 56° = 180°

y° + 146° = 180°

y° = 180° - 146°

y° = 34°

7 0
2 years ago
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