All categories

3 years ago

Let E = {(x, y) e R2|xy > 0}. Determine whether E is a subspace of R2 . X3

Mathematics

1 answer:

gayaneshka [121]3 years ago

5 0

Answer:

E is not a subspace of $\mathbb{R}^2$

Step-by-step explanation:

E is not a subspace of $\mathbb{R}^2$

In order to see this, we must find two points (a,b), (c,d) in E such that (a,b) + (c,d) is not in E.

Consider

(a,b) = (1,1)

(c,d) = (-1,-1)

It is easy to see that both (a,b) and (c,d) are in E since 1*1>0 and (1-)*(-1)>0.

But (a,b) + (c,d) = (1-1, 1-1) = (0,0)

and (0,0) is not in E.

By the way, it can be proved that in any vector space all sub spaces must have the vector zero.

You might be interested in

Need to know the area of the composite figure.

Deffense [45]

Answer:

51 m^2

Step-by-step explanation:

The shaded area is the difference between the area of the overall figure and that of the rectangular cutout.

The applicable formulas are ...

area of a triangle:

A = (1/2)bh

area of a rectangle:

A = bh

area of a trapezoid:

A = (1/2)(b1 +b2)h

___

We note that the area of a triangle depends only on the length of its base and its height. The actual shape does not matter. Thus, we can shift the peak of the triangular portion of the shape (that portion above the top horizontal line) so that it lines up with one vertical side or the other of the figure. That makes the overall shape a trapezoid with bases 16 m and 10 m. The area of that trapezoid is then ...

A = (1/2)(16 m + 10 m)(5 m) = 65 m^2

The area of the white internal rectangle is ...

A = (2 m)(7 m) = 14 m^2

So, the shaded area is the difference:

65 m^2 -14 m^2 = 51 m^2 . . . . shaded area of the composite figure

_____

<em>Alternate approach</em>

Of course, you can also figure the area by adding the area of the triangular "roof" to the area of the larger rectangle, then subtracting the area of the smaller rectangle. Using the above formulas, that approach gives ...

(1/2)(5 m)(16 m - 10 m) + (5 m)(10 m) - (2 m)(7 m) = 15 m^2 + 50 m^2 -14 m^2

= 51 m^2

7 0

3 years ago

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equat

NeTakaya

Answer:

The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

Step-by-step explanation:

Here is the complete question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.

y=35x; y=-0.05(x-400)²+9,492

what does the solution of the system represent in this context?

Solution

The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .

So, 35x = -0.05(x-400)² + 9,492.

Expanding the right side, we have

35x = -0.05(x² - 800x + 160000) + 9492

35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492

35x = -0.05x² +40x - 8000 + 9492

35x = -0.05x² +40x + 1492

Collecting all the terms to the left side, we have

0.05x² - 40x - 1492 + 35x = 0

0.05x² - 5x -1492 = 0

Using the quadratic formula,

$x = \frac{-(-5) +/- \sqrt{(-5)^{2} - 4 X 0.05 X - 1492} }{2X0.05} = \frac{5 +/- \sqrt{25 + 298.4} }{0.1} = \frac{5 +/- \sqrt{323.4} }{0.1}\\= \frac{5 +/- 17.983 }{0.1}\\= \frac{5 - 17.983 }{0.1} or \frac{5 + 17.983 }{0.1}\\= \frac{-12.983 }{0.1} or \frac{22.983 }{0.1}\\= -129.83 or 229.83$

We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.

The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

We confirm that by plugging in x = 229.83 in both equations.

y = 35x = 35(229.83) = 8044.05 ≅ 8044.1

y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1

3 0

3 years ago

Read 2 more answers

a baker has 6 pounds of sugar. she divides them equally into 4 containers. she then uses 1 container to bake pies.

-BARSIC- [3]

Hello,

<span>6 pounds of sugar ÷ 4 containers = 1.5 of sugar.
1.5 of sugar was used to make the pie.</span>

5 0

3 years ago

Bir kırtasiyeci aldığı kalemlerin tanesini

andrew11 [14]

Answer: Option B: 120.

Step-by-step explanation:

I will answer in English

This problem can be translated to:

A man bought N pens, (at a cost C) if he sells each pen at 2 lira, he will have a profit of 40 lira.

If he sells each pen at 1.5 lira, he will loss a total of 20 lira.

We want to find N, the number of pens that he bought.

if he sells the N pens at 2 lira each, the revenue is:

N*2 lira

And the profit is the difference between the revenue and the cost, then the profit (40 lira in this case) is:

N*2 lira - C = 40 lira.

When he sells each pen at 1.5 lira the equation is:

N*(1.5 lira) - C = -20 lira.

Then we have two equations:

N*2 lira - C = 40 lira.

N*(1.5 lira) - C = -20 lira.

To solve this we need to isolate the variable C in one of the equations, i will isolate C in the second equation:

N*(1.5 lira) + 20 lira = C.

Now we can replace this in the first equation to get:

N*(2 lira) - (N*(1.5 lira) + 20 lira) = 40 lira.

We can solve this for N.

N*(2 lira) - N*(1.5 lira) - 20 lira = 40 lira

N*(2 lira - 1.5 lira) = 60 lira

N*(0.5 lira) = 60 lira

N = (60lira/0.5lira) = 120

N = 120

This means that he bought 120 pens.

The correct option is B.

3 0

2 years ago

Write two numbers that multiply to the value on top and add to the value on bottom.

9966 [12]

The numbers are 3 and -30 They multiply and give -90 And add to give-27

8 0

2 years ago