NEED NOW URGENT PLEASE

the lenghty of a rectangal is 8 feet more than its width. the pirimete of the rectangle is 72 feet. Find the width

morpeh [17]

Width of the rectangle is 14 ft

Step-by-step explanation:

Step 1: Let the width of the rectangle be x. Then length = 8 + x. Perimeter = 72 ft.

Perimeter = 2(length + width)

72 = 2 (8 + x + x)

72 = 16 + 4x

4x = 56

x = 56/4 = 14

∴ Width of the rectangle is 14 ft

3 0

3 years ago

Assume {v1, . . . , vn} is a basis of a vector space V , and T : V ------> W is an isomorphism where W is another vector spac

Degger [83]

Answer:

Step-by-step explanation:

To prove that $w_1,\dots w_n$ form a basis for W, we must check that this set is a set of linearly independent vector and it generates the whole space W. We are given that T is an isomorphism. That is, T is injective and surjective. A linear transformation is injective if and only if it maps the zero of the domain vector space to the codomain's zero and that is the only vector that is mapped to 0. Also, a linear transformation is surjective if for every vector w in W there exists v in V such that T(v) =w

Recall that the set $w_1,\dots w_n$ is linearly independent if and only if the equation

$\lambda_1w_1+\dots \lambda_n w_n=0$ implies that

$\lambda_1 = \cdots = \lambda_n$ .

Recall that $w_i = T(v_i)$ for i=1,...,n. Consider $T^{-1}$ to be the inverse transformation of T. Consider the equation

$\lambda_1w_1+\dots \lambda_n w_n=0$

If we apply $T^{-1}$ to this equation, then, we get

$T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) =T^{-1}(0) = 0$

Since T is linear, its inverse is also linear, hence

$T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) = \lambda_1T^{-1}(w_1)+\dots + \lambda_nT^{-1}(w_n)=0$

which is equivalent to the equation

$\lambda_1v_1+\dots + \lambda_nv_n =0$

Since $v_1,\dots,v_n$ are linearly independt, this implies that $\lambda_1=\dots \lambda_n =0$ , so the set $\{w_1, \dots, w_n\}$ is linearly independent.

Now, we will prove that this set generates W. To do so, let w be a vector in W. We must prove that there exist $a_1, \dots a_n$ such that

$w = a_1w_1+\dots+a_nw_n$

Since T is surjective, there exists a vector v in V such that T(v) = w. Since $v_1,\dots, v_n$ is a basis of v, there exist $a_1,\dots a_n$ , such that

$a_1v_1+\dots a_nv_n=v$

Then, applying T on both sides, we have that

$T(a_1v_1+\dots a_nv_n)=a_1T(v_1)+\dots a_n T(v_n) = a_1w_1+\dots a_n w_n= T(v) =w$

which proves that $w_1,\dots w_n$ generate the whole space W. Hence, the set $\{w_1, \dots, w_n\}$ is a basis of W.

Consider the linear transformation $T:\mathbb{R}^2\to \mathbb{R}^2$ , given by T(x,y) = T(x,0). This transformations fails to be injective, since T(1,2) = T(1,3) = (1,0). Consider the base of $\mathbb{R}^2$ given by (1,0), (0,1). We have that T(1,0) = (1,0), T(0,1) = (0,0). This set is not linearly independent, and hence cannot be a base of $\mathbb{R}^2$

8 0

3 years ago

Find the distance between the points (-5, 0) and (-4, 1).

choli [55]

The formula of a distance between two points A and B is :

$AB=\sqrt{(x_{B}- x_{A})^2 +( y_{B}- y_{A})^2 }$

You should this formula by heart.

Then, you just have to apply it ! :D

Here :

$x_{A}=-5$
$y_{A} =0$

$x_{B} =-4$
$y_{B}= 1$

Therefore :

$\sqrt{(-4-(-5))^2+(1-0)^2}$
$= \sqrt{1^2+1^2}$
$= \sqrt{1+1}$
$= \sqrt{2}$

In short, the answer would be the first option : $\sqrt{2}$ .

Hope this helps !

Photon

6 0

3 years ago

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10. Suppose y varies directly as x, and y = 9 when x = 3/2. Find y when x = 1

pogonyaev

Answer:

y = 6

Step-by-step explanation:

We need to interpret the question

y varies directly as x

y varies x

To equate it, we need to add a constant K

y = K/x

Using the information we are provided with

y = 9

x = 3/2

insert into

y = Kx

9 = K * 3/2

9 = 3K/ 2

3K = 9 *2

3k = 18

To get K, divide through by 3

3K/3 = 18/3

K = 6

Since we've gotten our K = 6

y = Kx

Using the new information

y = ?

x = 1

K = 6

y = 6* 1

y = 6

The new y = 6 , x =1

6 0

3 years ago

CAN SOMEONE HELP ME ASAP

BARSIC [14]

Answer:

3 minutes

Step-by-step explanation:

To calculate this, you have to multiply 4.5 minutes by 8. This will give you the amount of pages that Wafa will print.

4.5 x 8 = 36 pages

Now that you have the amount of pages, you should divide it by the speed of the Sure-Fire printer. 12 ppm means that 12 pages can be printed in 1 minute.

36/12 = 3

Therefore, it would take 3 minutes if Wafa were to use her brother's Sure-Fire printer.

5 0

3 years ago

Read 2 more answers