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3 years ago

The profit function of a manufacturer, in dollars, when x units of a certain commodity are produced and sold is given by

Mathematics

1 answer:

Annette [7]3 years ago

4 0

Answer:

Derivative: P’(x) = 200 - 2x

If P’(x) = 0 , x = 100

Therefore P’ is positive and P increases until x = 100

So the maximum units to maximize profits is 100 units

And for 100 units the profit in dollar is:

20000 - 10000 = 10000

10000 dollars

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Consider the vectors v1, v2, v3 in R2. Vectors v1 and v2 are parallel.How many solutions x, y does the system xv1 + yv2 = v3 hav

ANEK [815]

We want to see how many solutions has an equation given some restrictions on the vectors of the equation.

We have 3 vectors in R2.

v₁, v₂, and v₃.

Where we know that v₁ and v₂ are parallel. And two vectors are parallel if one is a scalar times the other.

Then we can write:

v₂ = c*v₁

Where c is a real number.

Then our system:

x*v₁ + y*v₂ = v₃

Can be rewriten to:

x*v₁ + y*c*v₁ = v₃

(x + y*c)*v₁ = v₃

Assuming x, y, and c are real numbers, this only has a solution if v₁ is also parallel to v₃, because as you can see, the equation says that v₃ is a scallar times v₁.

Geometrically, this means that if we sum two parallel vectors, we will get a vector that is parallel to the two that we added.

If you want to learn more, you can read:

brainly.com/question/13322477

6 0

2 years ago

Find the slopes of the liner functions

LuckyWell [14K]

Answer:

The slope of the line given by the linear equation is -2

The slope of the line shown in the graph is -1

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

m is the slope

b is the y-intercept

The rule of the slope of a line is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points lie on the line

Let us use these rules to answer the question

∵ The linear equation is y = -2x + 7

→ By comparing it with the form of the linear equation above

∴ m = -2

∵ m is the slope of the line represented by the given equation

∴ The slope of the line given by the linear equation is -2

From the given figure

∵ The line passes through points (6, 0) and (0, 6)

∴ x1 = 6 and y1 = 0

∴ x2 = 0 and y2 = 6

→ Substitute them in the rule of the slope above to find it

∵ m = $\frac{6-0}{0-6}=\frac{6}{-6}$

∴ m = -1

∵ m is the slope of the line shown in the graph

∴ The slope of the line shown in the graph is -1

6 0

3 years ago

-5x + 11 __) Please show your work!

timofeeve [1]

-1 (5x 11) i hope that helps

5 0

3 years ago

Erik makes 75% of his free throws in his basketball game. He took a total of 16 free throws; how many did he make?

xxMikexx [17]

Answer:

maf is bad

Step-by-step explanation:

8 0

3 years ago

HELP!!! I will rate brainliest to fastest and correctly: Paula invests 10,000 for 5 years at an interest rate of 10% per year. I

Tomtit [17]

15,000

Since her interest is simple, it adds the 10% to the original amount.

So, we multiply her amount (10,000) by the interest rate (.1) and by the amount of years (5).

10,000 * .1 * 5= 5,000

This is how much she has gained from said interest. Adding this to 10,000 gives us 15,000, which is the amount she will have.

Another way to do this would be to make a chart/table:

Start: 10,000
1. 11,000
2. 12,000
3. 13,000
4. 14,000
5. 15,000

And thus, we get the same answer.

7 0

3 years ago